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Spacekime Analytics (Time Complexity and Inferential Uncertainty)
European Economic Spacekime Analysis Part 1 – Longitudinal Modeling
SOCR Team
01/20/2022
library(dplyr)
library(plotly)
library(pracma)
library(ggplot2)
require(magrittr)
library(gridExtra)1 Data Preprocessing
load("EU_Econ_rawdata.RData")#super sample the dataset
cleardata <- function(mat) {
for (i in 1:ncol(mat)) {
mat[is.na(mat[,i]),i]<-mean(mat[,i],na.rm = T) + rnorm(sum(is.na(mat[,i])),sd = sd(mat[,i],na.rm = T))
}
return(mat)
}
# 1. Find all "Common" features (highly-observed and congruent Econ indicators)
countryNames <- unique(time_series$country); length(countryNames); # countryNames
# initialize 3D array of DF's that will store the data for each of the countries into a 2D frame
countryData <- list() # countryData[[listID==Country]][1-time-72, 1-feature-197]
for (i in 1:length(countryNames)) {
countryData[[i]] <- filter(time_series, country == countryNames[i])
}
# Check countryData[[2]][2, 3] == Belgium[2,3]
list_of_dfs_CommonFeatures <- list() # list of data for supersampled countries 360 * 197
# 2. General function that ensures the XReg predictors for ALL 31 EU countries are homologous
completeHomologousX_features <- function (list_of_dfs) {
# delete features that are missing at all time points
for (j in 1:length(list_of_dfs)) {
print(paste0("Pre-processing Country: ...", countryNames[j], "... "))
data = list_of_dfs[[j]]
data = data[ , colSums(is.na(data)) != nrow(data)]
data = dplyr::select(data, !any_of(c("time", "country")))
DataMatrix = as.matrix(data)
DataMatrix = cleardata(DataMatrix)
DataMatrix = DataMatrix[ , colSums(is.na(DataMatrix)) == 0] # remove features with only 1 value
DataMatrix = DataMatrix[ , colSums(DataMatrix) != 0] # remove features with all values=0
# Supersample 72 --*5--> 360 timepoints
#DataMatrix = splinecreate(DataMatrix)
DataSuperSample = as.data.frame(DataMatrix) # super-Sample the data
# remove some of features
#DataSuperSample = DataSuperSample[, -c(50:80)]; dim(X) # 360 167
# ensure full-rank design matrix, DataSuperSample
DataSuperSample <-
DataSuperSample[ , qr(DataSuperSample)$pivot[seq_len(qr(DataSuperSample)$rank)]]
print(paste0("dim()=(", dim(DataSuperSample)[1], ",", dim(DataSuperSample)[2], ") ..."))
# update the current DF/Country
list_of_dfs_CommonFeatures[[j]] <- DataSuperSample
}
# Identify All Xreg features that are homologous (same feature columns) across All 31 countries
# Identify Common Columns (features)
comCol <- Reduce(intersect, lapply(list_of_dfs_CommonFeatures, colnames))
list_of_dfs_CommonFeatures <- lapply(list_of_dfs_CommonFeatures, function(x) x[comCol])
for (j in 1:length(list_of_dfs_CommonFeatures)) {
list_of_dfs_CommonFeatures[[j]] <- subset(list_of_dfs_CommonFeatures[[j]], select = comCol)
print(paste0("dim(", countryNames[j], ")=(", dim(list_of_dfs_CommonFeatures[[j]])[1],
",", dim(list_of_dfs_CommonFeatures[[j]])[2], ")!")) # 72 * 197
}
return(list_of_dfs_CommonFeatures)
}
# Test completeHomologousX_features: dim(AllCountries)=(360,42)!
list_of_dfs_CommonFeatures <- completeHomologousX_features(countryData);
length(list_of_dfs_CommonFeatures); dim(list_of_dfs_CommonFeatures[[1]]) # Austria data matrix 360*422 Laplace Transform
x2 = seq(from = 1, to = 11, length.out = 50)
# drop the first row to avoid real part value of 0
y2 = seq(from = -5, to = 5, length.out = 50)
# drop the first column to avoid imaginary part value of 0
XY = expand.grid(X=x2, Y=y2)
complex_xy = mapply(complex, real=XY$X,imaginary=XY$Y)
X<-1:72
time_points <- seq(0+0.01, 2*pi, length.out = 72)# create the LT
NuLT = function(datax, datay, inputz, k = 3, fitwarning = FALSE, mirror = FALSE, range = 2*pi) {
datax = as.numeric(datax)
datay = as.numeric(datay)
n = length(datax)
x1 = n/(n+0.5)*((datax-min(datax))/(max(datax)-min(datax)))*range
if(mirror){
x1 = c(x1,rev(2*range - x1))/2
n = 2*n
datay = c(datay, rev(datay))
#plot(x1, datay)
}
#generate the coefficients in indefinite integral of t^n*exp(-zt)
coef = 1;
coefm = as.matrix(coef)
for(i in 1:k){
coefm = cbind(coefm,0)
coef = c(coef*i,1)
coefm = rbind(coefm,coef)
}
# these coefficients ordered by ^0, ^1, ^2, ... in column format
# compute 1, z, z^2...,z^k
zz = cbind(1,inputz)
zt = inputz
for (i in 2:k){
zt = zt*inputz
zz = cbind(zz,zt)
}
zd = zt*inputz
# compute 1, x, x^2...,x^k
tx = x1;
xm = cbind(1,x1)
for (i in 2:k){
tx = tx*x1
xm = cbind(xm,tx)
}
# sum over intervals
result = 0*inputz
ii = 1
while(ii+k<=n)
{
A = xm[seq(ii,ii+k),c(0:k+1)]
b = datay[seq(ii,ii+k)]
# polyfit might be faster when using polynomial basis, while matrix inverse, `solve()`,
# is the more general approach that works for any function basis
polyc = as.numeric(solve(A,b))
#ordered by ^0, ^1, ^2, ... in column format
# Enter a new function variable qualityCheck=FALSE
# check fit quality; this step can be skipped for speed/efficiency
# if (qualityCheck) { .... }
if (fitwarning){
xx = seq(A[1,2],A[k+1,2],length.out = 100);
yy = polyval(rev(polyc),xx)
if(max(abs(yy-mean(b)))>2*max(abs(b-mean(b)))){
print(c("Warning: Poor Fit at ",ii,", Largest Deviation is",max(abs(yy-mean(b)))))
print(c("Spline Polynomial is", polyc),3);
#print(c(polyval(rev(polyc),A[,2]),b))
plot(xx, yy, main="Polynomial fit", ylab="", type="l", col="blue")
lines(A[,2],b, col="red")
legend("topleft",c("fit","data"),fill=c("blue","red"))
print(" ")
}
}
# Use vector/matrix operations to avoid looping,
# some of the expressions look weird
# May need to actually compare the efficiency/speed of
# vector based vs. standard numeric calculations
m1 = t(t(polyc*coefm)*A[1,])
m11 = as.numeric(tapply(m1, col(m1)-row(m1), sum))[0:k+1]
m2 = t(t(polyc*coefm)*A[k+1,])
m22 = as.numeric(tapply(m2, col(m2)-row(m2), sum))[0:k+1]
intgl = (exp(-inputz*A[1,2])*colSums(t(zz)*m11)-
exp(-inputz*A[k+1,2])*colSums(t(zz)*m22))/zd
result = result+intgl
ii=ii+k
}
# Computations over the last interval
if(ii<n){
nk = n-ii;
A = xm[seq(ii,ii+nk),c(0:nk+1)]
b = datay[seq(ii,ii+nk)]
nc = as.numeric(solve(A,b))
nc = c(nc,seq(0,0,length.out = k-nk))
A = xm[seq(ii,ii+nk),]
m1 = t(t(nc*coefm)*A[1,])
m11 = as.numeric(tapply(m1, col(m1)-row(m1), sum))[0:k+1]
m2 = t(t(nc*coefm)*A[nk+1,])
m22 = as.numeric(tapply(m2, col(m2)-row(m2), sum))[0:k+1]
# cc = colSums(coefm*polyc)
intgl = (exp(-inputz*A[1,2])*colSums(t(zz)*m11)-
exp(-inputz*A[nk+1,2])*colSums(t(zz)*m22))/zd
result = result+intgl
}
#offset = 0.05*pi
#result = result + datay[n]*(exp(-2*pi*inputz)-exp(-(2*pi+offset)*inputz))/inputz
return(result)
}tensor_all<-array(dim=c(30,33,50,50))
for(m in 1:30)
{
for(i in 1:33){
Y=list_of_dfs_CommonFeatures[[m]][,i]
poly_z<-NuLT(time_points, Y, complex_xy, k = 3, fitwarning = FALSE)
dim(poly_z) = c(length(x2), length(y2))
tensor_all[m,i,,]<-poly_z
}
} X_tensor<-tensor_all[,-31,,]
Y_tensor<-tensor_all[,31,,]3 Kimesurface of GDP for 30 EU countries
magnitude_feature<-lapply(1:33,function(i) Mod(tensor_all[,i,,]))
phase_feature<-lapply(1:33,function(i) atan2(Im(tensor_all[,i,,]), Re(tensor_all[,i,,])))
#xy2<-expand.grid(1:20,1:20)
colorscale = cbind(seq(0, 1, by=1/(length(x2) - 1)), rainbow(length(x2)))
commonefeature<-colnames(list_of_dfs_CommonFeatures[[31]])
p_feature<- plot_ly(hoverinfo="none", showscale = FALSE) %>% layout(title=commonefeature[31])
for (j in 1:5)
{
for (i in 1:6){
xx2<-1:50+50*(j-1)
yy2<-1:50+50*(i-1)
p_feature <- p_feature %>%
add_trace(x=xx2,y=yy2, z =magnitude_feature[[31]][j+(i-1)*5,,],
surfacecolor=phase_feature[[31]][j+(i-1)*5,,], colorscale=colorscale, #Phase-based color
type = 'surface',name=substr(countryNames[j+(i-1)*5],0,50),opacity=0.7,showlegend=TRUE)
}
}p_feature4 Inverse Laplace Transform
ctILT = function(
LTF,
tini = 0.001,
tend = 9,
nnt = 200){
if (TRUE){
a=8; ns=100; nd=29;
} #% implicit parameters
N = ns+nd+1
radt=seq(tini,tend*nnt /(nnt + 0.5),length.out = nnt); # time vector
if (tini==0){
#radt=radt[c(2:nnt)]
} # t=0 is not allowed
#tic % measure the CPU time
alfa = seq(1,ns+1+nd)
beta = alfa
for (j in seq(1,ns+1+nd)){# % prepare necessary coefficients
alfa[j]=a+(j-1)*pi*1i;
beta[j]=-exp(a)*(-1)^j;
}
#print(beta)
n = c(1:nd)
bdif=rev(cumsum(gamma(nd+1)/gamma(nd+2-n)/gamma(n)))/(2^nd)
#print(beta[ns+2:ns+1+nd])
temp = beta[seq(ns+2,ns+1+nd)]*bdif
print(temp)
beta[seq(ns+2,ns+1+nd)]= temp
beta[1]=beta[1]/2;
ft2 = seq(1,nnt)
Qz = c()
for (kt in seq(1,nnt)){ # cycle for time t
tt=radt[kt];
s=alfa/tt; # complex frequency s
Qz = c(Qz,s)
}
LTQz = LTF(Qz)
for (kt in seq(1,nnt)){ # cycle for time t
tt=radt[kt];
s=alfa/tt; # complex frequency s
bt=beta/tt;
#btF=bt*NuLT(datax, datay, s); # functional value F(s)
btF = bt*LTQz[seq((kt-1)*N+1,kt*N)]
ft2[kt]=sum(Re(btF)); # original f(tt)
if(is.na(ft2[kt])){
print(kt)
print(LTQz[seq((kt-1)*N+1,kt*N)])
print(btF)
}
}
return(ft2)
}rge = 2*pi
tnd = 2*pi
z2_funct<- function(z) NuLT(time_points,list_of_dfs_CommonFeatures[[2]][,31],inputz = z,mirror = TRUE, range = rge)
inv_result<-ctILT(z2_funct,tend = tnd, nnt=72*2)
z2_funct<- function(z) NuLT(time_points,list_of_dfs_CommonFeatures[[3]][,31],inputz = z,mirror = TRUE, range = rge)
inv_result_2<-ctILT(z2_funct,tend = tnd, nnt=72*2)
z2_funct<- function(z) NuLT(time_points,list_of_dfs_CommonFeatures[[10]][,31],inputz = z,mirror = TRUE, range = rge)
inv_result_3<-ctILT(z2_funct,tend = tnd, nnt=72*2)
z2_funct<- function(z) NuLT(time_points,list_of_dfs_CommonFeatures[[21]][,31],inputz = z,mirror = TRUE, range = rge)
inv_result_4<-ctILT(z2_funct,tend = tnd, nnt=72*2)valsn_df_1 <- as.data.frame(cbind(inv_result=inv_result[1:72],
time_series=list_of_dfs_CommonFeatures[[2]][,31], time_points=time_points))
x <- list(
title = "Time"
)
y <- list(
title = "GDP of Belgium"
)
p1=plot_ly(valsn_df_1, x = ~time_points,y = ~time_series, name = 'original_ts',mode = 'lines', type = 'scatter')
p1<- p1 %>% add_trace(y = ~ inv_result, name = 'inv_result',mode = 'lines', line=list(dash='dot'))
p1 <- p1 %>% layout(xaxis = x, yaxis = y)valsn_df_2 <- as.data.frame(cbind(inv_result=inv_result_2[1:72],
time_series=list_of_dfs_CommonFeatures[[3]][,31], time_points=time_points))
x <- list(
title = "Time"
)
y <- list(
title = "GDP of Bulgaria"
)
p2=plot_ly(valsn_df_2, x = ~time_points,y = ~time_series, name = 'original_ts',mode = 'lines', type = 'scatter')
p2<- p2 %>% add_trace(y = ~ inv_result, name = 'inv_result',mode = 'lines', line=list(dash='dot'))
p2 <- p2 %>% layout(xaxis = x, yaxis = y)valsn_df_3 <- as.data.frame(cbind(inv_result=inv_result_3[1:72],
time_series=list_of_dfs_CommonFeatures[[10]][,31], time_points=time_points))
x <- list(
title = "Time"
)
y <- list(
title = "GDP of France"
)
p3=plot_ly(valsn_df_3, x = ~time_points,y = ~time_series, name = 'original_ts',mode = 'lines', type = 'scatter')
p3 <- p3 %>% add_trace(y = ~ inv_result, name = 'inv_result',mode = 'lines', line=list(dash='dot'))
p3 <- p3 %>% layout(xaxis = x, yaxis = y)valsn_df_4 <- as.data.frame(cbind(inv_result=inv_result_4[1:72],
time_series=list_of_dfs_CommonFeatures[[21]][,31], time_points=time_points))
x <- list(
title = "Time"
)
y <- list(
title = "GDP of Netherlands"
)
p4=plot_ly(valsn_df_4, x = ~time_points,y = ~time_series, name = 'original_ts',mode = 'lines', type = 'scatter')
p4 <- p4 %>% add_trace(y = ~ inv_result, name = 'inv_result',mode = 'lines', line=list(dash='dot'))
p4 <- p4 %>% layout(xaxis = x, yaxis = y)fig<-subplot(
p1,
p2,
p3,
p4,
nrows = 2,
titleY = TRUE,margin = 0.05,shareX = TRUE
)%>% layout(title ="Original Time-series and Reconstructed Time-series by ILT")
fig5 Data Preprocessing
Loading all packages that are required.
library(dplyr)
library(arm)
library(tidyr)
library(ggplot2)
library(ggrepel)
library(plot3D)
library(scatterplot3d)
library(plotly)
library(fastDummies)
library(forecast)
# Load Previously Computed Workspace:
load("E:/Ivo.dir/Research/UMichigan/Publications_Books/2018/others/4D_Time_Space_Book_Ideas/ARIMAX_EU_DataAnalytics/EU_Econ_SpaceKime.RData")Load the data and preprocess the data.
setwd("E:/Ivo.dir/Research/UMichigan/Publications_Books/2018/others/4D_Time_Space_Book_Ideas/ARIMAX_EU_DataAnalytics")
eu <- read.csv("Master_Aggregate_EU_Econ_Data_11_29_2018_TimeTransform.csv", stringsAsFactors = F)[,-5]
colnames(eu) <- c("country","time","feature","value")
eu <- filter(eu,!country %in% c("European Union (25 countries)","D1_Country",""))
eu$value <- sapply(c(1:nrow(eu)),function(x) as.numeric(gsub(":|,","",eu$value[x])))
eu <- filter(eu, feature != "")
dim(eu)## [1] 667368 46 Reformat the data into a 3D array (country * feature * time)
unq_country <- sort(unique(eu$country))
unq_time <- sort(unique(eu$time))
unq_fea <- sort(unique(eu$feature))
num_country <- length(unq_country)
num_time <- length(unq_time)
num_fea <- length(unq_fea)
eu <- arrange(eu,country,time,feature)
eu_3d_array <- array(NA,dim = c(num_country,num_time,num_fea),dimnames = list(unq_country,unq_time,unq_fea))
for (i in 1:num_country){
for (j in 1:num_time){
for (k in 1:num_fea){
eu_3d_array[i,j,k] = eu$value[(i-1)*num_time*num_fea + (j-1)*num_fea + k]
}
}
}
eu_3d_array[1:10,1:10,1]## 2000Q1 2000Q2 2000Q3 2000Q4 2001Q1 2001Q2 2001Q3 2001Q4
## Austria NA NA NA NA NA NA 0.0 1306.2
## Belgium 42016.2 2241.6 1454.3 182.9 515.2 2220.900 358.5 1644.1
## Bulgaria NA 2.5 3.3 1603.0 16174.0 -7002.800 2479.9 888.4
## Croatia NA NA 2214.3 NA 12.1 459.100 15.0 NA
## Cyprus 7.7 881.2 0.8 0.8 48.4 8.200 5.7 968.0
## Czech Republic 1989.8 191.1 NA 9265.2 NA NA 171.9 NA
## Denmark NA NA 115.7 3.2 6.1 78.854 NA 5.6
## Estonia -4.0 61.7 1.5 -3.8 NA 10.800 -6.0 85.2
## Finland 525.8 148.2 -2.3 NA 15.5 5.000 2811.7 28.3
## France NA NA 1547.7 NA NA 1270.600 NA NA
## 2002Q1 2002Q2
## Austria NA 762.0
## Belgium 894.0 998.3
## Bulgaria 1782.6 945.7
## Croatia 353.6 274.1
## Cyprus 9.5 NA
## Czech Republic NA 486.7
## Denmark 31.1 4.8
## Estonia -2.7 0.2
## Finland -6.2 1444.2
## France 791.1 4.27 Data visualization
eu <- arrange(eu,time,feature,country)
eu_visualization <- dplyr::select(eu,time,feature,country,value)
eu_visualization$time <- sapply(c(1:nrow(eu_visualization)),function(x) as.numeric(gsub("Q",".",eu_visualization$time[x])))
eu_visualization$feature <- as.factor(eu_visualization$feature)
eu_visualization$country <- as.factor(eu_visualization$country)
eu_visualization$value <- as.numeric(eu_visualization$value)
eu_visualization$feature <- sapply(c(1:nrow(eu_visualization)),function(x) substr(eu_visualization$feature[x],1,20))
#plot_ly(eu_visualization, x = ~time, y = ~country, z = ~value, color = ~feature,split = ~ country,type = 'scatter3d', mode = 'lines')8 Time series format
#Find the duplicates
eu_time_series <- na.omit(eu)
allFeatures = as.character(unique(eu_time_series$feature))
allTime = unique(eu_time_series$time)
allCountry = as.character(unique(eu_time_series$country))
allCombination = length(allFeatures)*length(allTime)*length(allCountry)
dup = c()
for (i in 1:length(allFeatures)){
for (j in 1:length(allCountry)){
for (k in 1:length(allTime)){
if (nrow(filter(eu_time_series,country == allCountry[j] & feature == allFeatures[i] & time == allTime[k]))>1){
dup = c(dup,as.character(allFeatures[i]))
break
}
}
break
}
}
dup #These features have multiple observations at the same time point## [1] "Employment by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels"
## [2] "Labor cost for LCI excluding bonuses"
## [3] "Labor costs other than wages or salaries"
## [4] "Labour cost for LCI (compensation of employees plus taxes minus subsidies)"
## [5] "Labour cost for LCI excluding bonuses"
## [6] "Labour costs other than wages and salaries"
## [7] "Wages and salaries (total)"Remove duplicates.
removeDup = filter(eu_time_series, feature != "Employment by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels" &
feature != "Labor cost for LCI excluding bonuses" &
feature != "Labor costs other than wages or salaries" &
feature != "Labour cost for LCI (compensation of employees plus taxes minus subsidies)" &
feature != "Labour cost for LCI excluding bonuses" &
feature != "Labour costs other than wages and salaries" &
feature != "Wages and salaries (total)")
time_series = spread(removeDup,feature,value)
dim(time_series)## [1] 2232 1979 Fit the ARIMA model for each country
9.1 Belgium
Extract Belgium data.
#Chose Belgium and fit the arima
belgium = filter(time_series,country == "Belgium")
belgium = belgium[, colSums(is.na(belgium)) != nrow(belgium)] #delete the feature that is missing at all the time point
belgium = dplyr::select(belgium,-time,-country)
dim(belgium)## [1] 72 170Manually clean (preprocess) the Belgium data and fit ARIMAX model \[Y = BelguimSuperSample\$'Unemployment,\ Females,\ From\ 15-64\ years,\ Total',\]
\[X = XReg\ (all\ other\ covariates\ -starts\_with('Unemployment')).\]
#super sample the dataset
cleardata <- function(mat) {
for (i in 1:ncol(mat)) {
mat[is.na(mat[,i]),i]<-mean(mat[,i],na.rm = T) + rnorm(sum(is.na(mat[,i])),sd = sd(mat[,i],na.rm = T))
}
return(mat)
}
#use spline regression model to expand the dataset
splinecreate <- function(mat) {
res<-NULL
for (i in 1:ncol(mat)) {
sp<-smooth.spline(seq(1:72),mat[,i])
spresult<-predict(sp,seq(from=0,by=1/5,length.out = 360))
spfeat<-spresult$y+rnorm(360,sd=sd(mat[,i]))
res<-cbind(res,spfeat)
}
colnames(res)<-colnames(mat)
return(res)
}
BelguimMatrix = as.matrix(belgium)
BelguimMatrix = cleardata(BelguimMatrix)
BelguimMatrix = splinecreate(BelguimMatrix)
BelguimSuperSample = as.data.frame(BelguimMatrix)
#############################
# Outcome Features to examine, predict, forecast, spacekime-analyze
# "Gross domestic product at market prices"
# "Unemployment , Females, From 15-64 years, Total"
# "Capital transfers, payable"
# "Capital transfers, receivable"
# "Debt securities"
# "Government consolidated gross debt"
# ... View(colnames(BelguimMatrix))
#############################
################################################
# "Unemployment , Females, From 15-64 years, Total"
Y = dplyr::select(BelguimSuperSample, "Unemployment , Females, From 15-64 years, Total"); dim(Y)## [1] 360 1X = dplyr::select(BelguimSuperSample, -starts_with("Unemployment")); dim(X)## [1] 360 143fitArimaX = auto.arima(Y, xreg=as.matrix(X[,-112])); fitArimaX$arma## [1] 1 0 0 0 1 0 0################################################
# "Government consolidated gross debt"
#Y = select(BelguimSuperSample, "Government consolidated gross debt"); dim(Y)
#X = select(BelguimSuperSample, -matches("debt|Debt")); dim(X)
# X_scale <- scale(X); Matrix::rankMatrix(X_scale); any(is.na(X_scale)); any(is.infinite(X_scale))
# remove columns with infinite or missing value
# X_scale_1 <- X_scale[ , !is.infinite(colSums(X_scale)) & !is.na(colSums(X_scale))]
#X_1 <- X[ , !is.infinite(colSums(X)) & !is.na(colSums(X))]; dim(X_1); Matrix::rankMatrix(X_1)
#X_2 <- X_1[, qr(X_1)$pivot[seq_len(qr(X_1)$rank)]]; dim(X_2)
#
#fitArimaX = auto.arima(Y, xreg=as.matrix(X_2), method = "CSS", # "SANN", method = "CSS", optim.method = "BFGS"
# optim.control=list(maxit = 20000, temp = 20), optim.method = "BFGS")
#fitArimaX; View(sort(fitArimaX$coef)[1:10]); fitArimaX$arma
################################################
# "Gross domestic product at market prices"
Y = dplyr::select(BelguimSuperSample, "Gross domestic product at market prices"); dim(Y)## [1] 360 1X = dplyr::select(BelguimSuperSample, -matches("debt|Debt")); dim(X) # 360 167## [1] 360 168X <- X[, qr(X)$pivot[seq_len(qr(X)$rank)]]; dim(X)## [1] 360 167ts_Y <- ts(Y, start=c(2000,1), end=c(2017, 20), frequency = 20); length(ts_Y)## [1] 360set.seed(1234)
fitArimaX = auto.arima(ts_Y, xreg=as.matrix(X[ , -c(50:60)])); fitArimaX$arma## [1] 1 0 1 0 20 0 0# 5 0 2 0 20 0 0
# sigma^2 estimated as 57.04: log likelihood=-1132.78 AIC=2593.55 AICc=2871.09 BIC=3230.88
pred_arimaX_5_0_2_Y_Belgium_train300_Belgium_test60 <-
predict(fitArimaX, n.ahead = 60, newxreg = as.matrix(X[301:360 , -c(50:60)]))$pred
plot(forecast(fitArimaX, xreg = as.matrix(X[301:360 , -c(50:60)])), # ARIMA forecast
include=120, lwd=4, lty=3, xlab="Time", ylab="GDP", ylim=c(50, 150),
main = "ARIMAX Analytics (Train: 2000-2017; Test: 2018-2020) GDP Forecasting\n
based on fitting ARIMAX Models on raw (spline interpolated) Belgium data")
lines(pred_arimaX_5_0_2_Y_Belgium_train300_Belgium_test60, col = "red", lwd = 4, lty=3)
legend("topleft", bty="n", legend=c("Belgium Training Data (2000-2017)",
"ARIMAX(5,0,2)-model GDP Forecasting (2018-2020)",
"ARIMAX(5,0,2)-model GDP Forecasting (2018-2020)"),
col=c("black", "blue", "red"),
lty=c(3,3,3), lwd=c(4,4,4), cex=1.2, x.intersp=1.5, y.intersp=0.6)
text(2015, 60, expression(atop(paste("Training Region (2000-2017)"),
paste(Model(Unempl) %->% "ARIMAX(p, q, r) ; ",
XReg %==% X[i], " ", i %in% {1 : 167}))), cex=1.5)
text(2019.5, 60, expression(atop(paste("Validation Region (2018-2020)"),
paste(hat(Unempl) %<-% "ARIMAX(5,0 ,2); ",
XReg %==% X[i], " ", i %in% {1 : 167}))), cex=1.5)
- GDP Description: GDP (gross domestic product) is an indicator for a nation’s economic situation. It reflects the total value of all goods and services produced less the value of goods and services used for intermediate consumption in their production. Expressing GDP in PPS (purchasing power standards) eliminates differences in price levels between countries, and calculations on a per head basis allows for the comparison of economies significantly different in absolute size.
GDP unit of measure represents the Current prices, euro per capita. The volume index of GDP per capita in Purchasing Power Standards (PPS) is intended for cross-country comparisons rather than for temporal comparisons. GDP per capita when expressed in PPS eliminates the differences in price levels between countries allowing meaningful volume comparisons of GDP between countries. Expressed in relation to the European Union (EU27 GDP = 100), a country with an index that is higher than \(100\) or lower than \(100\) corresponds to that country’s level of GDP per head being higher or lower than the EU average, respectively.
9.2 Bulgaria
Define a new function that (1) cleans the data, and (2) fits the ARIMA model estimating the seasonal and non-seasonal time-series parameters \((p,d,q)\) and the effect-sizes (\(\beta\)’s) for the exogenous regression features (\(X\)).
library(dplyr)
#write a function of clean the data and fit the ARIMA model
Fit_ARIMA <- function(countryData=Belgium, start=2000, end=2017, frequency=20,
feature="Unemployment , Females, From 15-64 years, Total")
{
#delete features that are missing at all time points
countryData = countryData[, colSums(is.na(countryData)) != nrow(countryData)]
countryData = dplyr::select(countryData, -time, -country)
DataMatrix = as.matrix(countryData)
DataMatrix = cleardata(DataMatrix)
DataMatrix = DataMatrix[ , colSums(is.na(DataMatrix)) == 0] # remove feature that only has one value
DataMatrix = DataMatrix[ , colSums(DataMatrix) != 0] # remove feature that all the values are 0
DataMatrix = splinecreate(DataMatrix)
DataSuperSample = as.data.frame(DataMatrix)
if (feature=="Unemployment , Females, From 15-64 years, Total") {
Y = dplyr::select(DataSuperSample, "Unemployment , Females, From 15-64 years, Total")
X = dplyr::select(DataSuperSample, -starts_with("Unemployment"))
} else if (feature=="Gross domestic product at market prices") {
Y = dplyr::select(DataSuperSample, "Gross domestic product at market prices"); dim(Y)
X = dplyr::select(DataSuperSample, -matches("debt|Debt")); dim(X) # 360 167
print(paste0("dim(X)=(", dim(X)[1], ",", dim(X)[2], "); ",
" dim(Y)=(", dim(Y)[1], ",", dim(Y)[2], ") ..."))
X <- X[, qr(X)$pivot[seq_len(qr(X)$rank)]]; dim(X) # ensure full-rank design matrix, X
}
else {
print(paste0("This feature ", feature, " is not implemented yet! Exiting Fit_ARIMA() method ..."))
return(NULL)
}
ts_Y <- ts(Y, start=c(start, 1), end=c(end, frequency), frequency = frequency); length(ts_Y)
set.seed(1234)
fitArimaX = auto.arima(ts_Y, xreg=as.matrix(X))
return(fitArimaX)
}
Bulgaria = filter(time_series,country == "Bulgaria")
BulgariaARIMA = Fit_ARIMA(countryData=Bulgaria, start=2000, end=2017, frequency=20,
feature="Gross domestic product at market prices")## [1] "dim(X)=(360,168); dim(Y)=(360,1) ..."BulgariaARIMA$arma## [1] 0 0 0 0 20 0 0# Extend the Fit-ARIMA method to ensure testing-training modeling/assessment for 2 countries works
preprocess_ARIMA <- function(countryData=Belgium, start=2000, end=2017, frequency=20,
feature="Unemployment , Females, From 15-64 years, Total")
{
#delete features that are missing at all time points
countryData = countryData[, colSums(is.na(countryData)) != nrow(countryData)]
countryData = dplyr::select(countryData, !any_of(c("time", "country")))
DataMatrix = as.matrix(countryData)
DataMatrix = cleardata(DataMatrix)
DataMatrix = DataMatrix[ , colSums(is.na(DataMatrix)) == 0] # remove features with only 1 value
DataMatrix = DataMatrix[ , colSums(DataMatrix) != 0] # remove features with all values=0
DataMatrix = splinecreate(DataMatrix)
DataSuperSample = as.data.frame(DataMatrix) # super-Sample the data
print(paste0("Processing feature: ...", feature, "... "))
if (feature=="Unemployment , Females, From 15-64 years, Total") {
Y = dplyr::select(DataSuperSample, "Unemployment , Females, From 15-64 years, Total")
X = dplyr::select(DataSuperSample, -starts_with("Unemployment"))
} else if (feature=="Gross domestic product at market prices") {
Y = dplyr::select(DataSuperSample, "Gross domestic product at market prices"); dim(Y)
X = dplyr::select(DataSuperSample, -matches("debt|Debt"));
X <- X [, -c(50:80)]; dim(X) # 360 167
} else {
print(paste0("This feature: ...", feature, "... is not implemented yet! Exiting preprocess_ARIMA() method ..."))
return(NULL)
}
# reduce the number of observations (matrix rows) to specified time range
len_1 <- (end + 1 - start) * frequency; print(paste0("dim(X)[1]=", len_1))
X <- X[1:len_1 , qr(X[1:len_1 , ])$pivot[seq_len(qr(X[1:len_1 , ])$rank)]]; dim(X)
# ensure full-rank design matrix, X
Y <- as.data.frame(Y[1:len_1 , ])
print(paste0("dim(X)=(", dim(X)[1], ",", dim(X)[2], "); ", # 300 136
" dim(Y)=(", dim(Y)[1], ",", dim(Y)[2], ") ...")) # 300 1
return(list("X"=X, "Y"=Y))
}
# Outcome Variable to be modeled, as a timeseries: 2000 - 2017 (18 years, Quarterly measures)
# Spline interpolation *5; 2000-01 - 2014-20 (300 observations for training): 60 observations (2015-2017) for Testing
Belgium <- filter(time_series, country == "Belgium")
Bulgaria <- filter(time_series, country == "Bulgaria")
Netherlands <- filter(time_series, country == "Netherlands")
# Test preprocess_ARIMA()
#preprocess_Belgium <- preprocess_ARIMA(countryData=Belgium, start=2000, end=2014,
# frequency=20, feature="Gross domestic product at market prices")
#preprocess_Bulgaria <- preprocess_ARIMA(countryData=Bulgaria, start=2000, end=2014,
# frequency=20, feature="Gross domestic product at market prices")
# General function that ensures the XReg predictors for 2 countries are homologous
homologousX_features <- function (X_Country1, X_Country2){
# Check if the Belgium and Bulgaria Xreg are homologous (same feature columns)
common_cols <- intersect(colnames(X_Country1), colnames(X_Country2))
X_Country1 <- subset(X_Country1, select = common_cols)
X_Country2 <- subset(X_Country2, select = common_cols)
print(paste0("dim(X1)=(", dim(X_Country1)[1], ",", dim(X_Country1)[2], "); ", # 300 131
" dim(X2)=(", dim(X_Country2)[1], ",", dim(X_Country2)[2], ")!")) # 300 131
return(list("X_Country1"=X_Country1, "X_Country2"=X_Country2))
}
# Test homologousX_features
# homoFeat <- homologousX_features(preprocess_Belgium$X, preprocess_Bulgaria$X)
# X_Belgium <- homoFeat$X_Country1
# X_Bulgaria <- homoFeat$X_Country2
fit_ARIMA <- function(country1Data=Belgium, country2Data=Bulgaria,
start=2000, end=2014, frequency=20,
feature="Gross domestic product at market prices") {
preprocess_Country1 <- preprocess_ARIMA(countryData=country1Data,
start=start, end=end, frequency=frequency, feature=feature)
preprocess_Country2 <- preprocess_ARIMA(countryData=country2Data,
start=start, end=end, frequency=frequency, feature=feature)
ts_Y_Country1 <- ts(preprocess_Country1$Y, start=c(start, 1),
end=c(end, frequency), frequency = frequency); length(ts_Y_Country1)
homoFeat <- homologousX_features(preprocess_Country1$X, preprocess_Country2$X)
X_Country1 <- homoFeat$X_Country1
X_Country2 <- homoFeat$X_Country2
set.seed(1234)
fitArimaX_Country1 = auto.arima(ts_Y_Country1, xreg=as.matrix(X_Country1))
return(fitArimaX_Country1)
}
# Belgium = filter(time_series,country == "Belgium")
BelgiumARIMA = fit_ARIMA(country1Data=Belgium,
country2Data=Bulgaria, # country2Data=Netherlands,
start=2000, end=2014, frequency=20,
feature="Gross domestic product at market prices")## [1] "Processing feature: ...Gross domestic product at market prices... "
## [1] "dim(X)[1]=300"
## [1] "dim(X)=(300,136); dim(Y)=(300,1) ..."
## [1] "Processing feature: ...Gross domestic product at market prices... "
## [1] "dim(X)[1]=300"
## [1] "dim(X)=(300,137); dim(Y)=(300,1) ..."
## [1] "dim(X1)=(300,131); dim(X2)=(300,131)!"BelgiumARIMA$arma # [1] 4 0 2 0 20 0 0## [1] 0 0 2 0 20 0 0# sigma^2 estimated as 45.99: log likelihood=-919.13 AIC=2116.26 AICc=2359.51 BIC=2631.09
# Outcome Variable to be modeled, as a timeseries: 2000 - 2017 (18 years, Quarterly measures)
# Spline interpolation x5; 2000-01 - 2014-20 (300 observations for training)
# ts_Y_Belgium_train <- ts(Y_Belgium_train, start=c(2000,1), end=c(2014, 20), frequency=20)
# length(ts_Y_Belgium_train)
# ts_Y_Belgium_test <- ts(Y_Belgium_test, start=c(2015,1), end=c(2017, 20), frequency = 20)
#length(ts_Y_Belgium_test)
# Find ARIMAX model
# arimaX_Belgium_train <- auto.arima(ts_Y_Belgium_train, xreg=as.matrix(X_Belgium_train)); # arimaX_Belgium_train$arma10 TS Forecasting
10.1 Perform ARIMAX modeling
Predict Y={Gross domestic product at market prices}, using all other features not directly related to *GDP. Recall the core data organization:
- 131 (common BE + BG)
XregPredictors and 1 Outcome Variable to be modeled as a timeseries: 2000 - 2014 (15 years, Quarterly measures, 5-fold spline interpolation, \(15*4*5=300\)); - Spline interpolation x5 (freq=20 observations per year); 2000-01 to 2014-20 (300 timepoint observations over 15 years, for
training). The remaining 60 timepoints used fortesting(2015-01 to 2017-20).
Report ARIMA(p,d,q) params and quality metrics AIC/BIC.
# Previously, we already extracted the Belgium and Bulgaria Data, preprocess it,
# and fit the ARIMAX (Belgium-training) model. Now, we will assess the model on Bulgaria_testing sets
# BelgiumARIMA = fit_ARIMA(country1Data=Belgium, country2Data=Bulgaria,
# start=2000, end=2014, frequency=20,
# feature="Gross domestic product at market prices")
# BelgiumARIMA$arma # [1] 4 0 2 0 20 0 0
# View rank-ordered ARIMAX effects:
# View(BelgiumARIMA$coef[order(BelgiumARIMA$coef)])
sort(BelgiumARIMA$coef)[1:10]## Labor cost for LCI (compensation of employees plus taxes minus subsidies)
## -0.58331526
## Labor cost other than wages and salaries
## -0.46307313
## sar1
## -0.38733039
## Unemployment , Males, From 15-64 years, from 18 to 23 months
## -0.21974189
## Unemployment , Males, From 15-64 years, 48 months or over
## -0.17358002
## Unemployment , Males, From 15-64 years, Less than 1 month
## -0.15551403
## Unemployment , Females, From 15-64 years, Less than 1 month
## -0.09753506
## Unemployment , Males, From 15-64 years, from 24 to 47 months
## -0.05964248
## Unemployment , Females, From 15-64 years, 48 months or over
## -0.05802372
## Agriculture, forestry and fishing, Wages and salaries
## -0.05716910# Unemployment , Females, From 15-64 years, From 18 to 23 months
# -1.5203281
# ar2
# -1.1808472
# Labor cost other than wages and salaries
# -0.8380554
# Unemployment , Females, From 15-64 years, From 12 to 17 months
# -0.7037336
# ar4
# -0.6360880
# sar2
# -0.6260002
# Unemployment , Females, From 15-64 years, From 3 to 5 months
# -0.5262376
# Labor cost for LCI (compensation of employees plus taxes minus subsidies)
# -0.2885038
# Unemployment , Females, From 15-64 years, 48 months or over
# -0.2773650
# Unemployment , Males, From 15-64 years, from 3 to 5 months
# -0.2567934
#Get the Prospective Xreg=X design matrices ready (2015-2017, 60 rows)
preprocess_Belgium <- preprocess_ARIMA(countryData=Belgium,
start=2000, end=2017, frequency=20,
feature="Gross domestic product at market prices")## [1] "Processing feature: ...Gross domestic product at market prices... "
## [1] "dim(X)[1]=360"
## [1] "dim(X)=(360,136); dim(Y)=(360,1) ..."preprocess_Bulgaria <- preprocess_ARIMA(countryData=Bulgaria, #Netherlands
start=2000, end=2017, frequency=20,
feature="Gross domestic product at market prices")## [1] "Processing feature: ...Gross domestic product at market prices... "
## [1] "dim(X)[1]=360"
## [1] "dim(X)=(360,137); dim(Y)=(360,1) ..."homoFeat <- homologousX_features(preprocess_Belgium$X, preprocess_Bulgaria$X)## [1] "dim(X1)=(360,131); dim(X2)=(360,131)!"X_Belgium_test <- homoFeat$X_Country1[301:360, ]; dim(X_Belgium_test)## [1] 60 131X_Bulgaria_test <- homoFeat$X_Country2[301:360, ]; dim(X_Bulgaria_test)## [1] 60 131# Get Predictions
pred_arimaX_4_0_2_Y_Belgium_train300_Bulgaria_test60 <-
forecast(BelgiumARIMA, xreg = as.matrix(X_Bulgaria_test))$mean
pred_arimaX_4_0_2_Y_Belgium_train300_Belgium_test60 <-
forecast(BelgiumARIMA, xreg = as.matrix(X_Belgium_test))$mean
pred_arimaX_4_0_2_Y_Belgium_train300_Offset_Bulgaria_test60 <-
forecast(BelgiumARIMA, xreg = as.matrix(X_Bulgaria_test))$mean +
mean(pred_arimaX_4_0_2_Y_Belgium_train300_Belgium_test60) -
mean(pred_arimaX_4_0_2_Y_Belgium_train300_Bulgaria_test60)
cor(pred_arimaX_4_0_2_Y_Belgium_train300_Belgium_test60, ts_Y_Belgium_test) # 0.11## [1] 0.1175167mean(pred_arimaX_4_0_2_Y_Belgium_train300_Belgium_test60) # [1] 118## [1] 103.0763# Alternative predictions:
# X_Country1 <- X_Belgium_test; X_Country2 <- X_Bulgaria_test
# pred_arimaX_1_0_2_Y_Belgium_train300_Bulgaria_test60 <- predict(BelgiumARIMA, n.ahead = 60, newxreg = X_Bulgaria_test)$pred
# pred_arimaX_1_0_2_Y_Belgium_train300_Belgium_test60 <- predict(BelgiumARIMA, n.ahead = 60, newxreg = X_Belgium_test)$pred10.2 Display the alternative (spacetime) analytical models (ARIMAX)
Plot only the last 5-years of training (2010-2014), \(100TimePoints=5Years\times 4Quarters\times 5SuperSample\) and the 3-year prospective forecasting \(60TimePoints=3Years\times 4Quarters\times 5SuperSample\).
ts_Y_Belgium_test <- ts(preprocess_Belgium$Y[301:360, ],
start=c(2015,1), end=c(2017, 20), frequency = 20)
length(ts_Y_Belgium_test)## [1] 60# windows(width=14, height=10)
plot(forecast(BelgiumARIMA, xreg = as.matrix(X_Belgium_test)), # ARIMA forecast
include=100, lwd=4, lty=3, xlab="Time", ylab="GDP Purchasing Power Standards (PPS)",
ylim=c(25, 150),
main = "ARIMAX Analytics (Train: 2000-2014; Test: 2015-2017) GDP (PPS) Forecasting\n
based on fitting ARIMAX Models on raw (spline interpolated) Belgium data")
lines(pred_arimaX_4_0_2_Y_Belgium_train300_Belgium_test60, col = "green", lwd = 4, lty=2) # Belgium train+test
lines(pred_arimaX_4_0_2_Y_Belgium_train300_Bulgaria_test60, col = "purple", lwd = 4, lty=1) # Belgium train+Bulgaria test
lines(pred_arimaX_4_0_2_Y_Belgium_train300_Offset_Bulgaria_test60, col = "orange", lwd = 4, lty=1)
# Belgium train+ Offset Bulgaria test: 188.3753 - 416.5375
lines(ts_Y_Belgium_test, col = "red", lwd = 6, lty=1) # Observed Y_Test timeseries
legend("topleft", bty="n", legend=c("Belgium Training Data (2000-2014)",
"ARIMAX(4,0,2)-model GDP Forecasting (2015-2017)",
"ARIMAX(4,0,2) Belgium train + XReg=Belgium test (2015-2017)",
"ARIMAX(4,0,2) Belgium train + XReg=Bulgaria test (2015-2017)",
"Offset ARIMAX(4,0,2) Belgium train + XReg=Bulgaria test (2015-2017)",
"Belgium Official Reported GDP (2015-2017)"),
col=c("black", "blue", "green", "purple", "orange", "red"),
lty=c(3,1,2,1, 1, 1), lwd=c(4,4,4,4,4, 6), cex=1.2, x.intersp=1.5, y.intersp=0.7)
text(2012.5, 30, expression(atop(paste("Training Region (2000-2014)"),
paste(Model(GDP) %->% "ARIMAX(p, q, r) ; ",
XReg %==% X[i], " ", i %in% {1 : 131}))), cex=1.2)
text(2016.5, 30, expression(atop(paste("Validation Region (2015-2017)"),
paste(hat(GDP) %<-% "ARIMAX(4, 0, 2); ",
XReg %==% X[i], " ", i %in% {1 : 131}))), cex=1.2)
Plot entire 15-year training time-span (2000-2014), \(300TimePoints=15Years\times 4Quarters\times 5SuperSample\) and the 3-year prospective forecasting \(60TimePoints=3Years\times 4Quarters\times 5SuperSample\).
ts_Y_Belgium_test <- ts(preprocess_Belgium$Y[301:360, ],
start=c(2015,1), end=c(2017, 20), frequency = 20)
length(ts_Y_Belgium_test)## [1] 60# windows(width=14, height=10)
plot(forecast(BelgiumARIMA, xreg = as.matrix(X_Belgium_test)), # ARIMA forecast
lwd=4, lty=3, xlab="Time", ylab="GDP Purchasing Power Standards (PPS)",
ylim=c(25, 150),
main = "ARIMAX Analytics (Train: 2000-2014; Test: 2015-2017) GDP (PPS) Forecasting\n
based on fitting ARIMAX Models on raw (spline interpolated) Belgium data")
lines(pred_arimaX_4_0_2_Y_Belgium_train300_Belgium_test60, col = "green", lwd = 4, lty=2) # Belgium train+test
lines(pred_arimaX_4_0_2_Y_Belgium_train300_Bulgaria_test60, col = "purple", lwd = 4, lty=1) # Belgium train+Bulgaria test
lines(pred_arimaX_4_0_2_Y_Belgium_train300_Offset_Bulgaria_test60, col = "orange", lwd = 4, lty=1)
# Belgium train+ Offset Bulgaria test: 188.3753 - 416.5375
lines(ts_Y_Belgium_test, col = "red", lwd = 6, lty=1) # Observed Y_Test timeseries
legend("topleft", bty="n", legend=c("Belgium Training Data (2000-2014)",
"ARIMAX(4,0,2)-model GDP Forecasting (2015-2017)",
"ARIMAX(4,0,2) Belgium train + XReg=Belgium test (2015-2017)",
"ARIMAX(4,0,2) Belgium train + XReg=Bulgaria test (2015-2017)",
"Offset ARIMAX(4,0,2) Belgium train + XReg=Bulgaria test (2015-2017)",
"Belgium Official Reported GDP (2015-2017)"),
col=c("black", "blue", "green", "purple", "orange", "red"),
lty=c(3,1,2,1, 1, 1), lwd=c(4,4,4,4,4, 6), cex=1.2, x.intersp=1.5, y.intersp=0.7)
text(2005, 30, expression(atop(paste("Training Region (2000-2014)"),
paste(Model(GDP) %->% "ARIMAX(p, q, r) ; ",
XReg %==% X[i], " ", i %in% {1 : 131}))), cex=1.2)
text(2015, 30, expression(atop(paste("Validation Region (2015-2017)"),
paste(hat(GDP) %<-% "ARIMAX(4, 0, 2); ",
XReg %==% X[i], " ", i %in% {1 : 131}))), cex=1.2)
11 Spacekime analytics
11.1 Generic K-Space transformations (FT/IFT)
Let’s start by defining the generic k-space transformation.
# FT/Spacekime Analytics
# 1D timeseries FFT SHIFT
fftshift1D <- function(img_ff) {
rows <- length(img_ff)
rows_half <- ceiling(rows/2)
return(append(img_ff[(rows_half+1):rows], img_ff[1:rows_half]))
}
# Generic function to Transform Data ={all predictors (X) and outcome (Y)} to k-space (Fourier domain)
kSpaceTransform <- function(data, inverse = FALSE, reconPhases = NULL) {
# ForwardFT (rawData, FALSE, NULL)
# InverseFT(magnitudes, TRUE, reconPhasesToUse) or InverseFT(FT_data, TRUE, NULL)
FT_data <- array(complex(), c(dim(data)[1], dim(data)[2]))
mag_FT_data <- array(complex(), c(dim(data)[1], dim(data)[2]))
phase_FT_data <- array(complex(), c(dim(data)[1], dim(data)[2]))
IFT_reconPhases_data <- array(complex(), c(dim(data)[1], dim(data)[2]))
for (i in 1:dim(data)[2]) {
if (inverse == FALSE | is.null(reconPhases)) {
FT_data[ , i] <- fft(data[ , i], inverse)
X2 <- FT_data[ , i]
# plot(fftshift1D(log(Re(X2)+2)), main = "log(fftshift1D(Re(FFT(timeseries))))")
mag_FT_data[ , i] <- sqrt(Re(X2)^2+Im(X2)^2);
# plot(log(fftshift1D(Re(mag_FT_MCSI_data))), main = "log(Magnitude(FFT(timeseries)))")
phase_FT_data[ , i] <- atan2(Im(X2), Re(X2));
# plot(Re(fftshift1D(phase_FT_MCSI_data[ , 1])), main = "Shift(Phase(FFT(timeseries)))")
}
else { # for IFT synthesis using user-provided Phases, typically from kime-phase aggregators
Real <- data[ , i] * cos(reconPhases[ , i])
Imaginary <- data[ , i] * sin(reconPhases[ , i])
IFT_reconPhases_data[ ,i] <-
Re(fft(Real+1i*Imaginary, inverse = TRUE)/length(data[ , i]))
}
}
######### Test the FT-IFT analysis-synthesis back-and-forth transform process
# to confirm calculations
# X2 <- FT_data[ , 1]; mag_FT_data[ , 1] <- sqrt(Re(X2)^2+Im(X2)^2);
# phase_FT_data[ , 1] <- atan2(Im(X2), Re(X2));
# Real2 = mag_FT_data[ , 1] * cos(phase_FT_data[ , 1])
# Imaginary2 = mag_FT_data[ , 1] * sin(phase_FT_data[ , 1])
# man_hat_X2 = Re(fft(Real2 + 1i*Imaginary2, inverse = T)/length(X2))
# ifelse(abs(man_hat_X2[5] - data[5, 1]) < 0.001, "Perfect Synthesis", "Problems!!!")
#########
if (inverse == FALSE | is.null(reconPhases)) {
return(list("magnitudes"=mag_FT_data, "phases"=phase_FT_data))
# Use kSpaceTransform$magnitudes & kSpaceTransform$phases to retrieve teh Mags and Phases
}
else {
return(IFT_reconPhases_data)
# Use Re(kSpaceTransform) to extract spacetime Real-valued reconstructed data
}
}11.2 Kime-Phase Distributions
Examine the Kime-direction Distributions of the Phases for all Belgium features (predictors + outcome). Define a generic function that plots the Phase distributions.
library(tidyr)
library(ggplot2)
plotPhaseDistributions <- function (dataFT, dataColnames, size=10, ...) {
df.phase <- as.data.frame(Re(dataFT$phases))
df.phase %>% gather() %>% head()
colnames(df.phase) <- dataColnames
phaseDistributions <- gather(df.phase)
colnames(phaseDistributions) <- c("Feature", "Phase")
if (is.null(size)) size=10
# map the value as our x variable, and use facet_wrap to separate by the key column:
ggplot(phaseDistributions, aes(Phase)) +
# geom_histogram(bins = 10) +
geom_histogram(aes(y=..density..), bins = 10) +
facet_wrap( ~Feature, scales = 'free_x') +
xlim(-pi, pi) +
theme(strip.text.x = element_text(size = size, colour = "black", angle = 0))
}
# homoFeat <- homologousX_features(preprocess_Belgium$X, preprocess_Bulgaria$X)
X_Belgium <- homoFeat$X_Country1; dim(X_Belgium)## [1] 360 131Y_Belgium <- preprocess_Belgium$Y; dim(Y_Belgium)## [1] 360 1FT_Belgium <- kSpaceTransform(cbind(X_Belgium, Y_Belgium), FALSE, NULL)
dataColnames <- c(colnames(X_Belgium), "Y_GDP_Belgium")
plotPhaseDistributions(FT_Belgium, dataColnames)
IFT_FT_Belgium <- kSpaceTransform(FT_Belgium$magnitudes, TRUE, FT_Belgium$phases)
# Check IFT(FT) == I:
# ifelse(abs(cbind(X_Belgium, Y_Belgium)[5,4] - Re(IFT_FT_Belgium[5,4])) < 0.001, "Perfect Synthesis", "Problems!!!")11.3 Nil-Phase Synthesis and ARIMAX re-modeling
Perform Nil-Phase reconstruction - IFT_NilPhase_FT_Belgium - and then re-fit the ARIMAX model
# 1. Nil-Phase data synthesis (reconstruction)
temp_Data <- cbind(X_Belgium, Y_Belgium)
nilPhase_FT_data <- array(complex(real=0, imaginary=0), c(dim(temp_Data)[1], dim(temp_Data)[2]))
dim(nilPhase_FT_data) # ; head(nilPhase_FT_data)## [1] 360 132# [1] 360 132
IFT_NilPhase_FT_Belgium <- array(complex(), c(dim(temp_Data)[1], dim(temp_Data)[2]))
# Invert back to spacetime the FT_Belgium$magnitudes[ , i] signal with nil-phase
IFT_NilPhase_FT_Belgium <- Re(kSpaceTransform(FT_Belgium$magnitudes, TRUE, nilPhase_FT_data))
colnames(IFT_NilPhase_FT_Belgium) <- c(colnames(X_Belgium), "Y_GDP_Belgium")
dim(IFT_NilPhase_FT_Belgium); dim(FT_Belgium$magnitudes)## [1] 360 132## [1] 360 132colnames(IFT_NilPhase_FT_Belgium); head(IFT_NilPhase_FT_Belgium); # head(temp_Data)## [1] "Acquisitions less disposals of non-financial non-produced assets"
## [2] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels"
## [3] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [4] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)"
## [5] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [6] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels"
## [7] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [8] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8)"
## [9] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [10] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels"
## [11] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [12] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8)"
## [13] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [14] "Agriculture, forestry and fishing"
## [15] "Agriculture, forestry and fishing - Compensation of employees"
## [16] "Agriculture, forestry and fishing - Employers' social contributions"
## [17] "Agriculture, forestry and fishing, Wages and salaries"
## [18] "All ISCED 2011 levels "
## [19] "All ISCED 2011 levels, Females"
## [20] "All ISCED 2011 levels, Males"
## [21] "Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Compensation of employees"
## [22] "Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Employers' social contributions"
## [23] "Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Value added, gross"
## [24] "Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Wages and salaries"
## [25] "Capital taxes, receivable"
## [26] "Capital transfers, payable"
## [27] "Capital transfers, receivable"
## [28] "Changes in inventories and acquisitions less disposals of valuables"
## [29] "Collective consumption expenditure"
## [30] "Compensation of employees"
## [31] "Compensation of employees, payable"
## [32] "Construction, Compensation of employees"
## [33] "Construction, Employers' social contributions"
## [34] "Construction, Value added, gross"
## [35] "Construction, Wages and salaries"
## [36] "Consumption of fixed capital"
## [37] "Current taxes on income, wealth, etc., payable"
## [38] "Current taxes on income, wealth, etc., receivable"
## [39] "Employers' actual social contributions, receivable"
## [40] "Employers' social contributions"
## [41] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels "
## [42] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [43] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)"
## [44] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [45] "Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [46] "Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education "
## [47] "Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [48] "Information and communication, wages and salaries"
## [49] "Interest, payable"
## [50] "Interest, receivable"
## [51] "Intermediate consumption"
## [52] "ISCED11 Less than primary, primary and lower secondary education (levels 0-2)"
## [53] "ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Females"
## [54] "ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Males"
## [55] "ISCED11 Tertiary education (levels 5-8)"
## [56] "ISCED11 Tertiary education (levels 5-8), Females"
## [57] "ISCED11 Tertiary education (levels 5-8), Males"
## [58] "ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [59] "ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Females"
## [60] "ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Males"
## [61] "Labor cost for LCI (compensation of employees plus taxes minus subsidies)"
## [62] "Labor cost other than wages and salaries"
## [63] "Labour cost for LCI"
## [64] "Loans"
## [65] "Market output, output for own final use and payments for non-market output"
## [66] "Net lending (+) /net borrowing (-)"
## [67] "Net social contributions, receivable"
## [68] "Other capital transfers and investment grants, receivable"
## [69] "Other current taxes, receivable"
## [70] "Other current transfers, payable"
## [71] "Other current transfers, receivable"
## [72] "Other property income, receivable"
## [73] "Other subsidies on production, payable"
## [74] "Other taxes on production, receivable"
## [75] "Output"
## [76] "Professional, scientific and technical activities; administrative and support service activities, Compensation of employees"
## [77] "Professional, scientific and technical activities; administrative and support service activities, Employers' social contributions"
## [78] "Professional, scientific and technical activities; administrative and support service activities, Value added, gross"
## [79] "Professional, scientific and technical activities; administrative and support service activities, Wages and salaries"
## [80] "Property income, payable"
## [81] "Property income, receivable"
## [82] "Public administration, defence, education, human health and social work activities, Compensation of employees"
## [83] "Public administration, defence, education, human health and social work activities, Employers' social contributions"
## [84] "Public administration, defence, education, human health and social work activities, Value added, gross"
## [85] "Public administration, defence, education, human health and social work activities, Wages and salaries"
## [86] "Real estate activities, Compensation of employees"
## [87] "Savings, gross"
## [88] "Social benefits other than social transfers in kind and social transfers in kind ? purchased market production, payable"
## [89] "Social benefits other than social transfers in kind, payable"
## [90] "Social transfers in kind ? purchased market production, payable"
## [91] "Subsidies on products, payable"
## [92] "Subsidies, payable"
## [93] "Taxes on income, receivable"
## [94] "Taxes on production and imports, receivable"
## [95] "Taxes on products, receivable"
## [96] "Total general government expenditure"
## [97] "Total general government revenue"
## [98] "Unemployment , Females, From 15-64 years, 48 months or over"
## [99] "Unemployment , Females, From 15-64 years, From 1 to 2 months"
## [100] "Unemployment , Females, From 15-64 years, From 12 to 17 months"
## [101] "Unemployment , Females, From 15-64 years, From 18 to 23 months"
## [102] "Unemployment , Females, From 15-64 years, From 24 to 47 months"
## [103] "Unemployment , Females, From 15-64 years, From 3 to 5 months"
## [104] "Unemployment , Females, From 15-64 years, From 6 to 11 months"
## [105] "Unemployment , Females, From 15-64 years, Less than 1 month"
## [106] "Unemployment , Females, From 15-64 years, Total"
## [107] "Unemployment , Males, From 15-64 years"
## [108] "Unemployment , Males, From 15-64 years, 48 months or over"
## [109] "Unemployment , Males, From 15-64 years, from 1 to 2 months"
## [110] "Unemployment , Males, From 15-64 years, from 12 to 17 months"
## [111] "Unemployment , Males, From 15-64 years, from 18 to 23 months"
## [112] "Unemployment , Males, From 15-64 years, from 24 to 47 months"
## [113] "Unemployment , Males, From 15-64 years, from 3 to 5 months"
## [114] "Unemployment , Males, From 15-64 years, from 6 to 11 months"
## [115] "Unemployment , Males, From 15-64 years, Less than 1 month"
## [116] "Unemployment , Total, From 15-64 years, 48 months or over"
## [117] "Unemployment , Total, From 15-64 years, From 1 to 2 months"
## [118] "Unemployment , Total, From 15-64 years, From 12 to 17 months"
## [119] "Unemployment , Total, From 15-64 years, From 18 to 23 months"
## [120] "Unemployment , Total, From 15-64 years, From 24 to 47 months"
## [121] "Unemployment , Total, From 15-64 years, From 3 to 5 months"
## [122] "Unemployment , Total, From 15-64 years, From 6 to 11 months"
## [123] "Unemployment , Total, From 15-64 years, Less than 1 month"
## [124] "Unemployment by sex, age, duration. DurationNA not started"
## [125] "Value added, gross"
## [126] "VAT, receivable"
## [127] "Wages and salaries"
## [128] "Wholesale and retail trade, transport, accomodation and food service activities"
## [129] "Wholesale and retail trade, transport, accomodation and food service activities, Compensation of employees"
## [130] "Wholesale and retail trade, transport, accomodation and food service activities, Employers' social contributions"
## [131] "Wholesale and retail trade, transport, accomodation and food service activities, Wages and salaries"
## [132] "Y_GDP_Belgium"## Acquisitions less disposals of non-financial non-produced assets
## [1,] 1110.952039
## [2,] 79.273398
## [3,] 2.039761
## [4,] 10.910308
## [5,] 45.242577
## [6,] -4.814762
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels
## [1,] 5115.841
## [2,] 2549.495
## [3,] 2467.847
## [4,] 2521.276
## [5,] 2502.421
## [6,] 2379.511
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [1,] 1408.5307
## [2,] 538.5062
## [3,] 542.4742
## [4,] 542.2998
## [5,] 521.9520
## [6,] 563.0089
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)
## [1,] 3772.227
## [2,] 1304.520
## [3,] 1257.847
## [4,] 1382.174
## [5,] 1254.979
## [6,] 1168.356
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [1,] 1969.2992
## [2,] 942.4209
## [3,] 952.4655
## [4,] 949.4241
## [5,] 895.0917
## [6,] 877.1022
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels
## [1,] 3881.539
## [2,] 2749.023
## [3,] 2700.768
## [4,] 2722.559
## [5,] 2719.356
## [6,] 2686.458
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [1,] 2825.9532
## [2,] 928.5126
## [3,] 1140.8508
## [4,] 958.0191
## [5,] 919.0725
## [6,] 977.1562
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8)
## [1,] 2777.109
## [2,] 1125.496
## [3,] 1087.722
## [4,] 1164.688
## [5,] 1056.704
## [6,] 1073.331
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [1,] 2512.284
## [2,] 1305.521
## [3,] 1246.568
## [4,] 1237.675
## [5,] 1207.482
## [6,] 1174.302
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels
## [1,] 9001.534
## [2,] 5331.583
## [3,] 5366.846
## [4,] 5187.233
## [5,] 5068.680
## [6,] 5021.369
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [1,] 4153.903
## [2,] 1496.759
## [3,] 1512.630
## [4,] 1401.031
## [5,] 1481.221
## [6,] 1493.529
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8)
## [1,] 6554.407
## [2,] 2390.584
## [3,] 2465.636
## [4,] 2439.318
## [5,] 2187.070
## [6,] 2342.174
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [1,] 4317.963
## [2,] 2099.190
## [3,] 2136.939
## [4,] 2148.927
## [5,] 2095.408
## [6,] 1949.695
## Agriculture, forestry and fishing
## [1,] 2370.0689
## [2,] 770.7217
## [3,] 744.7749
## [4,] 749.6924
## [5,] 707.0577
## [6,] 814.2332
## Agriculture, forestry and fishing - Compensation of employees
## [1,] 668.2896
## [2,] 172.8269
## [3,] 191.0643
## [4,] 167.9324
## [5,] 153.4496
## [6,] 160.9177
## Agriculture, forestry and fishing - Employers' social contributions
## [1,] 189.24760
## [2,] 40.35185
## [3,] 49.18994
## [4,] 37.24327
## [5,] 34.71436
## [6,] 42.83946
## Agriculture, forestry and fishing, Wages and salaries
## [1,] 476.8198
## [2,] 120.0407
## [3,] 112.2229
## [4,] 120.6299
## [5,] 121.9007
## [6,] 124.7255
## All ISCED 2011 levels All ISCED 2011 levels, Females
## [1,] 11187.737 5667.927
## [2,] 7611.656 3772.543
## [3,] 7556.401 3813.524
## [4,] 7438.716 3716.739
## [5,] 7521.011 3756.469
## [6,] 7484.206 3787.299
## All ISCED 2011 levels, Males
## [1,] 5575.393
## [2,] 3798.539
## [3,] 3762.755
## [4,] 3741.972
## [5,] 3780.166
## [6,] 3724.618
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Compensation of employees
## [1,] 5018.889
## [2,] 1717.897
## [3,] 1624.863
## [4,] 1529.395
## [5,] 1490.645
## [6,] 1507.259
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Employers' social contributions
## [1,] 1545.1909
## [2,] 328.4201
## [3,] 372.5934
## [4,] 394.9282
## [5,] 274.0782
## [6,] 358.1225
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Value added, gross
## [1,] 7365.838
## [2,] 2428.441
## [3,] 2452.485
## [4,] 2643.919
## [5,] 2359.422
## [6,] 2317.616
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Wages and salaries
## [1,] 3684.881
## [2,] 1225.145
## [3,] 1177.893
## [4,] 1229.290
## [5,] 1224.005
## [6,] 1157.004
## Capital taxes, receivable Capital transfers, payable
## [1,] 5311.2712 18008.7852
## [2,] 1240.1301 972.3911
## [3,] 1152.5326 1585.9791
## [4,] 1103.8397 1004.8868
## [5,] 1176.2162 2074.6034
## [6,] 956.6173 1639.8812
## Capital transfers, receivable
## [1,] 5618.8165
## [2,] 1166.0053
## [3,] 1302.3042
## [4,] 1309.2322
## [5,] 899.9315
## [6,] 1435.5003
## Changes in inventories and acquisitions less disposals of valuables
## [1,] 1333.1490
## [2,] 114.1862
## [3,] 121.9083
## [4,] 102.4185
## [5,] 113.2441
## [6,] 128.0403
## Collective consumption expenditure Compensation of employees
## [1,] 29561.669 187968.51
## [2,] 10012.774 60067.37
## [3,] 9866.500 64849.81
## [4,] 9088.166 65069.74
## [5,] 9979.416 53502.23
## [6,] 9895.356 64473.99
## Compensation of employees, payable Construction, Compensation of employees
## [1,] 50997.88 9787.532
## [2,] 15381.88 2969.951
## [3,] 15172.17 2991.621
## [4,] 15928.91 3391.361
## [5,] 15272.76 3207.939
## [6,] 13634.38 3120.342
## Construction, Employers' social contributions
## [1,] 2740.2865
## [2,] 696.5691
## [3,] 695.8254
## [4,] 797.1233
## [5,] 792.0739
## [6,] 723.3330
## Construction, Value added, gross Construction, Wages and salaries
## [1,] 21261.698 6487.451
## [2,] 5677.061 2237.237
## [3,] 6290.153 2381.424
## [4,] 5933.587 2184.347
## [5,] 6238.234 2136.407
## [6,] 4967.684 1777.156
## Consumption of fixed capital
## [1,] 8736.463
## [2,] 2682.335
## [3,] 2825.130
## [4,] 2870.018
## [5,] 2789.571
## [6,] 2658.691
## Current taxes on income, wealth, etc., payable
## [1,] 384.241683
## [2,] 16.763146
## [3,] 27.413943
## [4,] 7.699611
## [5,] 17.827432
## [6,] 1.420111
## Current taxes on income, wealth, etc., receivable
## [1,] 87064.80
## [2,] 23526.02
## [3,] 18651.35
## [4,] 19946.12
## [5,] 19855.87
## [6,] 18128.51
## Employers' actual social contributions, receivable
## [1,] 38604.235
## [2,] 10230.055
## [3,] 11373.513
## [4,] 9643.841
## [5,] 10657.337
## [6,] 10204.508
## Employers' social contributions
## [1,] 55518.66
## [2,] 18735.32
## [3,] 17993.38
## [4,] 17083.09
## [5,] 17155.29
## [6,] 16312.77
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels
## [1,] 4796.925
## [2,] 2335.690
## [3,] 2291.466
## [4,] 2322.757
## [5,] 2217.430
## [6,] 2361.819
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [1,] 1273.1695
## [2,] 457.9986
## [3,] 468.3346
## [4,] 472.3599
## [5,] 463.3484
## [6,] 420.4853
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)
## [1,] 3655.666
## [2,] 1207.849
## [3,] 1220.648
## [4,] 1319.046
## [5,] 1252.369
## [6,] 1230.272
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [1,] 1882.1070
## [2,] 840.1865
## [3,] 859.5029
## [4,] 789.1881
## [5,] 789.5751
## [6,] 823.3809
## Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [1,] 2809.1901
## [2,] 964.6341
## [3,] 908.0070
## [4,] 814.0859
## [5,] 793.9166
## [6,] 840.7560
## Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education
## [1,] 2663.4905
## [2,] 1038.8113
## [3,] 1063.8285
## [4,] 1032.3179
## [5,] 989.8935
## [6,] 941.3314
## Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [1,] 2248.138
## [2,] 1172.508
## [3,] 1115.752
## [4,] 1110.391
## [5,] 1118.768
## [6,] 1129.697
## Information and communication, wages and salaries Interest, payable
## [1,] 5931.361 11538.712
## [2,] 1719.036 4808.676
## [3,] 1544.425 4829.389
## [4,] 1633.578 5078.359
## [5,] 1646.612 4572.569
## [6,] 1630.487 4460.760
## Interest, receivable Intermediate consumption
## [1,] 1246.4399 16834.126
## [2,] 452.6913 5219.191
## [3,] 493.1698 4842.911
## [4,] 472.4861 5236.730
## [5,] 445.4176 4737.645
## [6,] 454.4217 4690.434
## ISCED11 Less than primary, primary and lower secondary education (levels 0-2)
## [1,] 7656.025
## [2,] 2982.104
## [3,] 3208.122
## [4,] 3193.020
## [5,] 3189.413
## [6,] 2866.838
## ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Females
## [1,] 3881.721
## [2,] 1561.133
## [3,] 1434.978
## [4,] 1376.716
## [5,] 1447.825
## [6,] 1517.100
## ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Males
## [1,] 3753.100
## [2,] 1614.635
## [3,] 1510.767
## [4,] 1570.631
## [5,] 1544.967
## [6,] 1525.353
## ISCED11 Tertiary education (levels 5-8)
## [1,] 7638.883
## [2,] 2826.367
## [3,] 2783.861
## [4,] 2960.789
## [5,] 2881.201
## [6,] 2793.627
## ISCED11 Tertiary education (levels 5-8), Females
## [1,] 4753.638
## [2,] 1449.594
## [3,] 1584.511
## [4,] 1611.341
## [5,] 1456.303
## [6,] 1524.800
## ISCED11 Tertiary education (levels 5-8), Males
## [1,] 3390.078
## [2,] 1239.633
## [3,] 1295.376
## [4,] 1194.216
## [5,] 1306.501
## [6,] 1240.328
## ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [1,] 6013.811
## [2,] 2933.066
## [3,] 2936.574
## [4,] 3019.928
## [5,] 2914.473
## [6,] 2982.814
## ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Females
## [1,] 2690.655
## [2,] 1407.291
## [3,] 1401.688
## [4,] 1346.888
## [5,] 1405.729
## [6,] 1354.992
## ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Males
## [1,] 3490.582
## [2,] 1580.590
## [3,] 1755.093
## [4,] 1587.625
## [5,] 1660.435
## [6,] 1614.089
## Labor cost for LCI (compensation of employees plus taxes minus subsidies)
## [1,] 22.658592
## [2,] 3.959972
## [3,] 3.451979
## [4,] 3.990087
## [5,] 3.959758
## [6,] 3.957121
## Labor cost other than wages and salaries Labour cost for LCI Loans
## [1,] 32.044213 25.429264 375293.81
## [2,] 4.656361 5.716912 93873.34
## [3,] 6.043282 5.806560 74278.79
## [4,] 5.368016 5.424674 76882.52
## [5,] 5.574993 5.172957 83984.63
## [6,] 6.897791 5.628024 80117.61
## Market output, output for own final use and payments for non-market output
## [1,] 12941.821
## [2,] 3922.539
## [3,] 3525.540
## [4,] 3722.871
## [5,] 3952.803
## [6,] 3321.198
## Net lending (+) /net borrowing (-) Net social contributions, receivable
## [1,] 84941.16016 65606.08
## [2,] 5365.58136 21164.55
## [3,] 3080.96074 19610.62
## [4,] 1006.73424 17052.36
## [5,] -58.98774 18481.96
## [6,] -2455.75828 20307.00
## Other capital transfers and investment grants, receivable
## [1,] 1405.54594
## [2,] 94.65614
## [3,] 122.25907
## [4,] 106.98006
## [5,] 71.93741
## [6,] 49.53877
## Other current taxes, receivable Other current transfers, payable
## [1,] 1668.8598 10746.568
## [2,] 606.8070 2109.476
## [3,] 584.2219 2403.962
## [4,] 552.0474 2615.786
## [5,] 553.3794 2457.391
## [6,] 521.8593 2750.906
## Other current transfers, receivable Other property income, receivable
## [1,] 4232.8184 10471.2362
## [2,] 889.4634 485.6338
## [3,] 763.8716 320.8897
## [4,] 1007.4371 906.5636
## [5,] 858.5969 653.5641
## [6,] 837.0430 914.4398
## Other subsidies on production, payable
## [1,] 19689.922
## [2,] 4262.782
## [3,] 3364.440
## [4,] 4294.821
## [5,] 4055.007
## [6,] 4431.813
## Other taxes on production, receivable Output
## [1,] 10340.144 72481.77
## [2,] 2972.156 23113.76
## [3,] 2737.256 21503.84
## [4,] 2911.302 22128.71
## [5,] 2626.188 19644.70
## [6,] 2600.190 19111.84
## Professional, scientific and technical activities; administrative and support service activities, Compensation of employees
## [1,] 28037.738
## [2,] 8026.972
## [3,] 7778.509
## [4,] 7439.591
## [5,] 6653.721
## [6,] 7865.333
## Professional, scientific and technical activities; administrative and support service activities, Employers' social contributions
## [1,] 7325.986
## [2,] 1975.092
## [3,] 1395.567
## [4,] 2055.786
## [5,] 1798.087
## [6,] 2098.016
## Professional, scientific and technical activities; administrative and support service activities, Value added, gross
## [1,] 60912.48
## [2,] 17658.71
## [3,] 13652.18
## [4,] 15412.80
## [5,] 14929.74
## [6,] 14861.55
## Professional, scientific and technical activities; administrative and support service activities, Wages and salaries
## [1,] 20818.283
## [2,] 5758.576
## [3,] 5578.121
## [4,] 5095.911
## [5,] 4981.843
## [6,] 5124.062
## Property income, payable Property income, receivable
## [1,] 11992.439 10657.7791
## [2,] 4749.165 1128.3719
## [3,] 4719.448 1370.6664
## [4,] 4632.524 770.8398
## [5,] 4460.869 775.8355
## [6,] 4764.318 1148.6560
## Public administration, defence, education, human health and social work activities, Compensation of employees
## [1,] 75298.22
## [2,] 22377.32
## [3,] 25079.16
## [4,] 22364.27
## [5,] 19219.13
## [6,] 20845.66
## Public administration, defence, education, human health and social work activities, Employers' social contributions
## [1,] 23834.332
## [2,] 6729.113
## [3,] 7616.939
## [4,] 6802.881
## [5,] 8070.036
## [6,] 7008.634
## Public administration, defence, education, human health and social work activities, Value added, gross
## [1,] 84373.45
## [2,] 24753.83
## [3,] 24927.00
## [4,] 23761.60
## [5,] 24356.74
## [6,] 24691.42
## Public administration, defence, education, human health and social work activities, Wages and salaries
## [1,] 50543.14
## [2,] 14160.13
## [3,] 15351.02
## [4,] 14849.05
## [5,] 14880.23
## [6,] 13816.70
## Real estate activities, Compensation of employees Savings, gross
## [1,] 1215.4030 78283.4117
## [2,] 355.2658 3043.1957
## [3,] 288.8541 -372.6170
## [4,] 289.3314 -171.5510
## [5,] 289.4481 275.4573
## [6,] 295.1022 -1773.6328
## Social benefits other than social transfers in kind and social transfers in kind ? purchased market production, payable
## [1,] 108890.21
## [2,] 31119.87
## [3,] 34098.81
## [4,] 32880.10
## [5,] 31281.75
## [6,] 28626.04
## Social benefits other than social transfers in kind, payable
## [1,] 73026.95
## [2,] 20321.82
## [3,] 20587.93
## [4,] 21336.93
## [5,] 18576.75
## [6,] 22687.66
## Social transfers in kind ? purchased market production, payable
## [1,] 37892.674
## [2,] 9964.181
## [3,] 9295.339
## [4,] 10208.593
## [5,] 11752.535
## [6,] 9459.095
## Subsidies on products, payable Subsidies, payable
## [1,] 2333.3771 19804.719
## [2,] 784.0308 4792.885
## [3,] 775.5237 4634.783
## [4,] 678.1196 4200.692
## [5,] 672.8240 4347.674
## [6,] 749.3111 4273.734
## Taxes on income, receivable Taxes on production and imports, receivable
## [1,] 88503.22 50099.54
## [2,] 17339.70 16677.77
## [3,] 17496.04 16078.78
## [4,] 17601.59 17369.68
## [5,] 16620.98 15780.67
## [6,] 18932.88 15407.82
## Taxes on products, receivable Total general government expenditure
## [1,] 41977.91 224107.40
## [2,] 14105.06 73246.39
## [3,] 14548.69 66268.75
## [4,] 12550.40 63604.72
## [5,] 12583.78 64378.25
## [6,] 12863.48 62262.88
## Total general government revenue
## [1,] 217368.66
## [2,] 62396.61
## [3,] 62710.92
## [4,] 58284.82
## [5,] 62109.88
## [6,] 61183.36
## Unemployment , Females, From 15-64 years, 48 months or over
## [1,] 144.08523
## [2,] 44.78310
## [3,] 43.98445
## [4,] 45.84666
## [5,] 37.77682
## [6,] 43.53693
## Unemployment , Females, From 15-64 years, From 1 to 2 months
## [1,] 160.00794
## [2,] 32.01093
## [3,] 32.36596
## [4,] 33.66360
## [5,] 31.96159
## [6,] 33.03758
## Unemployment , Females, From 15-64 years, From 12 to 17 months
## [1,] 86.50302
## [2,] 22.38595
## [3,] 24.27081
## [4,] 21.56063
## [5,] 21.48057
## [6,] 25.07822
## Unemployment , Females, From 15-64 years, From 18 to 23 months
## [1,] 39.075604
## [2,] 10.784943
## [3,] 9.052963
## [4,] 10.750330
## [5,] 11.264218
## [6,] 9.477534
## Unemployment , Females, From 15-64 years, From 24 to 47 months
## [1,] 120.57045
## [2,] 29.76366
## [3,] 28.71212
## [4,] 32.29478
## [5,] 32.85321
## [6,] 31.84753
## Unemployment , Females, From 15-64 years, From 3 to 5 months
## [1,] 111.87664
## [2,] 32.45306
## [3,] 25.68834
## [4,] 27.41005
## [5,] 27.89939
## [6,] 31.50885
## Unemployment , Females, From 15-64 years, From 6 to 11 months
## [1,] 122.50339
## [2,] 34.24079
## [3,] 38.37464
## [4,] 31.60444
## [5,] 27.95826
## [6,] 34.79598
## Unemployment , Females, From 15-64 years, Less than 1 month
## [1,] 66.42257
## [2,] 13.52059
## [3,] 11.63051
## [4,] 10.57948
## [5,] 15.00120
## [6,] 12.28191
## Unemployment , Females, From 15-64 years, Total
## [1,] 507.9483
## [2,] 204.0347
## [3,] 200.9263
## [4,] 208.1368
## [5,] 186.6033
## [6,] 184.9805
## Unemployment , Males, From 15-64 years
## [1,] 749.1708
## [2,] 248.1187
## [3,] 256.6653
## [4,] 251.1941
## [5,] 252.1094
## [6,] 220.9268
## Unemployment , Males, From 15-64 years, 48 months or over
## [1,] 120.51623
## [2,] 38.14550
## [3,] 38.98878
## [4,] 42.89180
## [5,] 38.51626
## [6,] 39.59423
## Unemployment , Males, From 15-64 years, from 1 to 2 months
## [1,] 160.71789
## [2,] 37.42763
## [3,] 45.24768
## [4,] 36.14093
## [5,] 29.91350
## [6,] 40.88546
## Unemployment , Males, From 15-64 years, from 12 to 17 months
## [1,] 136.97394
## [2,] 39.04537
## [3,] 35.31847
## [4,] 36.66815
## [5,] 31.21844
## [6,] 34.06932
## Unemployment , Males, From 15-64 years, from 18 to 23 months
## [1,] 62.74028
## [2,] 17.54910
## [3,] 13.74389
## [4,] 17.34236
## [5,] 16.40364
## [6,] 14.59568
## Unemployment , Males, From 15-64 years, from 24 to 47 months
## [1,] 174.91975
## [2,] 47.20327
## [3,] 41.41940
## [4,] 43.58655
## [5,] 38.25741
## [6,] 39.75162
## Unemployment , Males, From 15-64 years, from 3 to 5 months
## [1,] 162.13101
## [2,] 41.87953
## [3,] 36.67742
## [4,] 33.62015
## [5,] 44.22370
## [6,] 39.53018
## Unemployment , Males, From 15-64 years, from 6 to 11 months
## [1,] 165.09747
## [2,] 49.58845
## [3,] 53.05674
## [4,] 51.04334
## [5,] 48.59763
## [6,] 46.42519
## Unemployment , Males, From 15-64 years, Less than 1 month
## [1,] 66.11920
## [2,] 13.94079
## [3,] 11.69558
## [4,] 11.65875
## [5,] 11.06154
## [6,] 13.30538
## Unemployment , Total, From 15-64 years, 48 months or over
## [1,] 226.88155
## [2,] 87.18973
## [3,] 82.46812
## [4,] 80.10929
## [5,] 78.14147
## [6,] 67.85621
## Unemployment , Total, From 15-64 years, From 1 to 2 months
## [1,] 299.24088
## [2,] 53.49000
## [3,] 59.95838
## [4,] 60.72738
## [5,] 70.27403
## [6,] 67.85004
## Unemployment , Total, From 15-64 years, From 12 to 17 months
## [1,] 196.34798
## [2,] 61.55912
## [3,] 60.18761
## [4,] 57.32327
## [5,] 62.80822
## [6,] 59.95380
## Unemployment , Total, From 15-64 years, From 18 to 23 months
## [1,] 95.24819
## [2,] 27.49534
## [3,] 29.64643
## [4,] 25.83156
## [5,] 23.59430
## [6,] 22.12151
## Unemployment , Total, From 15-64 years, From 24 to 47 months
## [1,] 251.99541
## [2,] 69.28373
## [3,] 74.10627
## [4,] 80.21957
## [5,] 80.94126
## [6,] 70.52314
## Unemployment , Total, From 15-64 years, From 3 to 5 months
## [1,] 234.82581
## [2,] 69.07026
## [3,] 65.22794
## [4,] 73.10979
## [5,] 65.48068
## [6,] 66.33769
## Unemployment , Total, From 15-64 years, From 6 to 11 months
## [1,] 274.21754
## [2,] 97.64810
## [3,] 94.77739
## [4,] 87.14297
## [5,] 91.37227
## [6,] 85.95887
## Unemployment , Total, From 15-64 years, Less than 1 month
## [1,] 132.14375
## [2,] 24.36142
## [3,] 25.40064
## [4,] 21.81581
## [5,] 24.19284
## [6,] 23.97403
## Unemployment by sex, age, duration. DurationNA not started
## [1,] 1178.5798
## [2,] 470.2241
## [3,] 446.4939
## [4,] 461.6102
## [5,] 444.5560
## [6,] 475.6336
## Value added, gross VAT, receivable Wages and salaries
## [1,] 58011.12 27478.459 132698.57
## [2,] 19224.34 8297.715 48323.08
## [3,] 17739.74 7930.142 44178.16
## [4,] 17864.52 7602.400 42780.74
## [5,] 18614.25 8495.267 42559.85
## [6,] 19028.83 8564.635 41559.69
## Wholesale and retail trade, transport, accomodation and food service activities
## [1,] 61988.11
## [2,] 25446.86
## [3,] 22904.95
## [4,] 21308.49
## [5,] 22774.10
## [6,] 19790.08
## Wholesale and retail trade, transport, accomodation and food service activities, Compensation of employees
## [1,] 38861.68
## [2,] 12130.41
## [3,] 13328.42
## [4,] 12100.54
## [5,] 10817.45
## [6,] 12316.29
## Wholesale and retail trade, transport, accomodation and food service activities, Employers' social contributions
## [1,] 11898.996
## [2,] 3436.565
## [3,] 3341.390
## [4,] 3587.932
## [5,] 3379.375
## [6,] 2996.473
## Wholesale and retail trade, transport, accomodation and food service activities, Wages and salaries
## [1,] 27992.141
## [2,] 9122.716
## [3,] 8496.243
## [4,] 9178.938
## [5,] 10295.140
## [6,] 8935.456
## Y_GDP_Belgium
## [1,] 257.1429
## [2,] 114.2978
## [3,] 115.0242
## [4,] 107.1860
## [5,] 120.0626
## [6,] 113.2050# 2. Perform ARIMAX modeling on IFT_NilPhase_FT_Belgium; report (p,d,q) params and quality metrics AIC/BIC
# library(forecast)
IFT_NilPhase_FT_Belgium_Y_train <- IFT_NilPhase_FT_Belgium[1:300, 132]; length(IFT_NilPhase_FT_Belgium_Y_train)## [1] 300IFT_NilPhase_FT_Belgium_Y_test <- IFT_NilPhase_FT_Belgium[301:360]; length(IFT_NilPhase_FT_Belgium_Y_test)## [1] 60# Training and Testing Data Covariates explaining the longitudinal outcome (Y)
IFT_NilPhase_FT_Belgium_X_train <- as.data.frame(IFT_NilPhase_FT_Belgium)[1:300, 1:131]; dim(IFT_NilPhase_FT_Belgium_X_train)## [1] 300 131IFT_NilPhase_FT_Belgium_X_test <- as.data.frame(IFT_NilPhase_FT_Belgium)[301:360, 1:131]; dim(IFT_NilPhase_FT_Belgium_X_test)## [1] 60 131# Outcome Variable to be ARIMAX-modeled, as a timeseries
ts_IFT_NilPhase_FT_Belgium_Y_train <-
ts(IFT_NilPhase_FT_Belgium_Y_train, start=c(2000,1), end=c(2014, 20), frequency = 20)
# Find ARIMAX model: 2 1 2 0 20 0 0
set.seed(1234)
modArima_IFT_NilPhase_FT_Belgium_Y_train <-
auto.arima(ts_IFT_NilPhase_FT_Belgium_Y_train, xreg=as.matrix(IFT_NilPhase_FT_Belgium_X_train))
modArima_IFT_NilPhase_FT_Belgium_Y_train$arma## [1] 0 0 0 0 20 0 0# Regression with ARIMA(2,0,1)(2,0,0)[20] errors
# Coefficients:
# ar1 ar2 ma1 sar1 sar2 Acquisitions less disposals of non-financial non-produced assets
# -1.4232 -0.8592 -0.987 0.0941 -0.3451 0.0123
#s.e. 0.0341 0.0311 NaN 0.0688 0.0742 0.0007
# sigma^2 estimated as 0.8622: log likelihood=-320.39 AIC=914.79 AICc=1148.19 BIC=1422.2
pred_arimax_2_0_1_Nil <- forecast(modArima_IFT_NilPhase_FT_Belgium_Y_train, xreg = as.matrix(IFT_NilPhase_FT_Belgium_X_test))
pred_arimax_2_0_1_Nil_2015_2017 <-
ts(pred_arimax_2_0_1_Nil$mean, frequency=20, start=c(2015,1), end=c(2017,20))
pred_arimax_2_0_1_Nil_2015_2017## Time Series:
## Start = c(2015, 1)
## End = c(2017, 20)
## Frequency = 20
## 301 302 303 304 305 306 307 308
## 88.30356 98.80439 98.82414 100.24958 98.20237 98.36554 96.30529 97.80899
## 309 310 311 312 313 314 315 316
## 94.99745 100.76216 99.15476 95.03449 97.22556 96.65118 95.79747 101.40819
## 317 318 319 320 321 322 323 324
## 101.47707 97.30270 94.43611 103.42894 103.05740 98.74251 100.89311 92.04458
## 325 326 327 328 329 330 331 332
## 100.34252 99.08458 101.33709 103.32193 102.62480 102.35424 100.96010 101.18495
## 333 334 335 336 337 338 339 340
## 102.88974 96.00394 109.61228 102.98695 105.63638 110.25446 104.92910 111.64195
## 341 342 343 344 345 346 347 348
## 108.38924 102.66525 107.82131 109.05657 111.32618 105.90575 106.44036 110.53353
## 349 350 351 352 353 354 355 356
## 118.99739 114.65406 109.89075 114.48486 113.51383 112.59303 118.39389 112.82340
## 357 358 359 360
## 117.50727 115.01641 112.03347 113.57481# alternatively:
# pred_arimax_1_0_1_2015_2017 <- predict(modArima_IFT_NilPhase_FT_Belgium_Y_train,
# n.ahead = 3*20, newxreg = IFT_NilPhase_FT_Belgium_X_test)$pred
sort(modArima_IFT_NilPhase_FT_Belgium_Y_train$coef)[1:10]## Labor cost other than wages and salaries
## -0.71870577
## Unemployment , Females, From 15-64 years, From 12 to 17 months
## -0.52259425
## Labor cost for LCI (compensation of employees plus taxes minus subsidies)
## -0.38187294
## Unemployment , Total, From 15-64 years, From 18 to 23 months
## -0.31033669
## Unemployment , Males, From 15-64 years, from 3 to 5 months
## -0.27676162
## Unemployment , Males, From 15-64 years, from 24 to 47 months
## -0.19742180
## Unemployment , Males, From 15-64 years, Less than 1 month
## -0.19479050
## Unemployment , Females, From 15-64 years, From 3 to 5 months
## -0.18181915
## Current taxes on income, wealth, etc., payable
## -0.09665561
## Unemployment , Total, From 15-64 years, From 1 to 2 months
## -0.04675708# Labor cost for LCI (compensation of employees plus taxes minus subsidies), effect=-1.5972295
# ar1, effect=-1.4231617
# Labor cost other than wages and salaries, effect=-1.2213214
# ma1, effect=-0.9869571
# ar2, effect=-0.8591937
# Unemployment , Females, From 15-64 years, From 12 to 17 months, effect=-0.7075454
# Unemployment , Total, From 15-64 years, From 18 to 23 months, effect=-0.5797656
# Unemployment , Males, From 15-64 years, from 3 to 5 months, effect=-0.5026139
# sar2, effect=-0.3450866
# Unemployment , Males, From 15-64 years, from 24 to 47 months, effect=-0.2965540
cor(pred_arimax_2_0_1_Nil$mean, ts_Y_Belgium_test) # 0.14## [1] 0.1052517mean(pred_arimax_2_0_1_Nil_2015_2017) # [1] 105## [1] 104.001111.4 Swapped-Phase Synthesis and ARIMAX Modeling
Space-time reconstructions by inverting back the mag_FT for each feature signal after swapping the feature-phases. In other words, we randomly shuffle the columns of the Phases-matrix (Training & Testing XReg Data) and use these swapped phases to synthesize the design covariate matrix (\(Xreg\)).
# 1. Swap Feature Phases and then synthesize the data (reconstruction)
# temp_Data <- cbind(X_Belgium, Y_Belgium)
swapped_phase_FT_Belgium_data <- FT_Belgium$phases
colnames(swapped_phase_FT_Belgium_data) <- c(colnames(X_Belgium), "Y_GDP_Belgium")
swapped_phase_FT_Belgium_data1 <- swapped_phase_FT_Belgium_data
dim(swapped_phase_FT_Belgium_data) # ; head(swappedPhase_FT_data)## [1] 360 132# [1] 360 132
IFT_SwappedPhase_FT_Belgium <- array(complex(), c(dim(temp_Data)[1], dim(temp_Data)[2]))
set.seed(12345) # sample randomly Phase-columns for each of the 131 covariates (X)
#swap_phase_FT_Belgium_indices <- sample(ncol(swapped_phase_FT_Belgium_data)-1)
# for (j in 1:131) { # for all columns of the design Xreg matrix, excluding Y, randomly swap columns phases
# swapped_phase_FT_Belgium_data1[ , j] <- swapped_phase_FT_Belgium_data[, swap_phase_FT_Belgium_indices[j]]
#}
swapped_phase_FT_Belgium_data1 <- as.data.frame(cbind(
swapped_phase_FT_Belgium_data[ , sample(ncol(swapped_phase_FT_Belgium_data[ , 1:131]))],
swapped_phase_FT_Belgium_data[ , 132]))
swapped_phase_FT_Belgium_data <- swapped_phase_FT_Belgium_data1
colnames(swapped_phase_FT_Belgium_data)[132] <- "Y_GDP_Belgium"
colnames(swapped_phase_FT_Belgium_data)## [1] "Taxes on products, receivable"
## [2] "Unemployment , Males, From 15-64 years, from 6 to 11 months"
## [3] "Unemployment , Females, From 15-64 years, From 1 to 2 months"
## [4] "Wholesale and retail trade, transport, accomodation and food service activities, Employers' social contributions"
## [5] "ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [6] "Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Compensation of employees"
## [7] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels "
## [8] "Loans"
## [9] "Social transfers in kind ? purchased market production, payable"
## [10] "Unemployment , Total, From 15-64 years, From 3 to 5 months"
## [11] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [12] "All ISCED 2011 levels, Females"
## [13] "Social benefits other than social transfers in kind and social transfers in kind ? purchased market production, payable"
## [14] "Acquisitions less disposals of non-financial non-produced assets"
## [15] "Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education "
## [16] "ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Males"
## [17] "Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [18] "Unemployment , Total, From 15-64 years, From 1 to 2 months"
## [19] "VAT, receivable"
## [20] "Unemployment , Males, From 15-64 years"
## [21] "Intermediate consumption"
## [22] "Consumption of fixed capital"
## [23] "Unemployment , Females, From 15-64 years, Total"
## [24] "Professional, scientific and technical activities; administrative and support service activities, Employers' social contributions"
## [25] "Other current taxes, receivable"
## [26] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [27] "Other taxes on production, receivable"
## [28] "ISCED11 Tertiary education (levels 5-8), Males"
## [29] "Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Wages and salaries"
## [30] "Interest, receivable"
## [31] "Property income, receivable"
## [32] "Unemployment , Total, From 15-64 years, From 12 to 17 months"
## [33] "Unemployment , Total, From 15-64 years, From 24 to 47 months"
## [34] "Net social contributions, receivable"
## [35] "Unemployment , Males, From 15-64 years, from 12 to 17 months"
## [36] "Construction, Wages and salaries"
## [37] "Public administration, defence, education, human health and social work activities, Employers' social contributions"
## [38] "Public administration, defence, education, human health and social work activities, Wages and salaries"
## [39] "Wages and salaries"
## [40] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [41] "Other property income, receivable"
## [42] "Employers' actual social contributions, receivable"
## [43] "Wholesale and retail trade, transport, accomodation and food service activities, Wages and salaries"
## [44] "Unemployment , Males, From 15-64 years, from 24 to 47 months"
## [45] "Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Value added, gross"
## [46] "Changes in inventories and acquisitions less disposals of valuables"
## [47] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels"
## [48] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)"
## [49] "Unemployment , Total, From 15-64 years, From 6 to 11 months"
## [50] "ISCED11 Less than primary, primary and lower secondary education (levels 0-2)"
## [51] "Professional, scientific and technical activities; administrative and support service activities, Wages and salaries"
## [52] "Unemployment , Females, From 15-64 years, 48 months or over"
## [53] "Capital taxes, receivable"
## [54] "Agriculture, forestry and fishing, Wages and salaries"
## [55] "Unemployment , Females, From 15-64 years, From 6 to 11 months"
## [56] "Current taxes on income, wealth, etc., receivable"
## [57] "ISCED11 Tertiary education (levels 5-8)"
## [58] "Taxes on production and imports, receivable"
## [59] "Construction, Compensation of employees"
## [60] "All ISCED 2011 levels "
## [61] "Unemployment , Males, From 15-64 years, 48 months or over"
## [62] "Wholesale and retail trade, transport, accomodation and food service activities, Compensation of employees"
## [63] "Unemployment , Total, From 15-64 years, From 18 to 23 months"
## [64] "Public administration, defence, education, human health and social work activities, Compensation of employees"
## [65] "Net lending (+) /net borrowing (-)"
## [66] "Agriculture, forestry and fishing - Compensation of employees"
## [67] "Labor cost other than wages and salaries"
## [68] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels"
## [69] "Professional, scientific and technical activities; administrative and support service activities, Compensation of employees"
## [70] "ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Females"
## [71] "Unemployment , Males, From 15-64 years, from 1 to 2 months"
## [72] "Compensation of employees, payable"
## [73] "Savings, gross"
## [74] "All ISCED 2011 levels, Males"
## [75] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [76] "Total general government expenditure"
## [77] "ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Females"
## [78] "Total general government revenue"
## [79] "Real estate activities, Compensation of employees"
## [80] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8)"
## [81] "Unemployment , Males, From 15-64 years, Less than 1 month"
## [82] "Capital transfers, payable"
## [83] "Unemployment , Females, From 15-64 years, From 12 to 17 months"
## [84] "Interest, payable"
## [85] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [86] "Property income, payable"
## [87] "Labour cost for LCI"
## [88] "Market output, output for own final use and payments for non-market output"
## [89] "ISCED11 Tertiary education (levels 5-8), Females"
## [90] "Other current transfers, receivable"
## [91] "Unemployment , Total, From 15-64 years, Less than 1 month"
## [92] "Construction, Employers' social contributions"
## [93] "Public administration, defence, education, human health and social work activities, Value added, gross"
## [94] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [95] "Capital transfers, receivable"
## [96] "Other current transfers, payable"
## [97] "Unemployment , Females, From 15-64 years, From 24 to 47 months"
## [98] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)"
## [99] "Value added, gross"
## [100] "Subsidies, payable"
## [101] "Unemployment by sex, age, duration. DurationNA not started"
## [102] "Unemployment , Total, From 15-64 years, 48 months or over"
## [103] "Collective consumption expenditure"
## [104] "Subsidies on products, payable"
## [105] "Wholesale and retail trade, transport, accomodation and food service activities"
## [106] "Unemployment , Females, From 15-64 years, From 3 to 5 months"
## [107] "Agriculture, forestry and fishing - Employers' social contributions"
## [108] "Unemployment , Males, From 15-64 years, from 3 to 5 months"
## [109] "Unemployment , Females, From 15-64 years, Less than 1 month"
## [110] "Social benefits other than social transfers in kind, payable"
## [111] "Other subsidies on production, payable"
## [112] "Other capital transfers and investment grants, receivable"
## [113] "Current taxes on income, wealth, etc., payable"
## [114] "Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [115] "Agriculture, forestry and fishing"
## [116] "Compensation of employees"
## [117] "Unemployment , Females, From 15-64 years, From 18 to 23 months"
## [118] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [119] "Information and communication, wages and salaries"
## [120] "Employers' social contributions"
## [121] "Output"
## [122] "Unemployment , Males, From 15-64 years, from 18 to 23 months"
## [123] "Construction, Value added, gross"
## [124] "ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Males"
## [125] "Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Employers' social contributions"
## [126] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [127] "Taxes on income, receivable"
## [128] "Professional, scientific and technical activities; administrative and support service activities, Value added, gross"
## [129] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8)"
## [130] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels"
## [131] "Labor cost for LCI (compensation of employees plus taxes minus subsidies)"
## [132] "Y_GDP_Belgium"dim(swapped_phase_FT_Belgium_data); dim(FT_Belgium$phases)## [1] 360 132## [1] 360 132# Invert back to spacetime the FT_Belgium$magnitudes[ , i] signal using the feature swapped phases
IFT_SwappedPhase_FT_Belgium <- Re(kSpaceTransform(FT_Belgium$magnitudes, TRUE, swapped_phase_FT_Belgium_data))
colnames(IFT_SwappedPhase_FT_Belgium) <- c(colnames(X_Belgium), "Y_GDP_Belgium")
dim(IFT_SwappedPhase_FT_Belgium); dim(FT_Belgium$magnitudes)## [1] 360 132## [1] 360 132colnames(IFT_SwappedPhase_FT_Belgium); tail(IFT_SwappedPhase_FT_Belgium); # tail(temp_Data)## [1] "Acquisitions less disposals of non-financial non-produced assets"
## [2] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels"
## [3] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [4] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)"
## [5] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [6] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels"
## [7] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [8] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8)"
## [9] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [10] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels"
## [11] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [12] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8)"
## [13] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [14] "Agriculture, forestry and fishing"
## [15] "Agriculture, forestry and fishing - Compensation of employees"
## [16] "Agriculture, forestry and fishing - Employers' social contributions"
## [17] "Agriculture, forestry and fishing, Wages and salaries"
## [18] "All ISCED 2011 levels "
## [19] "All ISCED 2011 levels, Females"
## [20] "All ISCED 2011 levels, Males"
## [21] "Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Compensation of employees"
## [22] "Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Employers' social contributions"
## [23] "Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Value added, gross"
## [24] "Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Wages and salaries"
## [25] "Capital taxes, receivable"
## [26] "Capital transfers, payable"
## [27] "Capital transfers, receivable"
## [28] "Changes in inventories and acquisitions less disposals of valuables"
## [29] "Collective consumption expenditure"
## [30] "Compensation of employees"
## [31] "Compensation of employees, payable"
## [32] "Construction, Compensation of employees"
## [33] "Construction, Employers' social contributions"
## [34] "Construction, Value added, gross"
## [35] "Construction, Wages and salaries"
## [36] "Consumption of fixed capital"
## [37] "Current taxes on income, wealth, etc., payable"
## [38] "Current taxes on income, wealth, etc., receivable"
## [39] "Employers' actual social contributions, receivable"
## [40] "Employers' social contributions"
## [41] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels "
## [42] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [43] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)"
## [44] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [45] "Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [46] "Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education "
## [47] "Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [48] "Information and communication, wages and salaries"
## [49] "Interest, payable"
## [50] "Interest, receivable"
## [51] "Intermediate consumption"
## [52] "ISCED11 Less than primary, primary and lower secondary education (levels 0-2)"
## [53] "ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Females"
## [54] "ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Males"
## [55] "ISCED11 Tertiary education (levels 5-8)"
## [56] "ISCED11 Tertiary education (levels 5-8), Females"
## [57] "ISCED11 Tertiary education (levels 5-8), Males"
## [58] "ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [59] "ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Females"
## [60] "ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Males"
## [61] "Labor cost for LCI (compensation of employees plus taxes minus subsidies)"
## [62] "Labor cost other than wages and salaries"
## [63] "Labour cost for LCI"
## [64] "Loans"
## [65] "Market output, output for own final use and payments for non-market output"
## [66] "Net lending (+) /net borrowing (-)"
## [67] "Net social contributions, receivable"
## [68] "Other capital transfers and investment grants, receivable"
## [69] "Other current taxes, receivable"
## [70] "Other current transfers, payable"
## [71] "Other current transfers, receivable"
## [72] "Other property income, receivable"
## [73] "Other subsidies on production, payable"
## [74] "Other taxes on production, receivable"
## [75] "Output"
## [76] "Professional, scientific and technical activities; administrative and support service activities, Compensation of employees"
## [77] "Professional, scientific and technical activities; administrative and support service activities, Employers' social contributions"
## [78] "Professional, scientific and technical activities; administrative and support service activities, Value added, gross"
## [79] "Professional, scientific and technical activities; administrative and support service activities, Wages and salaries"
## [80] "Property income, payable"
## [81] "Property income, receivable"
## [82] "Public administration, defence, education, human health and social work activities, Compensation of employees"
## [83] "Public administration, defence, education, human health and social work activities, Employers' social contributions"
## [84] "Public administration, defence, education, human health and social work activities, Value added, gross"
## [85] "Public administration, defence, education, human health and social work activities, Wages and salaries"
## [86] "Real estate activities, Compensation of employees"
## [87] "Savings, gross"
## [88] "Social benefits other than social transfers in kind and social transfers in kind ? purchased market production, payable"
## [89] "Social benefits other than social transfers in kind, payable"
## [90] "Social transfers in kind ? purchased market production, payable"
## [91] "Subsidies on products, payable"
## [92] "Subsidies, payable"
## [93] "Taxes on income, receivable"
## [94] "Taxes on production and imports, receivable"
## [95] "Taxes on products, receivable"
## [96] "Total general government expenditure"
## [97] "Total general government revenue"
## [98] "Unemployment , Females, From 15-64 years, 48 months or over"
## [99] "Unemployment , Females, From 15-64 years, From 1 to 2 months"
## [100] "Unemployment , Females, From 15-64 years, From 12 to 17 months"
## [101] "Unemployment , Females, From 15-64 years, From 18 to 23 months"
## [102] "Unemployment , Females, From 15-64 years, From 24 to 47 months"
## [103] "Unemployment , Females, From 15-64 years, From 3 to 5 months"
## [104] "Unemployment , Females, From 15-64 years, From 6 to 11 months"
## [105] "Unemployment , Females, From 15-64 years, Less than 1 month"
## [106] "Unemployment , Females, From 15-64 years, Total"
## [107] "Unemployment , Males, From 15-64 years"
## [108] "Unemployment , Males, From 15-64 years, 48 months or over"
## [109] "Unemployment , Males, From 15-64 years, from 1 to 2 months"
## [110] "Unemployment , Males, From 15-64 years, from 12 to 17 months"
## [111] "Unemployment , Males, From 15-64 years, from 18 to 23 months"
## [112] "Unemployment , Males, From 15-64 years, from 24 to 47 months"
## [113] "Unemployment , Males, From 15-64 years, from 3 to 5 months"
## [114] "Unemployment , Males, From 15-64 years, from 6 to 11 months"
## [115] "Unemployment , Males, From 15-64 years, Less than 1 month"
## [116] "Unemployment , Total, From 15-64 years, 48 months or over"
## [117] "Unemployment , Total, From 15-64 years, From 1 to 2 months"
## [118] "Unemployment , Total, From 15-64 years, From 12 to 17 months"
## [119] "Unemployment , Total, From 15-64 years, From 18 to 23 months"
## [120] "Unemployment , Total, From 15-64 years, From 24 to 47 months"
## [121] "Unemployment , Total, From 15-64 years, From 3 to 5 months"
## [122] "Unemployment , Total, From 15-64 years, From 6 to 11 months"
## [123] "Unemployment , Total, From 15-64 years, Less than 1 month"
## [124] "Unemployment by sex, age, duration. DurationNA not started"
## [125] "Value added, gross"
## [126] "VAT, receivable"
## [127] "Wages and salaries"
## [128] "Wholesale and retail trade, transport, accomodation and food service activities"
## [129] "Wholesale and retail trade, transport, accomodation and food service activities, Compensation of employees"
## [130] "Wholesale and retail trade, transport, accomodation and food service activities, Employers' social contributions"
## [131] "Wholesale and retail trade, transport, accomodation and food service activities, Wages and salaries"
## [132] "Y_GDP_Belgium"## Acquisitions less disposals of non-financial non-produced assets
## [355,] 104.63563
## [356,] 183.81516
## [357,] 27.95037
## [358,] 92.94846
## [359,] 43.90347
## [360,] 91.62674
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels
## [355,] 2194.778
## [356,] 1933.660
## [357,] 1971.632
## [358,] 2048.125
## [359,] 1929.089
## [360,] 1921.039
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [355,] 433.7417
## [356,] 305.7708
## [357,] 364.9509
## [358,] 401.6387
## [359,] 409.4068
## [360,] 392.7356
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)
## [355,] 1190.2872
## [356,] 1055.6932
## [357,] 1360.9037
## [358,] 1017.6076
## [359,] 863.2408
## [360,] 1071.4141
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] 779.5281
## [356,] 712.8801
## [357,] 852.5980
## [358,] 970.6792
## [359,] 780.8931
## [360,] 938.1565
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels
## [355,] 2742.813
## [356,] 2610.585
## [357,] 2809.321
## [358,] 2615.956
## [359,] 2693.697
## [360,] 2578.391
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [355,] 896.2236
## [356,] 866.4162
## [357,] 837.1428
## [358,] 810.1278
## [359,] 977.2650
## [360,] 702.6848
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8)
## [355,] 954.8499
## [356,] 1203.0639
## [357,] 1030.8765
## [358,] 1016.5546
## [359,] 1026.0785
## [360,] 1128.2338
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] 1126.3612
## [356,] 1054.6281
## [357,] 996.7854
## [358,] 1202.7936
## [359,] 1130.9409
## [360,] 1015.1722
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels
## [355,] 4847.666
## [356,] 4510.324
## [357,] 4640.071
## [358,] 4318.248
## [359,] 4298.936
## [360,] 4919.260
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [355,] 890.304
## [356,] 1258.879
## [357,] 1264.069
## [358,] 1245.880
## [359,] 1584.599
## [360,] 945.212
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8)
## [355,] 1671.482
## [356,] 2219.583
## [357,] 1998.156
## [358,] 1734.154
## [359,] 2087.160
## [360,] 1826.938
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] 2207.961
## [356,] 2229.160
## [357,] 1801.625
## [358,] 2044.524
## [359,] 1885.936
## [360,] 2031.547
## Agriculture, forestry and fishing
## [355,] 782.7298
## [356,] 785.9064
## [357,] 673.2951
## [358,] 774.9505
## [359,] 775.1704
## [360,] 700.4366
## Agriculture, forestry and fishing - Compensation of employees
## [355,] 149.6081
## [356,] 117.1734
## [357,] 169.9644
## [358,] 173.4791
## [359,] 142.5331
## [360,] 179.4616
## Agriculture, forestry and fishing - Employers' social contributions
## [355,] 0.3084501
## [356,] 8.5407729
## [357,] 14.8068099
## [358,] 13.9214203
## [359,] 3.2392421
## [360,] 0.8868538
## Agriculture, forestry and fishing, Wages and salaries
## [355,] 54.71539
## [356,] 23.33089
## [357,] 24.89676
## [358,] 80.29041
## [359,] 45.86220
## [360,] 89.01842
## All ISCED 2011 levels All ISCED 2011 levels, Females
## [355,] 7007.875 3607.903
## [356,] 6753.267 3650.055
## [357,] 7037.011 3532.239
## [358,] 6887.593 3809.413
## [359,] 6686.399 3627.667
## [360,] 6506.903 3544.054
## All ISCED 2011 levels, Males
## [355,] 3502.428
## [356,] 3606.158
## [357,] 3393.493
## [358,] 3458.854
## [359,] 3613.196
## [360,] 3479.315
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Compensation of employees
## [355,] 1176.022
## [356,] 1327.854
## [357,] 1180.254
## [358,] 1457.882
## [359,] 1307.593
## [360,] 1551.929
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Employers' social contributions
## [355,] 278.6323
## [356,] 478.7152
## [357,] 406.7277
## [358,] 278.6644
## [359,] 235.8254
## [360,] 358.2302
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Value added, gross
## [355,] 1143.8341
## [356,] 1811.7256
## [357,] 1076.3077
## [358,] 905.3798
## [359,] 1191.8808
## [360,] 808.7228
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Wages and salaries
## [355,] 929.8474
## [356,] 1206.9265
## [357,] 1005.0076
## [358,] 884.9588
## [359,] 944.7240
## [360,] 944.7460
## Capital taxes, receivable Capital transfers, payable
## [355,] 1013.6899 251.4963
## [356,] 396.2526 -785.3441
## [357,] 955.5030 451.7131
## [358,] 819.6556 2849.5112
## [359,] 950.9493 451.6687
## [360,] 1098.0629 1147.2541
## Capital transfers, receivable
## [355,] 832.6910
## [356,] 1219.4876
## [357,] 484.5599
## [358,] 678.8253
## [359,] 915.1145
## [360,] 854.8382
## Changes in inventories and acquisitions less disposals of valuables
## [355,] -18.06332
## [356,] 200.29511
## [357,] 253.37639
## [358,] 81.50803
## [359,] 43.89463
## [360,] 185.91548
## Collective consumption expenditure Compensation of employees
## [355,] 7435.184 44629.22
## [356,] 8703.161 44432.19
## [357,] 8723.072 48960.64
## [358,] 6828.940 37544.39
## [359,] 8263.601 36808.09
## [360,] 8998.159 40677.06
## Compensation of employees, payable
## [355,] 16756.970
## [356,] 13040.171
## [357,] 11034.951
## [358,] 13815.216
## [359,] 8126.489
## [360,] 13681.827
## Construction, Compensation of employees
## [355,] 2054.967
## [356,] 1871.427
## [357,] 2571.384
## [358,] 2672.280
## [359,] 2948.169
## [360,] 1946.492
## Construction, Employers' social contributions
## [355,] 612.6918
## [356,] 684.6918
## [357,] 840.9193
## [358,] 472.9918
## [359,] 589.9261
## [360,] 662.1801
## Construction, Value added, gross Construction, Wages and salaries
## [355,] 6358.000 1440.340
## [356,] 5341.678 1639.081
## [357,] 5049.728 1506.437
## [358,] 4768.045 1791.654
## [359,] 5610.758 1779.751
## [360,] 5955.052 1339.194
## Consumption of fixed capital
## [355,] 2589.705
## [356,] 2193.375
## [357,] 2563.840
## [358,] 2158.881
## [359,] 3075.499
## [360,] 2064.712
## Current taxes on income, wealth, etc., payable
## [355,] 46.3273109
## [356,] 108.4788848
## [357,] -0.1593484
## [358,] 16.3593394
## [359,] 16.5697711
## [360,] 35.8127292
## Current taxes on income, wealth, etc., receivable
## [355,] 23016.61
## [356,] 23728.14
## [357,] 17425.91
## [358,] 20298.50
## [359,] 16579.29
## [360,] 5211.15
## Employers' actual social contributions, receivable
## [355,] 7995.624
## [356,] 13095.651
## [357,] 7081.249
## [358,] 10290.963
## [359,] 8360.841
## [360,] 9491.557
## Employers' social contributions
## [355,] 17062.178
## [356,] 12421.977
## [357,] 11646.130
## [358,] 9594.248
## [359,] 11964.006
## [360,] 8241.052
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels
## [355,] 1731.694
## [356,] 1874.064
## [357,] 1681.828
## [358,] 1862.874
## [359,] 2263.992
## [360,] 2089.938
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [355,] 366.6878
## [356,] 464.1904
## [357,] 447.2827
## [358,] 489.3612
## [359,] 297.1273
## [360,] 461.1624
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)
## [355,] 975.9180
## [356,] 1238.2761
## [357,] 833.4466
## [358,] 913.9835
## [359,] 935.4075
## [360,] 1166.7251
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] 766.5496
## [356,] 741.1127
## [357,] 713.7667
## [358,] 722.7803
## [359,] 724.9593
## [360,] 696.7861
## Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [355,] 820.8808
## [356,] 715.4881
## [357,] 762.4165
## [358,] 747.6790
## [359,] 748.6201
## [360,] 544.8940
## Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education
## [355,] 995.2617
## [356,] 765.9782
## [357,] 909.4013
## [358,] 876.2673
## [359,] 972.5208
## [360,] 832.9789
## Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] 1002.1936
## [356,] 959.6324
## [357,] 1037.6228
## [358,] 1098.1296
## [359,] 1009.3724
## [360,] 972.9343
## Information and communication, wages and salaries Interest, payable
## [355,] 1717.111 3639.699
## [356,] 1071.523 3459.975
## [357,] 1367.105 3007.268
## [358,] 2047.543 2815.703
## [359,] 1604.612 3057.124
## [360,] 1486.829 3032.271
## Interest, receivable Intermediate consumption
## [355,] 241.5039 3763.360
## [356,] 204.9829 4338.950
## [357,] 247.2259 4271.244
## [358,] 279.7075 3679.953
## [359,] 338.3630 4317.026
## [360,] 263.0739 4536.847
## ISCED11 Less than primary, primary and lower secondary education (levels 0-2)
## [355,] 2283.842
## [356,] 1675.132
## [357,] 2234.585
## [358,] 2371.196
## [359,] 2133.840
## [360,] 1957.799
## ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Females
## [355,] 1216.346
## [356,] 1486.724
## [357,] 1332.125
## [358,] 1255.105
## [359,] 1248.817
## [360,] 1486.126
## ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Males
## [355,] 1505.605
## [356,] 1652.783
## [357,] 1305.766
## [358,] 1402.791
## [359,] 1582.153
## [360,] 1522.094
## ISCED11 Tertiary education (levels 5-8)
## [355,] 2135.684
## [356,] 1663.803
## [357,] 1523.697
## [358,] 1989.271
## [359,] 1476.900
## [360,] 2025.199
## ISCED11 Tertiary education (levels 5-8), Females
## [355,] 1318.867
## [356,] 1213.226
## [357,] 1229.115
## [358,] 1055.420
## [359,] 1054.107
## [360,] 1347.713
## ISCED11 Tertiary education (levels 5-8), Males
## [355,] 946.4616
## [356,] 1198.8561
## [357,] 1015.7798
## [358,] 1347.9387
## [359,] 1098.6277
## [360,] 1055.7041
## ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] 2874.305
## [356,] 2968.271
## [357,] 2820.423
## [358,] 2391.948
## [359,] 2852.964
## [360,] 2861.171
## ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Females
## [355,] 1340.962
## [356,] 1229.068
## [357,] 1289.943
## [358,] 1264.055
## [359,] 1440.854
## [360,] 1296.214
## ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Males
## [355,] 1580.525
## [356,] 1687.188
## [357,] 1428.573
## [358,] 1452.628
## [359,] 1597.876
## [360,] 1626.538
## Labor cost for LCI (compensation of employees plus taxes minus subsidies)
## [355,] 4.100944
## [356,] 2.697947
## [357,] 3.259655
## [358,] 2.951481
## [359,] 4.199684
## [360,] 2.336586
## Labor cost other than wages and salaries Labour cost for LCI Loans
## [355,] 3.0536942 1.2316684 94043.56
## [356,] 4.4391107 4.9094022 38340.23
## [357,] 0.9370984 0.9009772 86263.92
## [358,] 6.1824426 2.3577701 84491.17
## [359,] 2.2521098 1.3605964 111989.88
## [360,] 4.9208716 2.7734636 84369.96
## Market output, output for own final use and payments for non-market output
## [355,] -3615.191
## [356,] -2614.191
## [357,] -2181.353
## [358,] -2011.831
## [359,] -2973.185
## [360,] -1191.255
## Net lending (+) /net borrowing (-) Net social contributions, receivable
## [355,] 7869.205 13435.004
## [356,] 7618.584 8303.481
## [357,] 7731.101 10709.649
## [358,] 4272.050 9705.612
## [359,] 5619.858 9998.470
## [360,] 9054.337 17231.004
## Other capital transfers and investment grants, receivable
## [355,] 228.3325
## [356,] 148.8507
## [357,] 123.4851
## [358,] 249.2275
## [359,] 157.4368
## [360,] 221.6650
## Other current taxes, receivable Other current transfers, payable
## [355,] 434.5841 1405.282
## [356,] 606.8809 1737.630
## [357,] 450.0404 1639.135
## [358,] 385.8540 1015.107
## [359,] 507.3800 2127.101
## [360,] 461.0157 1607.341
## Other current transfers, receivable Other property income, receivable
## [355,] 386.6676 1326.4940
## [356,] 505.6395 1240.7438
## [357,] 331.8996 1646.1998
## [358,] 643.6520 287.5881
## [359,] 634.8581 1227.4108
## [360,] 405.9057 1920.8074
## Other subsidies on production, payable
## [355,] 945.7964
## [356,] 1235.4405
## [357,] 122.8925
## [358,] 1532.4591
## [359,] 1719.4631
## [360,] 2865.6740
## Other taxes on production, receivable Output
## [355,] 2463.085 9188.466
## [356,] 2873.573 11119.534
## [357,] 2449.316 12794.800
## [358,] 2939.850 12420.392
## [359,] 2267.123 14049.651
## [360,] 2516.112 14020.876
## Professional, scientific and technical activities; administrative and support service activities, Compensation of employees
## [355,] 5824.425
## [356,] 5829.445
## [357,] 5636.536
## [358,] 6618.613
## [359,] 8699.425
## [360,] 7098.227
## Professional, scientific and technical activities; administrative and support service activities, Employers' social contributions
## [355,] 1058.88309
## [356,] 391.20336
## [357,] 70.57811
## [358,] 744.51473
## [359,] 1342.10756
## [360,] 966.96726
## Professional, scientific and technical activities; administrative and support service activities, Value added, gross
## [355,] 14784.697
## [356,] 12144.026
## [357,] 9234.442
## [358,] 6438.187
## [359,] 9926.325
## [360,] 14339.602
## Professional, scientific and technical activities; administrative and support service activities, Wages and salaries
## [355,] 3958.230
## [356,] 5197.458
## [357,] 4294.481
## [358,] 4845.263
## [359,] 4641.704
## [360,] 3214.755
## Property income, payable Property income, receivable
## [355,] 4138.231 1406.0063
## [356,] 4358.463 1035.6502
## [357,] 4503.779 470.7505
## [358,] 4724.687 602.8572
## [359,] 4502.170 -1159.1704
## [360,] 4329.899 1403.7095
## Public administration, defence, education, human health and social work activities, Compensation of employees
## [355,] 9688.829
## [356,] 8980.594
## [357,] 11092.201
## [358,] 11489.448
## [359,] 9249.749
## [360,] 10652.826
## Public administration, defence, education, human health and social work activities, Employers' social contributions
## [355,] 3413.35251
## [356,] 4624.04481
## [357,] 4405.30878
## [358,] 3808.99000
## [359,] 4350.06195
## [360,] 88.24172
## Public administration, defence, education, human health and social work activities, Value added, gross
## [355,] 7028.706
## [356,] 14985.586
## [357,] 10220.290
## [358,] 12514.598
## [359,] 9965.288
## [360,] 12549.647
## Public administration, defence, education, human health and social work activities, Wages and salaries
## [355,] 11067.798
## [356,] 7590.724
## [357,] 10706.438
## [358,] 7654.645
## [359,] 7225.002
## [360,] 3466.250
## Real estate activities, Compensation of employees Savings, gross
## [355,] 78.66129 4357.708
## [356,] 135.31042 -2939.697
## [357,] 150.70146 -7411.369
## [358,] 126.80244 10182.972
## [359,] 14.27615 1283.296
## [360,] 91.60213 -2443.984
## Social benefits other than social transfers in kind and social transfers in kind ? purchased market production, payable
## [355,] 23574.53
## [356,] 26819.17
## [357,] 24593.24
## [358,] 28987.13
## [359,] 31877.07
## [360,] 25471.44
## Social benefits other than social transfers in kind, payable
## [355,] 13398.52
## [356,] 24021.09
## [357,] 18913.50
## [358,] 13918.16
## [359,] 17629.21
## [360,] 10263.84
## Social transfers in kind ? purchased market production, payable
## [355,] 7083.811
## [356,] 7575.056
## [357,] 8927.444
## [358,] 8743.134
## [359,] 6873.698
## [360,] 7701.483
## Subsidies on products, payable Subsidies, payable
## [355,] 505.0883 3482.919
## [356,] 400.0638 3548.122
## [357,] 418.5531 3039.477
## [358,] 338.1182 2730.229
## [359,] 547.2911 3306.274
## [360,] 641.5495 3719.799
## Taxes on income, receivable Taxes on production and imports, receivable
## [355,] 14914.29 9675.286
## [356,] 14124.98 15085.206
## [357,] 16716.16 10592.975
## [358,] 16415.46 14602.852
## [359,] 16114.09 8886.485
## [360,] 18809.88 8922.389
## Taxes on products, receivable Total general government expenditure
## [355,] 12365.432 70950.61
## [356,] 9976.599 64738.54
## [357,] 9402.528 54938.96
## [358,] 10829.371 61689.21
## [359,] 14704.786 44410.22
## [360,] 9287.185 52524.84
## Total general government revenue
## [355,] 39885.21
## [356,] 40927.20
## [357,] 25250.42
## [358,] 32992.35
## [359,] 43759.94
## [360,] 32614.78
## Unemployment , Females, From 15-64 years, 48 months or over
## [355,] 44.26375
## [356,] 43.63805
## [357,] 48.32079
## [358,] 46.29620
## [359,] 32.90277
## [360,] 30.73358
## Unemployment , Females, From 15-64 years, From 1 to 2 months
## [355,] 36.67683
## [356,] 39.94502
## [357,] 26.68424
## [358,] 28.72098
## [359,] 37.54207
## [360,] 32.45252
## Unemployment , Females, From 15-64 years, From 12 to 17 months
## [355,] 31.93704
## [356,] 26.85531
## [357,] 24.62529
## [358,] 24.38904
## [359,] 30.16427
## [360,] 21.37241
## Unemployment , Females, From 15-64 years, From 18 to 23 months
## [355,] 8.703274
## [356,] 10.160750
## [357,] 6.615979
## [358,] 3.753422
## [359,] 3.159336
## [360,] 8.131389
## Unemployment , Females, From 15-64 years, From 24 to 47 months
## [355,] 21.96971
## [356,] 29.90840
## [357,] 25.77686
## [358,] 24.53411
## [359,] 24.63642
## [360,] 16.20708
## Unemployment , Females, From 15-64 years, From 3 to 5 months
## [355,] 36.92633
## [356,] 24.62803
## [357,] 22.56067
## [358,] 23.37859
## [359,] 25.36642
## [360,] 30.36864
## Unemployment , Females, From 15-64 years, From 6 to 11 months
## [355,] 30.42053
## [356,] 27.20560
## [357,] 40.00681
## [358,] 27.68944
## [359,] 29.44199
## [360,] 35.78270
## Unemployment , Females, From 15-64 years, Less than 1 month
## [355,] 5.474987
## [356,] 13.847777
## [357,] 12.744780
## [358,] 13.946483
## [359,] 14.203907
## [360,] 16.801517
## Unemployment , Females, From 15-64 years, Total
## [355,] 161.1807
## [356,] 174.2341
## [357,] 202.0092
## [358,] 202.4076
## [359,] 172.6432
## [360,] 182.4742
## Unemployment , Males, From 15-64 years
## [355,] 199.4332
## [356,] 227.3327
## [357,] 209.3474
## [358,] 236.2509
## [359,] 209.6095
## [360,] 251.1366
## Unemployment , Males, From 15-64 years, 48 months or over
## [355,] 36.46994
## [356,] 33.06031
## [357,] 32.50719
## [358,] 25.45359
## [359,] 25.80790
## [360,] 30.09071
## Unemployment , Males, From 15-64 years, from 1 to 2 months
## [355,] 15.10009
## [356,] 22.50175
## [357,] 23.36179
## [358,] 21.44758
## [359,] 23.88397
## [360,] 21.30161
## Unemployment , Males, From 15-64 years, from 12 to 17 months
## [355,] 27.69017
## [356,] 30.71917
## [357,] 29.38429
## [358,] 37.90141
## [359,] 34.12842
## [360,] 30.89969
## Unemployment , Males, From 15-64 years, from 18 to 23 months
## [355,] 14.78610
## [356,] 17.49554
## [357,] 15.18436
## [358,] 13.48900
## [359,] 17.14973
## [360,] 15.61917
## Unemployment , Males, From 15-64 years, from 24 to 47 months
## [355,] 42.95997
## [356,] 55.40204
## [357,] 34.66920
## [358,] 36.50860
## [359,] 38.70316
## [360,] 49.73956
## Unemployment , Males, From 15-64 years, from 3 to 5 months
## [355,] 19.58920
## [356,] 19.27021
## [357,] 17.30009
## [358,] 21.52176
## [359,] 12.84473
## [360,] 11.30360
## Unemployment , Males, From 15-64 years, from 6 to 11 months
## [355,] 52.75818
## [356,] 39.10642
## [357,] 28.55584
## [358,] 35.44829
## [359,] 31.10992
## [360,] 28.78692
## Unemployment , Males, From 15-64 years, Less than 1 month
## [355,] 6.677551
## [356,] 13.587248
## [357,] 7.712757
## [358,] 11.500499
## [359,] 11.549871
## [360,] 7.830746
## Unemployment , Total, From 15-64 years, 48 months or over
## [355,] 71.85829
## [356,] 86.41705
## [357,] 72.81407
## [358,] 80.30035
## [359,] 83.80889
## [360,] 76.32618
## Unemployment , Total, From 15-64 years, From 1 to 2 months
## [355,] 55.00289
## [356,] 31.50567
## [357,] 35.47807
## [358,] 45.07450
## [359,] 71.70238
## [360,] 54.09086
## Unemployment , Total, From 15-64 years, From 12 to 17 months
## [355,] 46.95782
## [356,] 60.28374
## [357,] 54.57043
## [358,] 49.55663
## [359,] 33.95283
## [360,] 59.37699
## Unemployment , Total, From 15-64 years, From 18 to 23 months
## [355,] 25.44098
## [356,] 24.12769
## [357,] 24.31500
## [358,] 24.57162
## [359,] 22.85267
## [360,] 24.51571
## Unemployment , Total, From 15-64 years, From 24 to 47 months
## [355,] 61.49467
## [356,] 80.90714
## [357,] 75.10455
## [358,] 54.19599
## [359,] 88.27254
## [360,] 58.83252
## Unemployment , Total, From 15-64 years, From 3 to 5 months
## [355,] 77.06623
## [356,] 63.75588
## [357,] 74.94449
## [358,] 45.21632
## [359,] 58.90753
## [360,] 76.99224
## Unemployment , Total, From 15-64 years, From 6 to 11 months
## [355,] 65.88984
## [356,] 49.19114
## [357,] 49.18112
## [358,] 70.29789
## [359,] 68.90420
## [360,] 37.99438
## Unemployment , Total, From 15-64 years, Less than 1 month
## [355,] 24.60425
## [356,] 22.06589
## [357,] 20.46074
## [358,] 16.52468
## [359,] 20.71006
## [360,] 24.87523
## Unemployment by sex, age, duration. DurationNA not started
## [355,] 414.6124
## [356,] 376.9445
## [357,] 452.8626
## [358,] 337.7454
## [359,] 405.4227
## [360,] 407.2898
## Value added, gross VAT, receivable Wages and salaries
## [355,] 18938.37 5606.329 28451.42
## [356,] 19835.36 2421.998 37158.25
## [357,] 12600.80 4536.200 42898.30
## [358,] 12765.37 5614.248 37708.57
## [359,] 17100.78 4407.670 34371.07
## [360,] 15326.05 4300.637 30947.81
## Wholesale and retail trade, transport, accomodation and food service activities
## [355,] 18229.18
## [356,] 18094.47
## [357,] 19815.93
## [358,] 16556.79
## [359,] 20544.17
## [360,] 15638.81
## Wholesale and retail trade, transport, accomodation and food service activities, Compensation of employees
## [355,] 12336.901
## [356,] 10327.743
## [357,] 11901.645
## [358,] 8597.092
## [359,] 14859.473
## [360,] 12234.763
## Wholesale and retail trade, transport, accomodation and food service activities, Employers' social contributions
## [355,] 3292.212
## [356,] 2812.340
## [357,] 2139.540
## [358,] 3253.369
## [359,] 2302.971
## [360,] 2570.855
## Wholesale and retail trade, transport, accomodation and food service activities, Wages and salaries
## [355,] 4530.776
## [356,] 6862.214
## [357,] 4954.798
## [358,] 5936.021
## [359,] 5414.663
## [360,] 6905.742
## Y_GDP_Belgium
## [355,] 104.2869
## [356,] 113.5526
## [357,] 103.4512
## [358,] 110.4953
## [359,] 116.6313
## [360,] 109.8735# 2. Perform ARIMAX modeling on IFT_SwappedPhase_FT_Belgium; report (p,d,q) params and quality metrics AIC/BIC
# library(forecast)
IFT_SwappedPhase_FT_Belgium_Y_train <- IFT_SwappedPhase_FT_Belgium[1:300, 132]; length(IFT_SwappedPhase_FT_Belgium_Y_train)## [1] 300IFT_SwappedPhase_FT_Belgium_Y_test <- IFT_SwappedPhase_FT_Belgium[301:360]; length(IFT_SwappedPhase_FT_Belgium_Y_test)## [1] 60# Training and Testing Data Covariates explaining the longitudinal outcome (Y)
IFT_SwappedPhase_FT_Belgium_X_train <- as.data.frame(IFT_SwappedPhase_FT_Belgium)[1:300, 1:131]
dim(IFT_SwappedPhase_FT_Belgium_X_train)## [1] 300 131IFT_SwappedPhase_FT_Belgium_X_test <- as.data.frame(IFT_SwappedPhase_FT_Belgium)[301:360, 1:131]
dim(IFT_SwappedPhase_FT_Belgium_X_test)## [1] 60 131# Outcome Variable to be ARIMAX-modeled, as a timeseries
ts_IFT_SwappedPhase_FT_Belgium_Y_train <-
ts(IFT_SwappedPhase_FT_Belgium_Y_train, start=c(2000,1), end=c(2014, 20), frequency = 20)
# Find ARIMAX model: 1 0 2 0 20 0 0
set.seed(1234)
modArima_IFT_SwappedPhase_FT_Belgium_Y_train <-
auto.arima(ts_IFT_SwappedPhase_FT_Belgium_Y_train, xreg=as.matrix(IFT_SwappedPhase_FT_Belgium_X_train))
modArima_IFT_SwappedPhase_FT_Belgium_Y_train$arma## [1] 0 0 2 0 20 0 0# Regression with ARIMA(1,0,0)(2,0,0)[20] errors
# Coefficients:
# ar1 sar1 sar2 intercept Acquisitions less disposals of non-financial non-produced assets
# -0.3837 -0.2196 0.2827 46.1704 0.0063
#s.e. 0.1113 0.0903 0.0779 36.8492 0.0080
# sigma^2 estimated as 70: log likelihood=-976.01 AIC=2224.02 AICc=2452.63 BIC=2727.73
pred_arimax_1_0_0_Swapped <- forecast(modArima_IFT_SwappedPhase_FT_Belgium_Y_train, xreg = as.matrix(IFT_SwappedPhase_FT_Belgium_X_test))
pred_arimax_1_0_0_Swapped_2015_2017 <-
ts(pred_arimax_1_0_0_Swapped$mean, frequency=20, start=c(2015,1), end=c(2017,20))
pred_arimax_1_0_0_Swapped_2015_2017## Time Series:
## Start = c(2015, 1)
## End = c(2017, 20)
## Frequency = 20
## 301 302 303 304 305 306 307 308
## 109.34633 114.03305 96.21596 99.74230 118.35445 109.23083 102.71060 111.21992
## 309 310 311 312 313 314 315 316
## 115.15334 107.89386 103.71657 95.58576 102.44744 115.95669 112.84955 123.83254
## 317 318 319 320 321 322 323 324
## 108.20634 98.12844 113.13732 109.60619 119.80132 93.95825 111.33861 102.72526
## 325 326 327 328 329 330 331 332
## 112.89596 106.68498 108.05578 100.79787 101.59068 108.73299 103.79802 99.34906
## 333 334 335 336 337 338 339 340
## 112.85062 95.79558 102.60889 97.57914 114.94877 114.69943 102.57416 117.29406
## 341 342 343 344 345 346 347 348
## 114.72435 112.33459 105.87628 110.51348 109.50676 108.93145 105.20359 101.03515
## 349 350 351 352 353 354 355 356
## 105.85154 96.21134 102.42854 106.60770 100.82516 104.15029 103.84624 95.46414
## 357 358 359 360
## 95.08273 101.99499 100.79026 91.64176# alternatively:
# pred_arimax_1_0_0_Swapped_2015_2017 <- predict(modArima_IFT_SwappedPhase_FT_Belgium_Y_train,
# n.ahead = 3*20, newxreg = IFT_SwappedPhase_FT_Belgium_X_test)$pred
sort(modArima_IFT_SwappedPhase_FT_Belgium_Y_train$coef)[1:10]## Labor cost other than wages and salaries
## -0.31658994
## Unemployment , Females, From 15-64 years, From 18 to 23 months
## -0.31223255
## sar1
## -0.25026903
## Labor cost for LCI (compensation of employees plus taxes minus subsidies)
## -0.22914979
## Unemployment , Females, From 15-64 years, From 6 to 11 months
## -0.19488967
## Unemployment , Males, From 15-64 years, Less than 1 month
## -0.09931584
## Unemployment , Total, From 15-64 years, From 1 to 2 months
## -0.04217588
## Unemployment , Total, From 15-64 years, 48 months or over
## -0.03077726
## Unemployment , Males, From 15-64 years, from 1 to 2 months
## -0.02119638
## Interest, receivable
## -0.01779247# ar1, effect=-0.38372043
# Unemployment , Females, From 15-64 years, From 18 to 23 months, effect=-0.31137514
# Labor cost other than wages and salaries, effect=-0.31094561
# sar1, effect=-0.21964957
# Unemployment , Females, From 15-64 years, From 6 to 11 months, effect=-0.20878853
#Labor cost for LCI (compensation of employees plus taxes minus subsidies), effect=-0.12497311
# Unemployment , Males, From 15-64 years, Less than 1 month, effect=-0.10849013
# Unemployment , Total, From 15-64 years, 48 months or over, effect=-0.09066684
# Unemployment , Total, From 15-64 years, From 1 to 2 months, effect=-0.05852382
# Unemployment , Females, From 15-64 years, 48 months or over, effect=-0.05695172
cor(pred_arimax_1_0_0_Swapped$mean, ts_Y_Belgium_test) # 0.0## [1] -0.05675965mean(pred_arimax_1_0_0_Swapped_2015_2017) # [1] 105## [1] 106.141111.5 Random-Phase Synthesis and ARIMAX re-modeling
Perform Random-Phase reconstruction - IFT_RandPhase_FT_Belgium - by randomly sampling from the phase distributions for each feature and then re-fitting the ARIMAX model
# 1. Random-Phase data synthesis (reconstruction)
# temp_Data <- cbind(X_Belgium, Y_Belgium)
randPhase_FT_data <- array(complex(), c(dim(temp_Data)[1], dim(temp_Data)[2]))
dim(randPhase_FT_data) # ; head(randPhase_FT_data)## [1] 360 132# [1] 360 132
IFT_RandPhase_FT_Belgium <- array(complex(), c(dim(temp_Data)[1], dim(temp_Data)[2]))
randPhase_FT_data <- FT_Belgium$phases
for (i in 1:(dim(randPhase_FT_data)[2] -1)) {
if (i < dim(randPhase_FT_data)[2]) {
set.seed(12345) # sample randomly Phases for each of the 131 predictors covariates (X)
randPhase_FT_data[ , i] <- FT_Belgium$phases[sample(nrow(FT_Belgium$phases)), i]
} else { } # for the Y outcome (Last Column) - do not change the phases of the Y
}
# Invert back to spacetime the FT_Belgium$magnitudes[ , i] signal with avg-phase
IFT_RandPhase_FT_Belgium <- Re(kSpaceTransform(FT_Belgium$magnitudes, TRUE, randPhase_FT_data))
colnames(IFT_RandPhase_FT_Belgium) <- c(colnames(X_Belgium), "Y_GDP_Belgium")
dim(IFT_RandPhase_FT_Belgium); dim(FT_Belgium$magnitudes)## [1] 360 132## [1] 360 132colnames(IFT_RandPhase_FT_Belgium); tail(IFT_RandPhase_FT_Belgium); # tail(temp_Data)## [1] "Acquisitions less disposals of non-financial non-produced assets"
## [2] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels"
## [3] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [4] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)"
## [5] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [6] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels"
## [7] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [8] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8)"
## [9] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [10] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels"
## [11] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [12] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8)"
## [13] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [14] "Agriculture, forestry and fishing"
## [15] "Agriculture, forestry and fishing - Compensation of employees"
## [16] "Agriculture, forestry and fishing - Employers' social contributions"
## [17] "Agriculture, forestry and fishing, Wages and salaries"
## [18] "All ISCED 2011 levels "
## [19] "All ISCED 2011 levels, Females"
## [20] "All ISCED 2011 levels, Males"
## [21] "Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Compensation of employees"
## [22] "Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Employers' social contributions"
## [23] "Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Value added, gross"
## [24] "Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Wages and salaries"
## [25] "Capital taxes, receivable"
## [26] "Capital transfers, payable"
## [27] "Capital transfers, receivable"
## [28] "Changes in inventories and acquisitions less disposals of valuables"
## [29] "Collective consumption expenditure"
## [30] "Compensation of employees"
## [31] "Compensation of employees, payable"
## [32] "Construction, Compensation of employees"
## [33] "Construction, Employers' social contributions"
## [34] "Construction, Value added, gross"
## [35] "Construction, Wages and salaries"
## [36] "Consumption of fixed capital"
## [37] "Current taxes on income, wealth, etc., payable"
## [38] "Current taxes on income, wealth, etc., receivable"
## [39] "Employers' actual social contributions, receivable"
## [40] "Employers' social contributions"
## [41] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels "
## [42] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [43] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)"
## [44] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [45] "Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
## [46] "Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education "
## [47] "Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [48] "Information and communication, wages and salaries"
## [49] "Interest, payable"
## [50] "Interest, receivable"
## [51] "Intermediate consumption"
## [52] "ISCED11 Less than primary, primary and lower secondary education (levels 0-2)"
## [53] "ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Females"
## [54] "ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Males"
## [55] "ISCED11 Tertiary education (levels 5-8)"
## [56] "ISCED11 Tertiary education (levels 5-8), Females"
## [57] "ISCED11 Tertiary education (levels 5-8), Males"
## [58] "ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
## [59] "ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Females"
## [60] "ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Males"
## [61] "Labor cost for LCI (compensation of employees plus taxes minus subsidies)"
## [62] "Labor cost other than wages and salaries"
## [63] "Labour cost for LCI"
## [64] "Loans"
## [65] "Market output, output for own final use and payments for non-market output"
## [66] "Net lending (+) /net borrowing (-)"
## [67] "Net social contributions, receivable"
## [68] "Other capital transfers and investment grants, receivable"
## [69] "Other current taxes, receivable"
## [70] "Other current transfers, payable"
## [71] "Other current transfers, receivable"
## [72] "Other property income, receivable"
## [73] "Other subsidies on production, payable"
## [74] "Other taxes on production, receivable"
## [75] "Output"
## [76] "Professional, scientific and technical activities; administrative and support service activities, Compensation of employees"
## [77] "Professional, scientific and technical activities; administrative and support service activities, Employers' social contributions"
## [78] "Professional, scientific and technical activities; administrative and support service activities, Value added, gross"
## [79] "Professional, scientific and technical activities; administrative and support service activities, Wages and salaries"
## [80] "Property income, payable"
## [81] "Property income, receivable"
## [82] "Public administration, defence, education, human health and social work activities, Compensation of employees"
## [83] "Public administration, defence, education, human health and social work activities, Employers' social contributions"
## [84] "Public administration, defence, education, human health and social work activities, Value added, gross"
## [85] "Public administration, defence, education, human health and social work activities, Wages and salaries"
## [86] "Real estate activities, Compensation of employees"
## [87] "Savings, gross"
## [88] "Social benefits other than social transfers in kind and social transfers in kind ? purchased market production, payable"
## [89] "Social benefits other than social transfers in kind, payable"
## [90] "Social transfers in kind ? purchased market production, payable"
## [91] "Subsidies on products, payable"
## [92] "Subsidies, payable"
## [93] "Taxes on income, receivable"
## [94] "Taxes on production and imports, receivable"
## [95] "Taxes on products, receivable"
## [96] "Total general government expenditure"
## [97] "Total general government revenue"
## [98] "Unemployment , Females, From 15-64 years, 48 months or over"
## [99] "Unemployment , Females, From 15-64 years, From 1 to 2 months"
## [100] "Unemployment , Females, From 15-64 years, From 12 to 17 months"
## [101] "Unemployment , Females, From 15-64 years, From 18 to 23 months"
## [102] "Unemployment , Females, From 15-64 years, From 24 to 47 months"
## [103] "Unemployment , Females, From 15-64 years, From 3 to 5 months"
## [104] "Unemployment , Females, From 15-64 years, From 6 to 11 months"
## [105] "Unemployment , Females, From 15-64 years, Less than 1 month"
## [106] "Unemployment , Females, From 15-64 years, Total"
## [107] "Unemployment , Males, From 15-64 years"
## [108] "Unemployment , Males, From 15-64 years, 48 months or over"
## [109] "Unemployment , Males, From 15-64 years, from 1 to 2 months"
## [110] "Unemployment , Males, From 15-64 years, from 12 to 17 months"
## [111] "Unemployment , Males, From 15-64 years, from 18 to 23 months"
## [112] "Unemployment , Males, From 15-64 years, from 24 to 47 months"
## [113] "Unemployment , Males, From 15-64 years, from 3 to 5 months"
## [114] "Unemployment , Males, From 15-64 years, from 6 to 11 months"
## [115] "Unemployment , Males, From 15-64 years, Less than 1 month"
## [116] "Unemployment , Total, From 15-64 years, 48 months or over"
## [117] "Unemployment , Total, From 15-64 years, From 1 to 2 months"
## [118] "Unemployment , Total, From 15-64 years, From 12 to 17 months"
## [119] "Unemployment , Total, From 15-64 years, From 18 to 23 months"
## [120] "Unemployment , Total, From 15-64 years, From 24 to 47 months"
## [121] "Unemployment , Total, From 15-64 years, From 3 to 5 months"
## [122] "Unemployment , Total, From 15-64 years, From 6 to 11 months"
## [123] "Unemployment , Total, From 15-64 years, Less than 1 month"
## [124] "Unemployment by sex, age, duration. DurationNA not started"
## [125] "Value added, gross"
## [126] "VAT, receivable"
## [127] "Wages and salaries"
## [128] "Wholesale and retail trade, transport, accomodation and food service activities"
## [129] "Wholesale and retail trade, transport, accomodation and food service activities, Compensation of employees"
## [130] "Wholesale and retail trade, transport, accomodation and food service activities, Employers' social contributions"
## [131] "Wholesale and retail trade, transport, accomodation and food service activities, Wages and salaries"
## [132] "Y_GDP_Belgium"## Acquisitions less disposals of non-financial non-produced assets
## [355,] -11.407967
## [356,] -32.564592
## [357,] 21.444949
## [358,] -72.078483
## [359,] 7.881843
## [360,] 1.308009
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels
## [355,] -1876.607
## [356,] -1691.195
## [357,] -1787.687
## [358,] -1417.429
## [359,] -1464.609
## [360,] -1525.512
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [355,] 27.19345
## [356,] 39.18835
## [357,] 63.50065
## [358,] 18.08210
## [359,] 66.82969
## [360,] 24.42209
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)
## [355,] -1017.0543
## [356,] -958.4714
## [357,] -853.4765
## [358,] -905.4623
## [359,] -1103.3538
## [360,] -892.6141
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] -776.1546
## [356,] -887.0610
## [357,] -869.8730
## [358,] -867.5488
## [359,] -806.7218
## [360,] -836.4450
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels
## [355,] 417.7540
## [356,] 353.2607
## [357,] 321.4188
## [358,] 305.8060
## [359,] 419.3236
## [360,] 345.6235
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [355,] 622.5810
## [356,] 644.4750
## [357,] 713.6940
## [358,] 689.6499
## [359,] 688.5757
## [360,] 656.9369
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8)
## [355,] -562.3196
## [356,] -690.0676
## [357,] -612.5599
## [358,] -643.1745
## [359,] -654.9256
## [360,] -532.8569
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] -967.5576
## [356,] -1066.6309
## [357,] -1035.9485
## [358,] -1097.1691
## [359,] -1023.0768
## [360,] -1033.0121
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels
## [355,] 2243.414
## [356,] 1819.379
## [357,] 1991.700
## [358,] 1841.157
## [359,] 1719.560
## [360,] 1902.312
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [355,] -920.4673
## [356,] -815.5334
## [357,] -881.7839
## [358,] -1045.1989
## [359,] -913.3414
## [360,] -919.6714
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8)
## [355,] -1690.386
## [356,] -1809.441
## [357,] -1818.057
## [358,] -1648.665
## [359,] -1963.134
## [360,] -1613.587
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] 1334.907
## [356,] 1432.716
## [357,] 1235.563
## [358,] 1268.440
## [359,] 1388.710
## [360,] 1527.934
## Agriculture, forestry and fishing
## [355,] 565.9073
## [356,] 619.4125
## [357,] 621.5069
## [358,] 535.1259
## [359,] 563.1164
## [360,] 597.3747
## Agriculture, forestry and fishing - Compensation of employees
## [355,] 73.73733
## [356,] 98.98009
## [357,] 99.06414
## [358,] 99.43041
## [359,] 109.98934
## [360,] 93.05877
## Agriculture, forestry and fishing - Employers' social contributions
## [355,] -23.05750
## [356,] -24.65342
## [357,] -27.17187
## [358,] -24.77651
## [359,] -24.92524
## [360,] -29.66699
## Agriculture, forestry and fishing, Wages and salaries
## [355,] -66.67324
## [356,] -52.56202
## [357,] -72.07417
## [358,] -59.52216
## [359,] -45.15805
## [360,] -47.45481
## All ISCED 2011 levels All ISCED 2011 levels, Females
## [355,] 6289.060 3317.288
## [356,] 6159.593 3252.168
## [357,] 6335.007 3302.716
## [358,] 6175.513 3311.530
## [359,] 6423.565 3488.985
## [360,] 6576.852 3442.293
## All ISCED 2011 levels, Males
## [355,] -3453.820
## [356,] -3389.213
## [357,] -3437.699
## [358,] -3394.089
## [359,] -3331.647
## [360,] -3427.280
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Compensation of employees
## [355,] -1161.333
## [356,] -1498.709
## [357,] -1391.927
## [358,] -1243.267
## [359,] -1356.704
## [360,] -1121.635
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Employers' social contributions
## [355,] -134.49743
## [356,] -159.39595
## [357,] -185.66910
## [358,] -160.37069
## [359,] -98.22426
## [360,] -128.71823
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Value added, gross
## [355,] 773.2221
## [356,] 858.2712
## [357,] 799.1778
## [358,] 827.0446
## [359,] 942.3718
## [360,] 840.7767
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Wages and salaries
## [355,] -669.1910
## [356,] -662.9851
## [357,] -609.4612
## [358,] -775.4352
## [359,] -649.0695
## [360,] -446.0012
## Capital taxes, receivable Capital transfers, payable
## [355,] 381.2185 -856.19509
## [356,] 136.9044 -360.34309
## [357,] 465.3589 -1323.39079
## [358,] 407.7386 -33.09127
## [359,] 441.7819 -331.39802
## [360,] 137.3979 161.03922
## Capital transfers, receivable
## [355,] 649.3636
## [356,] 357.8514
## [357,] 346.0512
## [358,] 345.5883
## [359,] 297.9582
## [360,] 480.9614
## Changes in inventories and acquisitions less disposals of valuables
## [355,] 27.149174
## [356,] -4.630613
## [357,] 114.127874
## [358,] -35.017366
## [359,] 9.481564
## [360,] -32.265124
## Collective consumption expenditure Compensation of employees
## [355,] 7238.126 -47954.89
## [356,] 7140.035 -47254.53
## [357,] 6037.890 -51199.17
## [358,] 7692.088 -45482.58
## [359,] 6446.849 -34324.70
## [360,] 6015.950 -38245.61
## Compensation of employees, payable
## [355,] 6876.235
## [356,] 8389.647
## [357,] 9767.948
## [358,] 10430.723
## [359,] 6793.619
## [360,] 10316.283
## Construction, Compensation of employees
## [355,] -130.56279
## [356,] -683.35263
## [357,] -877.77597
## [358,] -53.05717
## [359,] -125.65051
## [360,] -208.31131
## Construction, Employers' social contributions
## [355,] 174.74875
## [356,] 244.33208
## [357,] 78.11979
## [358,] 210.01953
## [359,] 141.62772
## [360,] 111.64816
## Construction, Value added, gross Construction, Wages and salaries
## [355,] -3375.281 -611.2502
## [356,] -4197.377 -445.7706
## [357,] -3339.140 -504.3435
## [358,] -3508.715 -234.7040
## [359,] -3588.987 -341.8110
## [360,] -4170.875 -362.8273
## Consumption of fixed capital
## [355,] -1585.363
## [356,] -2182.878
## [357,] -1690.811
## [358,] -1516.929
## [359,] -1967.204
## [360,] -1934.556
## Current taxes on income, wealth, etc., payable
## [355,] 6.455748
## [356,] -12.961378
## [357,] 10.767303
## [358,] 13.039428
## [359,] -12.771502
## [360,] 14.801029
## Current taxes on income, wealth, etc., receivable
## [355,] -10262.186
## [356,] -9858.528
## [357,] -11023.399
## [358,] -8839.197
## [359,] -10325.053
## [360,] -9495.912
## Employers' actual social contributions, receivable
## [355,] 6198.882
## [356,] 6105.790
## [357,] 6289.885
## [358,] 5739.419
## [359,] 5987.175
## [360,] 6827.211
## Employers' social contributions
## [355,] 10726.63
## [356,] 13622.20
## [357,] 12509.22
## [358,] 13561.81
## [359,] 11823.04
## [360,] 11964.06
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels
## [355,] -245.44334
## [356,] -304.09250
## [357,] -285.64806
## [358,] -333.48807
## [359,] -232.88487
## [360,] -65.90955
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [355,] -43.90229
## [356,] 19.76653
## [357,] -77.79135
## [358,] -22.43823
## [359,] -88.18655
## [360,] -38.65091
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)
## [355,] 786.5564
## [356,] 640.2643
## [357,] 688.5407
## [358,] 675.1181
## [359,] 749.6349
## [360,] 781.5006
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] -44.46065
## [356,] -41.65236
## [357,] -22.87019
## [358,] -90.10079
## [359,] -43.28163
## [360,] 55.07213
## Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [355,] 280.1983
## [356,] 379.1233
## [357,] 351.9727
## [358,] 328.5446
## [359,] 294.2294
## [360,] 169.0767
## Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education
## [355,] -637.7784
## [356,] -787.9738
## [357,] -708.4048
## [358,] -664.3854
## [359,] -660.9345
## [360,] -625.8953
## Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] -710.2220
## [356,] -759.9432
## [357,] -757.0340
## [358,] -722.9969
## [359,] -712.3667
## [360,] -713.5261
## Information and communication, wages and salaries Interest, payable
## [355,] 964.1002 -3258.720
## [356,] 1176.5270 -2937.136
## [357,] 1134.6526 -3205.179
## [358,] 1320.2216 -3197.435
## [359,] 1079.3488 -3407.457
## [360,] 1124.9981 -3797.626
## Interest, receivable Intermediate consumption
## [355,] -316.7523 -399.153610
## [356,] -289.4306 303.911845
## [357,] -234.0275 234.567522
## [358,] -235.0668 -239.414339
## [359,] -239.2612 -3.076083
## [360,] -322.0127 -620.847954
## ISCED11 Less than primary, primary and lower secondary education (levels 0-2)
## [355,] -2063.334
## [356,] -1931.614
## [357,] -1909.825
## [358,] -1793.195
## [359,] -1608.362
## [360,] -1869.363
## ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Females
## [355,] -961.0794
## [356,] -927.0479
## [357,] -916.1430
## [358,] -1108.1635
## [359,] -1194.3212
## [360,] -985.0082
## ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Males
## [355,] -287.1661
## [356,] -320.1416
## [357,] -307.8221
## [358,] -258.0882
## [359,] -256.2474
## [360,] -299.8131
## ISCED11 Tertiary education (levels 5-8)
## [355,] -1477.046
## [356,] -1408.726
## [357,] -1500.342
## [358,] -1621.090
## [359,] -1989.353
## [360,] -1776.054
## ISCED11 Tertiary education (levels 5-8), Females
## [355,] -1144.9366
## [356,] -1259.0636
## [357,] -1454.6509
## [358,] -1173.1779
## [359,] -981.2342
## [360,] -1133.4022
## ISCED11 Tertiary education (levels 5-8), Males
## [355,] 810.5052
## [356,] 637.9402
## [357,] 699.1640
## [358,] 925.7338
## [359,] 708.9490
## [360,] 732.5261
## ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] 2415.219
## [356,] 2112.154
## [357,] 2233.640
## [358,] 2194.193
## [359,] 2254.809
## [360,] 2375.114
## ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Females
## [355,] -83.97216
## [356,] -101.94108
## [357,] -223.16011
## [358,] -173.98815
## [359,] -135.36718
## [360,] -183.41974
## ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Males
## [355,] 186.85050
## [356,] 246.28367
## [357,] 235.17309
## [358,] 73.40394
## [359,] 164.77332
## [360,] 193.24829
## Labor cost for LCI (compensation of employees plus taxes minus subsidies)
## [355,] 0.79743565
## [356,] 0.67207425
## [357,] -0.19423471
## [358,] 1.25881854
## [359,] 1.56955214
## [360,] 0.09790678
## Labor cost other than wages and salaries Labour cost for LCI Loans
## [355,] 3.046457 1.32004251 -19071.029
## [356,] 3.517158 0.09669155 -12460.178
## [357,] 3.024217 2.16108162 -14757.814
## [358,] 1.465028 1.22413054 -6074.798
## [359,] 2.027052 2.05360442 -3444.982
## [360,] 2.418594 2.07129763 -1035.968
## Market output, output for own final use and payments for non-market output
## [355,] 610.0124
## [356,] 899.7886
## [357,] 372.7192
## [358,] 1129.3051
## [359,] 765.9877
## [360,] 741.2933
## Net lending (+) /net borrowing (-) Net social contributions, receivable
## [355,] 1991.8241 11935.61
## [356,] 4728.9449 11146.49
## [357,] 1224.2467 12369.71
## [358,] 1762.5935 11710.86
## [359,] 680.2869 10396.03
## [360,] -5256.0393 11369.16
## Other capital transfers and investment grants, receivable
## [355,] -94.117556
## [356,] -103.216274
## [357,] -19.630414
## [358,] 75.726327
## [359,] 8.239301
## [360,] 12.719737
## Other current taxes, receivable Other current transfers, payable
## [355,] -473.1101 1826.183
## [356,] -474.6189 1191.361
## [357,] -483.8321 2055.895
## [358,] -466.3753 1519.210
## [359,] -428.1188 2153.889
## [360,] -484.2364 1574.715
## Other current transfers, receivable Other property income, receivable
## [355,] 60.75034 37.97405
## [356,] 260.54017 729.87075
## [357,] 271.85911 294.08292
## [358,] 384.81068 742.06817
## [359,] 184.29575 1203.33453
## [360,] 454.65712 -130.66761
## Other subsidies on production, payable
## [355,] -3836.099
## [356,] -4088.924
## [357,] -2557.891
## [358,] -2818.852
## [359,] -3033.305
## [360,] -2675.038
## Other taxes on production, receivable Output
## [355,] -1331.1506 -9707.876
## [356,] -1693.2269 -8300.822
## [357,] -1205.6258 -8451.847
## [358,] -1289.4003 -6509.365
## [359,] -1307.2154 -7423.260
## [360,] -724.3402 -3441.472
## Professional, scientific and technical activities; administrative and support service activities, Compensation of employees
## [355,] 1652.883
## [356,] 5695.660
## [357,] 4420.052
## [358,] 4837.257
## [359,] 3544.218
## [360,] 3857.244
## Professional, scientific and technical activities; administrative and support service activities, Employers' social contributions
## [355,] -1090.5983
## [356,] -456.1848
## [357,] -1117.6581
## [358,] -1069.0547
## [359,] -1146.4636
## [360,] -1005.3246
## Professional, scientific and technical activities; administrative and support service activities, Value added, gross
## [355,] 1204.063
## [356,] 3439.703
## [357,] 1844.088
## [358,] 2620.991
## [359,] 1745.960
## [360,] 1552.539
## Professional, scientific and technical activities; administrative and support service activities, Wages and salaries
## [355,] 1728.400
## [356,] 2899.744
## [357,] 1757.248
## [358,] 1808.353
## [359,] 3431.091
## [360,] 2315.924
## Property income, payable Property income, receivable
## [355,] 3837.742 -768.8739
## [356,] 4030.135 -1058.1332
## [357,] 4381.240 -1054.1937
## [358,] 4162.533 -240.5559
## [359,] 3638.767 -1202.0839
## [360,] 3296.886 -367.2426
## Public administration, defence, education, human health and social work activities, Compensation of employees
## [355,] -5521.414
## [356,] -9304.076
## [357,] -7427.396
## [358,] -7770.354
## [359,] -6055.413
## [360,] -7389.396
## Public administration, defence, education, human health and social work activities, Employers' social contributions
## [355,] -2501.972
## [356,] -3028.041
## [357,] -2415.267
## [358,] -1628.096
## [359,] -1726.522
## [360,] -1337.923
## Public administration, defence, education, human health and social work activities, Value added, gross
## [355,] 14179.01
## [356,] 11216.19
## [357,] 10919.91
## [358,] 15349.12
## [359,] 11314.34
## [360,] 13917.41
## Public administration, defence, education, human health and social work activities, Wages and salaries
## [355,] -4665.135
## [356,] -3717.992
## [357,] -8049.380
## [358,] -3810.252
## [359,] -5547.767
## [360,] -3576.049
## Real estate activities, Compensation of employees Savings, gross
## [355,] 21.27098 -684.7238
## [356,] -57.70449 5676.1892
## [357,] -18.12837 -1994.6068
## [358,] 62.57018 -905.8016
## [359,] -35.50801 2926.0927
## [360,] -12.97126 -5508.9193
## Social benefits other than social transfers in kind and social transfers in kind ? purchased market production, payable
## [355,] -8204.530
## [356,] -10078.326
## [357,] 693.194
## [358,] -3709.006
## [359,] -3858.092
## [360,] -2416.240
## Social benefits other than social transfers in kind, payable
## [355,] -7037.936
## [356,] -11856.242
## [357,] -9106.588
## [358,] -9614.633
## [359,] -11208.993
## [360,] -4802.191
## Social transfers in kind ? purchased market production, payable
## [355,] -2241.897
## [356,] -4656.311
## [357,] -2572.327
## [358,] -2827.190
## [359,] -4162.293
## [360,] -4007.559
## Subsidies on products, payable Subsidies, payable
## [355,] 225.0605 -2427.543
## [356,] 176.1449 -1996.596
## [357,] 320.4728 -2085.269
## [358,] 282.3426 -1736.503
## [359,] 308.9653 -1468.939
## [360,] 358.0095 -1167.056
## Taxes on income, receivable Taxes on production and imports, receivable
## [355,] 4097.496 -2313.353
## [356,] 2666.806 -3714.743
## [357,] 5199.308 -6134.680
## [358,] 3481.867 -3983.448
## [359,] 4052.052 -4441.170
## [360,] 7665.827 -3593.531
## Taxes on products, receivable Total general government expenditure
## [355,] 4915.374 -31042.01
## [356,] 3487.575 -21567.11
## [357,] 3318.037 -29164.37
## [358,] 2385.357 -20476.37
## [359,] 4395.357 -26312.51
## [360,] 5764.704 -23601.60
## Total general government revenue
## [355,] -4834.945
## [356,] -11622.938
## [357,] -13996.988
## [358,] -5469.329
## [359,] -17180.372
## [360,] -19633.388
## Unemployment , Females, From 15-64 years, 48 months or over
## [355,] -6.968291
## [356,] 4.447450
## [357,] -6.435313
## [358,] -4.591887
## [359,] -9.833091
## [360,] -5.241598
## Unemployment , Females, From 15-64 years, From 1 to 2 months
## [355,] -25.45065
## [356,] -28.18603
## [357,] -28.02709
## [358,] -26.49960
## [359,] -33.50749
## [360,] -29.18083
## Unemployment , Females, From 15-64 years, From 12 to 17 months
## [355,] 10.587728
## [356,] 9.210117
## [357,] 4.939326
## [358,] 10.955458
## [359,] 9.862456
## [360,] 6.512798
## Unemployment , Females, From 15-64 years, From 18 to 23 months
## [355,] -4.318693
## [356,] -4.340725
## [357,] -2.353096
## [358,] -4.261096
## [359,] -4.453699
## [360,] -4.464338
## Unemployment , Females, From 15-64 years, From 24 to 47 months
## [355,] 25.60289
## [356,] 23.53445
## [357,] 26.52410
## [358,] 23.04883
## [359,] 27.47028
## [360,] 22.01612
## Unemployment , Females, From 15-64 years, From 3 to 5 months
## [355,] -26.02388
## [356,] -22.03556
## [357,] -19.38117
## [358,] -23.65860
## [359,] -18.81823
## [360,] -20.13506
## Unemployment , Females, From 15-64 years, From 6 to 11 months
## [355,] 16.783532
## [356,] 6.733244
## [357,] 10.257872
## [358,] 14.781820
## [359,] 10.410363
## [360,] 8.306611
## Unemployment , Females, From 15-64 years, Less than 1 month
## [355,] 13.696251
## [356,] 12.497935
## [357,] 7.366424
## [358,] 12.318927
## [359,] 10.333482
## [360,] 11.996359
## Unemployment , Females, From 15-64 years, Total
## [355,] -170.4574
## [356,] -178.3692
## [357,] -157.8424
## [358,] -161.3442
## [359,] -190.9925
## [360,] -192.6608
## Unemployment , Males, From 15-64 years
## [355,] -153.0947
## [356,] -172.4467
## [357,] -137.4147
## [358,] -160.7338
## [359,] -117.1098
## [360,] -140.8040
## Unemployment , Males, From 15-64 years, 48 months or over
## [355,] -27.04470
## [356,] -23.33945
## [357,] -31.75924
## [358,] -33.81256
## [359,] -32.67748
## [360,] -29.58414
## Unemployment , Males, From 15-64 years, from 1 to 2 months
## [355,] -14.826563
## [356,] -11.736094
## [357,] -21.387001
## [358,] -7.891433
## [359,] -16.662251
## [360,] -15.264592
## Unemployment , Males, From 15-64 years, from 12 to 17 months
## [355,] 4.631872
## [356,] -3.159601
## [357,] 1.647292
## [358,] 5.572775
## [359,] 7.431482
## [360,] 4.396807
## Unemployment , Males, From 15-64 years, from 18 to 23 months
## [355,] -11.261589
## [356,] -13.876522
## [357,] -11.232225
## [358,] -10.435292
## [359,] -10.445054
## [360,] -7.146492
## Unemployment , Males, From 15-64 years, from 24 to 47 months
## [355,] 21.60521
## [356,] 11.80627
## [357,] 19.95666
## [358,] 19.86230
## [359,] 22.38771
## [360,] 30.08010
## Unemployment , Males, From 15-64 years, from 3 to 5 months
## [355,] 27.50534
## [356,] 20.01161
## [357,] 13.72708
## [358,] 21.29292
## [359,] 27.48875
## [360,] 19.47900
## Unemployment , Males, From 15-64 years, from 6 to 11 months
## [355,] -14.28988
## [356,] -19.49968
## [357,] -21.71209
## [358,] -24.11386
## [359,] -10.76200
## [360,] -21.55460
## Unemployment , Males, From 15-64 years, Less than 1 month
## [355,] 3.633473
## [356,] 3.571436
## [357,] 5.017218
## [358,] 1.844334
## [359,] 6.597317
## [360,] 6.326664
## Unemployment , Total, From 15-64 years, 48 months or over
## [355,] -44.36393
## [356,] -25.84350
## [357,] -38.39034
## [358,] -44.38326
## [359,] -44.94593
## [360,] -23.72349
## Unemployment , Total, From 15-64 years, From 1 to 2 months
## [355,] 67.23921
## [356,] 41.61202
## [357,] 62.58921
## [358,] 48.63882
## [359,] 51.14966
## [360,] 71.90111
## Unemployment , Total, From 15-64 years, From 12 to 17 months
## [355,] 33.03147
## [356,] 33.14263
## [357,] 26.12223
## [358,] 40.53084
## [359,] 24.97231
## [360,] 32.64010
## Unemployment , Total, From 15-64 years, From 18 to 23 months
## [355,] 4.843150
## [356,] 1.775321
## [357,] 3.966986
## [358,] 2.390264
## [359,] 7.010461
## [360,] 4.349881
## Unemployment , Total, From 15-64 years, From 24 to 47 months
## [355,] 37.18644
## [356,] 48.56215
## [357,] 27.12010
## [358,] 31.85748
## [359,] 35.23407
## [360,] 38.05378
## Unemployment , Total, From 15-64 years, From 3 to 5 months
## [355,] -54.20698
## [356,] -44.51155
## [357,] -52.91078
## [358,] -43.29595
## [359,] -43.08030
## [360,] -49.87989
## Unemployment , Total, From 15-64 years, From 6 to 11 months
## [355,] 36.41671
## [356,] 33.61737
## [357,] 34.94187
## [358,] 44.51279
## [359,] 47.74207
## [360,] 32.62204
## Unemployment , Total, From 15-64 years, Less than 1 month
## [355,] 4.721418
## [356,] 9.568220
## [357,] 11.626943
## [358,] -0.215808
## [359,] 8.562253
## [360,] 16.421598
## Unemployment by sex, age, duration. DurationNA not started
## [355,] 69.97419
## [356,] 47.69618
## [357,] 65.41465
## [358,] 21.41457
## [359,] 82.58741
## [360,] 52.72655
## Value added, gross VAT, receivable Wages and salaries
## [355,] 5611.456 -7201.120 9975.333
## [356,] 1110.151 -5618.080 14271.531
## [357,] 4136.464 -5221.767 6960.877
## [358,] 4064.018 -5927.018 16853.393
## [359,] 4795.829 -6543.477 10744.526
## [360,] 3528.674 -5154.082 19135.840
## Wholesale and retail trade, transport, accomodation and food service activities
## [355,] -16738.72
## [356,] -16246.15
## [357,] -13324.60
## [358,] -11598.16
## [359,] -12516.22
## [360,] -11090.22
## Wholesale and retail trade, transport, accomodation and food service activities, Compensation of employees
## [355,] -12769.179
## [356,] -12307.177
## [357,] -9803.067
## [358,] -12187.671
## [359,] -10291.847
## [360,] -11358.411
## Wholesale and retail trade, transport, accomodation and food service activities, Employers' social contributions
## [355,] -989.1350
## [356,] -1347.0145
## [357,] -895.3236
## [358,] -698.5680
## [359,] -959.6141
## [360,] -751.1416
## Wholesale and retail trade, transport, accomodation and food service activities, Wages and salaries
## [355,] 840.5270
## [356,] -1582.9001
## [357,] -918.8832
## [358,] 1167.5545
## [359,] 129.1688
## [360,] -174.6039
## Y_GDP_Belgium
## [355,] 104.2869
## [356,] 113.5526
## [357,] 103.4512
## [358,] 110.4953
## [359,] 116.6313
## [360,] 109.8735dim(IFT_RandPhase_FT_Belgium); head(Re(IFT_RandPhase_FT_Belgium)); tail(Re(IFT_RandPhase_FT_Belgium))## [1] 360 132## Acquisitions less disposals of non-financial non-produced assets
## [1,] -23.405196
## [2,] 43.173128
## [3,] 19.052743
## [4,] 3.143027
## [5,] 107.032304
## [6,] -38.518077
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels
## [1,] -1806.076
## [2,] -1701.934
## [3,] -1614.340
## [4,] -1642.334
## [5,] -1660.695
## [6,] -1710.976
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [1,] 170.43270
## [2,] 77.84080
## [3,] 77.43894
## [4,] -41.17455
## [5,] 34.17262
## [6,] 107.26618
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)
## [1,] -1053.9047
## [2,] -857.4495
## [3,] -1004.0227
## [4,] -924.4264
## [5,] -975.8087
## [6,] -875.8036
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [1,] -911.5811
## [2,] -853.8595
## [3,] -861.0611
## [4,] -802.1003
## [5,] -816.5385
## [6,] -842.9136
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels
## [1,] 362.1161
## [2,] 342.9182
## [3,] 381.9608
## [4,] 457.4212
## [5,] 467.2869
## [6,] 396.4700
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [1,] 1019.0326
## [2,] 715.6713
## [3,] 578.9018
## [4,] 538.0424
## [5,] 618.9855
## [6,] 431.6724
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8)
## [1,] -806.1293
## [2,] -561.4769
## [3,] -532.4453
## [4,] -642.4487
## [5,] -571.5193
## [6,] -656.2428
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [1,] -1119.0078
## [2,] -953.6663
## [3,] -988.7638
## [4,] -1043.1893
## [5,] -1049.1838
## [6,] -965.9875
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels
## [1,] 1715.617
## [2,] 1881.917
## [3,] 1947.278
## [4,] 1890.869
## [5,] 2078.669
## [6,] 1739.295
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [1,] -577.1123
## [2,] -757.6124
## [3,] -918.1375
## [4,] -1009.2448
## [5,] -860.7116
## [6,] -759.8981
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8)
## [1,] -2207.620
## [2,] -2053.380
## [3,] -2077.976
## [4,] -1831.501
## [5,] -1737.893
## [6,] -1543.247
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [1,] 1169.620
## [2,] 1573.276
## [3,] 1401.500
## [4,] 1461.816
## [5,] 1491.664
## [6,] 1339.815
## Agriculture, forestry and fishing
## [1,] 579.4982
## [2,] 545.0056
## [3,] 651.4645
## [4,] 452.7233
## [5,] 642.5685
## [6,] 531.9882
## Agriculture, forestry and fishing - Compensation of employees
## [1,] 43.42954
## [2,] 48.37002
## [3,] 104.65658
## [4,] 77.93357
## [5,] 128.75744
## [6,] 85.66742
## Agriculture, forestry and fishing - Employers' social contributions
## [1,] -26.07943
## [2,] -31.43791
## [3,] -18.28027
## [4,] -19.09274
## [5,] -29.44109
## [6,] -21.15502
## Agriculture, forestry and fishing, Wages and salaries
## [1,] -98.82770
## [2,] -85.31639
## [3,] -45.93403
## [4,] -49.48813
## [5,] -72.14163
## [6,] -60.47160
## All ISCED 2011 levels All ISCED 2011 levels, Females
## [1,] 6036.784 3268.049
## [2,] 6087.826 3417.979
## [3,] 6530.018 3322.380
## [4,] 6132.689 3507.518
## [5,] 6449.383 3538.145
## [6,] 6162.278 3469.006
## All ISCED 2011 levels, Males
## [1,] -3563.322
## [2,] -3307.973
## [3,] -3423.302
## [4,] -3417.489
## [5,] -3371.723
## [6,] -3329.195
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Compensation of employees
## [1,] -1597.3545
## [2,] -1077.9196
## [3,] -1316.8412
## [4,] -1089.9957
## [5,] -988.4564
## [6,] -1056.4412
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Employers' social contributions
## [1,] -129.71168
## [2,] -130.86547
## [3,] -153.60941
## [4,] -96.32962
## [5,] -140.83796
## [6,] -96.11475
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Value added, gross
## [1,] 386.1798
## [2,] 868.1032
## [3,] 992.3652
## [4,] 1043.8609
## [5,] 1018.2850
## [6,] 727.5349
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Wages and salaries
## [1,] -953.1461
## [2,] -500.8541
## [3,] -513.6608
## [4,] -609.7769
## [5,] -461.1771
## [6,] -578.7517
## Capital taxes, receivable Capital transfers, payable
## [1,] -158.94199 -406.1836
## [2,] -209.63080 -694.7497
## [3,] 71.18219 -329.2518
## [4,] 168.29202 -203.3770
## [5,] 247.89380 633.3752
## [6,] 135.60727 -668.1752
## Capital transfers, receivable
## [1,] 445.5229
## [2,] 437.2465
## [3,] 465.4707
## [4,] 464.8589
## [5,] 564.9274
## [6,] 276.3339
## Changes in inventories and acquisitions less disposals of valuables
## [1,] 87.853897
## [2,] -35.835436
## [3,] 9.825615
## [4,] -22.302281
## [5,] -41.381762
## [6,] 57.178211
## Collective consumption expenditure Compensation of employees
## [1,] 5057.878 -56134.54
## [2,] 6479.697 -41102.07
## [3,] 4802.668 -46936.46
## [4,] 5823.079 -42973.31
## [5,] 6164.841 -34320.92
## [6,] 6390.763 -38227.98
## Compensation of employees, payable Construction, Compensation of employees
## [1,] 9055.119 -32.03359
## [2,] 7729.346 390.73945
## [3,] 5109.232 -412.36008
## [4,] 9174.043 -36.92940
## [5,] 6774.615 396.08242
## [6,] 9668.712 -324.92639
## Construction, Employers' social contributions
## [1,] 142.75630
## [2,] 242.65567
## [3,] 240.84785
## [4,] 30.99227
## [5,] 275.92332
## [6,] 225.01074
## Construction, Value added, gross Construction, Wages and salaries
## [1,] -5400.380 -418.43509
## [2,] -3603.019 -289.26526
## [3,] -3204.828 -382.85426
## [4,] -4241.546 -339.04654
## [5,] -3398.915 -78.97114
## [6,] -3577.373 -161.53671
## Consumption of fixed capital
## [1,] -2242.336
## [2,] -2005.001
## [3,] -2423.953
## [4,] -2008.596
## [5,] -1482.909
## [6,] -1652.028
## Current taxes on income, wealth, etc., payable
## [1,] -15.240069
## [2,] 5.811887
## [3,] 20.198657
## [4,] -31.146502
## [5,] 9.519180
## [6,] 15.620969
## Current taxes on income, wealth, etc., receivable
## [1,] -11008.53
## [2,] -13280.97
## [3,] -13752.41
## [4,] -9684.00
## [5,] -7700.92
## [6,] -11686.14
## Employers' actual social contributions, receivable
## [1,] 2724.016
## [2,] 6200.829
## [3,] 6688.182
## [4,] 4722.719
## [5,] 8345.338
## [6,] 7336.883
## Employers' social contributions
## [1,] 10000.64
## [2,] 10883.20
## [3,] 11324.75
## [4,] 10926.67
## [5,] 11635.52
## [6,] 10128.91
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels
## [1,] -480.1787
## [2,] -381.9486
## [3,] -324.5176
## [4,] -404.2972
## [5,] -167.8553
## [6,] -148.0476
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [1,] 24.689863
## [2,] -9.058020
## [3,] -7.399001
## [4,] 39.279107
## [5,] -31.887017
## [6,] -69.437491
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)
## [1,] 418.6232
## [2,] 833.6751
## [3,] 722.7168
## [4,] 873.7008
## [5,] 752.6340
## [6,] 744.1974
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [1,] -132.77830
## [2,] -49.75617
## [3,] -24.86683
## [4,] -37.37249
## [5,] 38.22169
## [6,] 40.97519
## Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [1,] 393.6588
## [2,] 356.8297
## [3,] 308.5526
## [4,] 486.2488
## [5,] 397.6383
## [6,] 313.5600
## Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education
## [1,] -901.6799
## [2,] -682.1998
## [3,] -786.8608
## [4,] -635.1951
## [5,] -592.2898
## [6,] -640.1914
## Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [1,] -810.0106
## [2,] -763.9241
## [3,] -779.5250
## [4,] -739.2713
## [5,] -669.9011
## [6,] -673.4669
## Information and communication, wages and salaries Interest, payable
## [1,] 626.9456 -2504.437
## [2,] 1267.8736 -2846.118
## [3,] 1159.7314 -3242.881
## [4,] 844.0153 -2859.281
## [5,] 1306.8158 -3519.587
## [6,] 844.6558 -3392.774
## Interest, receivable Intermediate consumption
## [1,] -238.7849 -1660.6389
## [2,] -247.5846 -449.1587
## [3,] -266.9658 -718.6756
## [4,] -251.3310 -685.4104
## [5,] -330.5213 34.3315
## [6,] -198.9542 -171.2638
## ISCED11 Less than primary, primary and lower secondary education (levels 0-2)
## [1,] -1143.504
## [2,] -2132.025
## [3,] -1578.821
## [4,] -1330.938
## [5,] -1456.495
## [6,] -1861.280
## ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Females
## [1,] -812.0943
## [2,] -1031.1510
## [3,] -954.1354
## [4,] -949.0749
## [5,] -921.6141
## [6,] -937.3187
## ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Males
## [1,] -10.97279
## [2,] -121.57845
## [3,] -311.68570
## [4,] -256.26903
## [5,] -469.79215
## [6,] -356.15020
## ISCED11 Tertiary education (levels 5-8)
## [1,] -1933.948
## [2,] -1993.839
## [3,] -1737.343
## [4,] -1293.428
## [5,] -1568.786
## [6,] -1328.043
## ISCED11 Tertiary education (levels 5-8), Females
## [1,] -1236.9100
## [2,] -1044.8394
## [3,] -1270.0072
## [4,] -1104.9557
## [5,] -1292.1068
## [6,] -893.0858
## ISCED11 Tertiary education (levels 5-8), Males
## [1,] 630.2213
## [2,] 627.1584
## [3,] 773.7732
## [4,] 800.8087
## [5,] 880.6548
## [6,] 853.1893
## ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [1,] 2198.505
## [2,] 2061.097
## [3,] 2400.748
## [4,] 2111.773
## [5,] 2297.637
## [6,] 2226.192
## ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Females
## [1,] -125.0334
## [2,] -139.0613
## [3,] -134.5081
## [4,] -132.6704
## [5,] -187.0787
## [6,] -102.3990
## ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Males
## [1,] 95.19051
## [2,] 235.03407
## [3,] 109.58798
## [4,] 139.56394
## [5,] 293.21848
## [6,] 132.52363
## Labor cost for LCI (compensation of employees plus taxes minus subsidies)
## [1,] 0.07803056
## [2,] 1.22987925
## [3,] 0.60414599
## [4,] 0.34686324
## [5,] 0.63341626
## [6,] 0.57185585
## Labor cost other than wages and salaries Labour cost for LCI Loans
## [1,] 1.6597076 2.0581173 -35788.452
## [2,] 1.4034469 1.3448725 10134.911
## [3,] 1.9560695 0.9456385 18285.949
## [4,] 0.6129504 0.8183674 -27506.726
## [5,] 0.9674443 -0.2408192 -24528.863
## [6,] 1.8765129 -0.4935838 6739.717
## Market output, output for own final use and payments for non-market output
## [1,] -463.0275
## [2,] 454.6377
## [3,] -121.7442
## [4,] 968.5927
## [5,] 797.4128
## [6,] 1280.9230
## Net lending (+) /net borrowing (-) Net social contributions, receivable
## [1,] -413.4259 8222.535
## [2,] 487.6347 11195.476
## [3,] -1034.6827 13965.124
## [4,] 3614.2913 9309.130
## [5,] 2015.0789 13039.077
## [6,] -7385.5039 13777.123
## Other capital transfers and investment grants, receivable
## [1,] -142.431134
## [2,] -121.230089
## [3,] -96.180050
## [4,] -1.108032
## [5,] -46.240478
## [6,] 3.805251
## Other current taxes, receivable Other current transfers, payable
## [1,] -543.3544 1668.878
## [2,] -415.3821 2215.517
## [3,] -394.7113 2082.164
## [4,] -507.8607 1677.231
## [5,] -370.5077 1608.734
## [6,] -413.2149 1799.986
## Other current transfers, receivable Other property income, receivable
## [1,] 545.9178 -323.36451
## [2,] 196.9071 622.45852
## [3,] 229.2778 463.48245
## [4,] 463.2099 181.10118
## [5,] 240.1508 413.07681
## [6,] 123.8226 -67.46717
## Other subsidies on production, payable
## [1,] -5408.9004
## [2,] -2606.1753
## [3,] -3670.6449
## [4,] -2880.3236
## [5,] -915.7243
## [6,] -4572.6007
## Other taxes on production, receivable Output
## [1,] -589.8968 -9359.871
## [2,] -1109.1132 -6059.698
## [3,] -1403.5145 -9263.685
## [4,] -1971.0520 -7165.680
## [5,] -1334.4774 -6721.667
## [6,] -1508.4393 -2972.982
## Professional, scientific and technical activities; administrative and support service activities, Compensation of employees
## [1,] 2370.290
## [2,] 4023.532
## [3,] 5292.778
## [4,] 4344.948
## [5,] 3625.291
## [6,] 5499.078
## Professional, scientific and technical activities; administrative and support service activities, Employers' social contributions
## [1,] -1439.2642
## [2,] -1523.4070
## [3,] -1393.3572
## [4,] -918.4171
## [5,] -1040.9794
## [6,] -1181.6116
## Professional, scientific and technical activities; administrative and support service activities, Value added, gross
## [1,] 281.9928
## [2,] -1904.1510
## [3,] 572.5234
## [4,] 1613.8648
## [5,] 4834.5935
## [6,] 552.0339
## Professional, scientific and technical activities; administrative and support service activities, Wages and salaries
## [1,] 1890.282
## [2,] 2203.504
## [3,] 2721.191
## [4,] 2069.940
## [5,] 2730.196
## [6,] 1688.913
## Property income, payable Property income, receivable
## [1,] 4248.206 -1145.3279
## [2,] 3796.697 -658.5325
## [3,] 4194.787 -694.6738
## [4,] 3306.755 -1349.1142
## [5,] 3782.695 -392.2683
## [6,] 3308.004 -697.5432
## Public administration, defence, education, human health and social work activities, Compensation of employees
## [1,] -12013.117
## [2,] -4758.031
## [3,] -8377.748
## [4,] -5494.099
## [5,] -5501.706
## [6,] -10651.661
## Public administration, defence, education, human health and social work activities, Employers' social contributions
## [1,] -4236.067
## [2,] -1540.989
## [3,] -1944.227
## [4,] -2204.540
## [5,] -2910.189
## [6,] -3446.313
## Public administration, defence, education, human health and social work activities, Value added, gross
## [1,] 17007.57
## [2,] 14544.04
## [3,] 15306.90
## [4,] 15853.30
## [5,] 12909.20
## [6,] 12769.26
## Public administration, defence, education, human health and social work activities, Wages and salaries
## [1,] -7503.806
## [2,] -6196.700
## [3,] -5363.691
## [4,] -5495.713
## [5,] -9135.961
## [6,] -7478.635
## Real estate activities, Compensation of employees Savings, gross
## [1,] 71.142459 5563.536
## [2,] 25.136348 -3339.637
## [3,] -49.010459 -2252.469
## [4,] 21.078971 -3867.107
## [5,] 28.408894 1875.055
## [6,] -3.297825 -4236.648
## Social benefits other than social transfers in kind and social transfers in kind ? purchased market production, payable
## [1,] -8135.4407
## [2,] -6399.4962
## [3,] -8335.3364
## [4,] -8306.5371
## [5,] -9526.1439
## [6,] -949.4063
## Social benefits other than social transfers in kind, payable
## [1,] -14091.745
## [2,] -11580.329
## [3,] -11870.747
## [4,] -11790.205
## [5,] -6190.984
## [6,] -7875.134
## Social transfers in kind ? purchased market production, payable
## [1,] -8673.296
## [2,] -4826.865
## [3,] -1643.734
## [4,] -3820.769
## [5,] -6296.588
## [6,] -3107.981
## Subsidies on products, payable Subsidies, payable
## [1,] 282.7129 -3583.4739
## [2,] 241.1698 -2552.6835
## [3,] 248.0952 -1610.6819
## [4,] 247.7505 -665.0974
## [5,] 244.8618 -1131.6455
## [6,] 318.7130 -1232.1198
## Taxes on income, receivable Taxes on production and imports, receivable
## [1,] -3567.971 -4852.667
## [2,] 1969.038 -4731.690
## [3,] 1898.659 -1611.178
## [4,] -1152.053 -4408.099
## [5,] 3400.526 -3023.850
## [6,] 7337.203 -3066.102
## Taxes on products, receivable Total general government expenditure
## [1,] 2917.769 -38975.93
## [2,] 3680.044 -22177.41
## [3,] 2814.753 -17580.06
## [4,] 3600.736 -25129.27
## [5,] 5600.301 -10496.26
## [6,] 6002.737 -19553.62
## Total general government revenue
## [1,] -24838.81
## [2,] -20843.99
## [3,] -23312.70
## [4,] -12095.24
## [5,] -16292.26
## [6,] -11121.36
## Unemployment , Females, From 15-64 years, 48 months or over
## [1,] 15.0256575
## [2,] -6.1753233
## [3,] -4.8294394
## [4,] -10.8335211
## [5,] -0.9826679
## [6,] -12.9363400
## Unemployment , Females, From 15-64 years, From 1 to 2 months
## [1,] -33.58912
## [2,] -25.32372
## [3,] -28.00886
## [4,] -43.47288
## [5,] -26.22868
## [6,] -35.06382
## Unemployment , Females, From 15-64 years, From 12 to 17 months
## [1,] 5.351838
## [2,] 11.166158
## [3,] 12.657777
## [4,] 12.066788
## [5,] 11.438174
## [6,] 10.787076
## Unemployment , Females, From 15-64 years, From 18 to 23 months
## [1,] -4.183610
## [2,] -4.518417
## [3,] -5.144815
## [4,] -3.807126
## [5,] -5.169003
## [6,] -4.432471
## Unemployment , Females, From 15-64 years, From 24 to 47 months
## [1,] 25.90885
## [2,] 25.90470
## [3,] 21.51744
## [4,] 22.52728
## [5,] 19.07222
## [6,] 25.69913
## Unemployment , Females, From 15-64 years, From 3 to 5 months
## [1,] -18.93081
## [2,] -23.14841
## [3,] -17.38271
## [4,] -22.35471
## [5,] -23.99618
## [6,] -19.37115
## Unemployment , Females, From 15-64 years, From 6 to 11 months
## [1,] 20.310130
## [2,] 8.843866
## [3,] 11.328384
## [4,] 19.891684
## [5,] 12.117454
## [6,] 9.385628
## Unemployment , Females, From 15-64 years, Less than 1 month
## [1,] 8.947155
## [2,] 10.545803
## [3,] 11.162778
## [4,] 7.792036
## [5,] 11.318484
## [6,] 11.435154
## Unemployment , Females, From 15-64 years, Total
## [1,] -199.1541
## [2,] -197.2248
## [3,] -173.9743
## [4,] -161.8938
## [5,] -185.9137
## [6,] -172.4733
## Unemployment , Males, From 15-64 years
## [1,] -119.3302
## [2,] -129.9045
## [3,] -148.9712
## [4,] -122.3812
## [5,] -140.6038
## [6,] -140.0638
## Unemployment , Males, From 15-64 years, 48 months or over
## [1,] -20.83327
## [2,] -28.82506
## [3,] -26.55334
## [4,] -30.33892
## [5,] -28.09160
## [6,] -32.89264
## Unemployment , Males, From 15-64 years, from 1 to 2 months
## [1,] -19.11717
## [2,] -17.55892
## [3,] -15.31296
## [4,] -16.40299
## [5,] -12.12851
## [6,] -20.58958
## Unemployment , Males, From 15-64 years, from 12 to 17 months
## [1,] 12.442687
## [2,] -4.579661
## [3,] 5.025245
## [4,] 5.531552
## [5,] 13.327160
## [6,] 7.182447
## Unemployment , Males, From 15-64 years, from 18 to 23 months
## [1,] -13.76453
## [2,] -12.77997
## [3,] -12.98452
## [4,] -10.85271
## [5,] -11.42596
## [6,] -12.16828
## Unemployment , Males, From 15-64 years, from 24 to 47 months
## [1,] 24.82791
## [2,] 26.27296
## [3,] 26.42592
## [4,] 21.77157
## [5,] 29.53239
## [6,] 14.00912
## Unemployment , Males, From 15-64 years, from 3 to 5 months
## [1,] 19.73516
## [2,] 22.58997
## [3,] 21.23991
## [4,] 13.52400
## [5,] 17.77327
## [6,] 25.35932
## Unemployment , Males, From 15-64 years, from 6 to 11 months
## [1,] -33.28560
## [2,] -25.56030
## [3,] -19.38101
## [4,] -19.83015
## [5,] -17.20057
## [6,] -20.31524
## Unemployment , Males, From 15-64 years, Less than 1 month
## [1,] -0.991563
## [2,] 2.102143
## [3,] 4.505262
## [4,] 3.674292
## [5,] 5.583035
## [6,] 1.582963
## Unemployment , Total, From 15-64 years, 48 months or over
## [1,] -28.28911
## [2,] -34.56930
## [3,] -35.13452
## [4,] -36.85802
## [5,] -48.82317
## [6,] -48.19224
## Unemployment , Total, From 15-64 years, From 1 to 2 months
## [1,] 67.38049
## [2,] 68.50615
## [3,] 55.76096
## [4,] 43.87049
## [5,] 70.44249
## [6,] 74.14804
## Unemployment , Total, From 15-64 years, From 12 to 17 months
## [1,] 33.17425
## [2,] 35.74814
## [3,] 27.52258
## [4,] 28.82565
## [5,] 26.56900
## [6,] 32.60738
## Unemployment , Total, From 15-64 years, From 18 to 23 months
## [1,] -2.8170347
## [2,] 7.6520338
## [3,] 3.4610577
## [4,] 2.1264482
## [5,] 7.4878651
## [6,] 0.5569513
## Unemployment , Total, From 15-64 years, From 24 to 47 months
## [1,] 32.32272
## [2,] 36.40787
## [3,] 41.07205
## [4,] 48.13106
## [5,] 38.96244
## [6,] 40.26881
## Unemployment , Total, From 15-64 years, From 3 to 5 months
## [1,] -59.79349
## [2,] -46.46723
## [3,] -34.58640
## [4,] -56.73976
## [5,] -49.39037
## [6,] -46.60263
## Unemployment , Total, From 15-64 years, From 6 to 11 months
## [1,] 18.99274
## [2,] 23.08856
## [3,] 24.84964
## [4,] 28.71772
## [5,] 19.55496
## [6,] 22.45859
## Unemployment , Total, From 15-64 years, Less than 1 month
## [1,] 16.417438
## [2,] 8.604605
## [3,] 19.251930
## [4,] 9.523556
## [5,] 8.564624
## [6,] 17.092719
## Unemployment by sex, age, duration. DurationNA not started
## [1,] 57.89486
## [2,] 61.17631
## [3,] 97.75774
## [4,] 69.58263
## [5,] 86.88914
## [6,] 30.28833
## Value added, gross VAT, receivable Wages and salaries
## [1,] -410.2742 -9526.952 2868.358
## [2,] 2707.2690 -7314.802 13149.041
## [3,] 3049.3796 -6466.113 10804.602
## [4,] 6242.0799 -7151.804 4206.189
## [5,] 5043.9854 -6729.021 7493.031
## [6,] 5382.4331 -8021.886 10937.449
## Wholesale and retail trade, transport, accomodation and food service activities
## [1,] -15921.21
## [2,] -15343.05
## [3,] -14794.59
## [4,] -12999.46
## [5,] -13201.06
## [6,] -14712.09
## Wholesale and retail trade, transport, accomodation and food service activities, Compensation of employees
## [1,] -11603.61
## [2,] -11306.32
## [3,] -10721.89
## [4,] -11642.98
## [5,] -11551.10
## [6,] -10521.28
## Wholesale and retail trade, transport, accomodation and food service activities, Employers' social contributions
## [1,] -1411.6592
## [2,] -996.4307
## [3,] -268.6955
## [4,] -877.0814
## [5,] -411.2117
## [6,] -1035.7081
## Wholesale and retail trade, transport, accomodation and food service activities, Wages and salaries
## [1,] -1241.3085
## [2,] -628.6097
## [3,] 483.0824
## [4,] 632.8085
## [5,] -1107.4233
## [6,] -1050.3603
## Y_GDP_Belgium
## [1,] 75.39522
## [2,] 88.70439
## [3,] 72.20113
## [4,] 93.28383
## [5,] 81.51278
## [6,] 75.06695## Acquisitions less disposals of non-financial non-produced assets
## [355,] -11.407967
## [356,] -32.564592
## [357,] 21.444949
## [358,] -72.078483
## [359,] 7.881843
## [360,] 1.308009
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels
## [355,] -1876.607
## [356,] -1691.195
## [357,] -1787.687
## [358,] -1417.429
## [359,] -1464.609
## [360,] -1525.512
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [355,] 27.19345
## [356,] 39.18835
## [357,] 63.50065
## [358,] 18.08210
## [359,] 66.82969
## [360,] 24.42209
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)
## [355,] -1017.0543
## [356,] -958.4714
## [357,] -853.4765
## [358,] -905.4623
## [359,] -1103.3538
## [360,] -892.6141
## Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] -776.1546
## [356,] -887.0610
## [357,] -869.8730
## [358,] -867.5488
## [359,] -806.7218
## [360,] -836.4450
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels
## [355,] 417.7540
## [356,] 353.2607
## [357,] 321.4188
## [358,] 305.8060
## [359,] 419.3236
## [360,] 345.6235
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [355,] 622.5810
## [356,] 644.4750
## [357,] 713.6940
## [358,] 689.6499
## [359,] 688.5757
## [360,] 656.9369
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8)
## [355,] -562.3196
## [356,] -690.0676
## [357,] -612.5599
## [358,] -643.1745
## [359,] -654.9256
## [360,] -532.8569
## Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] -967.5576
## [356,] -1066.6309
## [357,] -1035.9485
## [358,] -1097.1691
## [359,] -1023.0768
## [360,] -1033.0121
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels
## [355,] 2243.414
## [356,] 1819.379
## [357,] 1991.700
## [358,] 1841.157
## [359,] 1719.560
## [360,] 1902.312
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [355,] -920.4673
## [356,] -815.5334
## [357,] -881.7839
## [358,] -1045.1989
## [359,] -913.3414
## [360,] -919.6714
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8)
## [355,] -1690.386
## [356,] -1809.441
## [357,] -1818.057
## [358,] -1648.665
## [359,] -1963.134
## [360,] -1613.587
## Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] 1334.907
## [356,] 1432.716
## [357,] 1235.563
## [358,] 1268.440
## [359,] 1388.710
## [360,] 1527.934
## Agriculture, forestry and fishing
## [355,] 565.9073
## [356,] 619.4125
## [357,] 621.5069
## [358,] 535.1259
## [359,] 563.1164
## [360,] 597.3747
## Agriculture, forestry and fishing - Compensation of employees
## [355,] 73.73733
## [356,] 98.98009
## [357,] 99.06414
## [358,] 99.43041
## [359,] 109.98934
## [360,] 93.05877
## Agriculture, forestry and fishing - Employers' social contributions
## [355,] -23.05750
## [356,] -24.65342
## [357,] -27.17187
## [358,] -24.77651
## [359,] -24.92524
## [360,] -29.66699
## Agriculture, forestry and fishing, Wages and salaries
## [355,] -66.67324
## [356,] -52.56202
## [357,] -72.07417
## [358,] -59.52216
## [359,] -45.15805
## [360,] -47.45481
## All ISCED 2011 levels All ISCED 2011 levels, Females
## [355,] 6289.060 3317.288
## [356,] 6159.593 3252.168
## [357,] 6335.007 3302.716
## [358,] 6175.513 3311.530
## [359,] 6423.565 3488.985
## [360,] 6576.852 3442.293
## All ISCED 2011 levels, Males
## [355,] -3453.820
## [356,] -3389.213
## [357,] -3437.699
## [358,] -3394.089
## [359,] -3331.647
## [360,] -3427.280
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Compensation of employees
## [355,] -1161.333
## [356,] -1498.709
## [357,] -1391.927
## [358,] -1243.267
## [359,] -1356.704
## [360,] -1121.635
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Employers' social contributions
## [355,] -134.49743
## [356,] -159.39595
## [357,] -185.66910
## [358,] -160.37069
## [359,] -98.22426
## [360,] -128.71823
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Value added, gross
## [355,] 773.2221
## [356,] 858.2712
## [357,] 799.1778
## [358,] 827.0446
## [359,] 942.3718
## [360,] 840.7767
## Arts, entertainment and recreation; other service activities; activities of household and extra-territorial organizations and bodies, Wages and salaries
## [355,] -669.1910
## [356,] -662.9851
## [357,] -609.4612
## [358,] -775.4352
## [359,] -649.0695
## [360,] -446.0012
## Capital taxes, receivable Capital transfers, payable
## [355,] 381.2185 -856.19509
## [356,] 136.9044 -360.34309
## [357,] 465.3589 -1323.39079
## [358,] 407.7386 -33.09127
## [359,] 441.7819 -331.39802
## [360,] 137.3979 161.03922
## Capital transfers, receivable
## [355,] 649.3636
## [356,] 357.8514
## [357,] 346.0512
## [358,] 345.5883
## [359,] 297.9582
## [360,] 480.9614
## Changes in inventories and acquisitions less disposals of valuables
## [355,] 27.149174
## [356,] -4.630613
## [357,] 114.127874
## [358,] -35.017366
## [359,] 9.481564
## [360,] -32.265124
## Collective consumption expenditure Compensation of employees
## [355,] 7238.126 -47954.89
## [356,] 7140.035 -47254.53
## [357,] 6037.890 -51199.17
## [358,] 7692.088 -45482.58
## [359,] 6446.849 -34324.70
## [360,] 6015.950 -38245.61
## Compensation of employees, payable
## [355,] 6876.235
## [356,] 8389.647
## [357,] 9767.948
## [358,] 10430.723
## [359,] 6793.619
## [360,] 10316.283
## Construction, Compensation of employees
## [355,] -130.56279
## [356,] -683.35263
## [357,] -877.77597
## [358,] -53.05717
## [359,] -125.65051
## [360,] -208.31131
## Construction, Employers' social contributions
## [355,] 174.74875
## [356,] 244.33208
## [357,] 78.11979
## [358,] 210.01953
## [359,] 141.62772
## [360,] 111.64816
## Construction, Value added, gross Construction, Wages and salaries
## [355,] -3375.281 -611.2502
## [356,] -4197.377 -445.7706
## [357,] -3339.140 -504.3435
## [358,] -3508.715 -234.7040
## [359,] -3588.987 -341.8110
## [360,] -4170.875 -362.8273
## Consumption of fixed capital
## [355,] -1585.363
## [356,] -2182.878
## [357,] -1690.811
## [358,] -1516.929
## [359,] -1967.204
## [360,] -1934.556
## Current taxes on income, wealth, etc., payable
## [355,] 6.455748
## [356,] -12.961378
## [357,] 10.767303
## [358,] 13.039428
## [359,] -12.771502
## [360,] 14.801029
## Current taxes on income, wealth, etc., receivable
## [355,] -10262.186
## [356,] -9858.528
## [357,] -11023.399
## [358,] -8839.197
## [359,] -10325.053
## [360,] -9495.912
## Employers' actual social contributions, receivable
## [355,] 6198.882
## [356,] 6105.790
## [357,] 6289.885
## [358,] 5739.419
## [359,] 5987.175
## [360,] 6827.211
## Employers' social contributions
## [355,] 10726.63
## [356,] 13622.20
## [357,] 12509.22
## [358,] 13561.81
## [359,] 11823.04
## [360,] 11964.06
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels
## [355,] -245.44334
## [356,] -304.09250
## [357,] -285.64806
## [358,] -333.48807
## [359,] -232.88487
## [360,] -65.90955
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [355,] -43.90229
## [356,] 19.76653
## [357,] -77.79135
## [358,] -22.43823
## [359,] -88.18655
## [360,] -38.65091
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)
## [355,] 786.5564
## [356,] 640.2643
## [357,] 688.5407
## [358,] 675.1181
## [359,] 749.6349
## [360,] 781.5006
## Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] -44.46065
## [356,] -41.65236
## [357,] -22.87019
## [358,] -90.10079
## [359,] -43.28163
## [360,] 55.07213
## Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)
## [355,] 280.1983
## [356,] 379.1233
## [357,] 351.9727
## [358,] 328.5446
## [359,] 294.2294
## [360,] 169.0767
## Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education
## [355,] -637.7784
## [356,] -787.9738
## [357,] -708.4048
## [358,] -664.3854
## [359,] -660.9345
## [360,] -625.8953
## Employment by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] -710.2220
## [356,] -759.9432
## [357,] -757.0340
## [358,] -722.9969
## [359,] -712.3667
## [360,] -713.5261
## Information and communication, wages and salaries Interest, payable
## [355,] 964.1002 -3258.720
## [356,] 1176.5270 -2937.136
## [357,] 1134.6526 -3205.179
## [358,] 1320.2216 -3197.435
## [359,] 1079.3488 -3407.457
## [360,] 1124.9981 -3797.626
## Interest, receivable Intermediate consumption
## [355,] -316.7523 -399.153610
## [356,] -289.4306 303.911845
## [357,] -234.0275 234.567522
## [358,] -235.0668 -239.414339
## [359,] -239.2612 -3.076083
## [360,] -322.0127 -620.847954
## ISCED11 Less than primary, primary and lower secondary education (levels 0-2)
## [355,] -2063.334
## [356,] -1931.614
## [357,] -1909.825
## [358,] -1793.195
## [359,] -1608.362
## [360,] -1869.363
## ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Females
## [355,] -961.0794
## [356,] -927.0479
## [357,] -916.1430
## [358,] -1108.1635
## [359,] -1194.3212
## [360,] -985.0082
## ISCED11 Less than primary, primary and lower secondary education (levels 0-2), Males
## [355,] -287.1661
## [356,] -320.1416
## [357,] -307.8221
## [358,] -258.0882
## [359,] -256.2474
## [360,] -299.8131
## ISCED11 Tertiary education (levels 5-8)
## [355,] -1477.046
## [356,] -1408.726
## [357,] -1500.342
## [358,] -1621.090
## [359,] -1989.353
## [360,] -1776.054
## ISCED11 Tertiary education (levels 5-8), Females
## [355,] -1144.9366
## [356,] -1259.0636
## [357,] -1454.6509
## [358,] -1173.1779
## [359,] -981.2342
## [360,] -1133.4022
## ISCED11 Tertiary education (levels 5-8), Males
## [355,] 810.5052
## [356,] 637.9402
## [357,] 699.1640
## [358,] 925.7338
## [359,] 708.9490
## [360,] 732.5261
## ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4)
## [355,] 2415.219
## [356,] 2112.154
## [357,] 2233.640
## [358,] 2194.193
## [359,] 2254.809
## [360,] 2375.114
## ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Females
## [355,] -83.97216
## [356,] -101.94108
## [357,] -223.16011
## [358,] -173.98815
## [359,] -135.36718
## [360,] -183.41974
## ISCED11 Upper secondary and post-secondary non-tertiary education (levels 3 and 4), Males
## [355,] 186.85050
## [356,] 246.28367
## [357,] 235.17309
## [358,] 73.40394
## [359,] 164.77332
## [360,] 193.24829
## Labor cost for LCI (compensation of employees plus taxes minus subsidies)
## [355,] 0.79743565
## [356,] 0.67207425
## [357,] -0.19423471
## [358,] 1.25881854
## [359,] 1.56955214
## [360,] 0.09790678
## Labor cost other than wages and salaries Labour cost for LCI Loans
## [355,] 3.046457 1.32004251 -19071.029
## [356,] 3.517158 0.09669155 -12460.178
## [357,] 3.024217 2.16108162 -14757.814
## [358,] 1.465028 1.22413054 -6074.798
## [359,] 2.027052 2.05360442 -3444.982
## [360,] 2.418594 2.07129763 -1035.968
## Market output, output for own final use and payments for non-market output
## [355,] 610.0124
## [356,] 899.7886
## [357,] 372.7192
## [358,] 1129.3051
## [359,] 765.9877
## [360,] 741.2933
## Net lending (+) /net borrowing (-) Net social contributions, receivable
## [355,] 1991.8241 11935.61
## [356,] 4728.9449 11146.49
## [357,] 1224.2467 12369.71
## [358,] 1762.5935 11710.86
## [359,] 680.2869 10396.03
## [360,] -5256.0393 11369.16
## Other capital transfers and investment grants, receivable
## [355,] -94.117556
## [356,] -103.216274
## [357,] -19.630414
## [358,] 75.726327
## [359,] 8.239301
## [360,] 12.719737
## Other current taxes, receivable Other current transfers, payable
## [355,] -473.1101 1826.183
## [356,] -474.6189 1191.361
## [357,] -483.8321 2055.895
## [358,] -466.3753 1519.210
## [359,] -428.1188 2153.889
## [360,] -484.2364 1574.715
## Other current transfers, receivable Other property income, receivable
## [355,] 60.75034 37.97405
## [356,] 260.54017 729.87075
## [357,] 271.85911 294.08292
## [358,] 384.81068 742.06817
## [359,] 184.29575 1203.33453
## [360,] 454.65712 -130.66761
## Other subsidies on production, payable
## [355,] -3836.099
## [356,] -4088.924
## [357,] -2557.891
## [358,] -2818.852
## [359,] -3033.305
## [360,] -2675.038
## Other taxes on production, receivable Output
## [355,] -1331.1506 -9707.876
## [356,] -1693.2269 -8300.822
## [357,] -1205.6258 -8451.847
## [358,] -1289.4003 -6509.365
## [359,] -1307.2154 -7423.260
## [360,] -724.3402 -3441.472
## Professional, scientific and technical activities; administrative and support service activities, Compensation of employees
## [355,] 1652.883
## [356,] 5695.660
## [357,] 4420.052
## [358,] 4837.257
## [359,] 3544.218
## [360,] 3857.244
## Professional, scientific and technical activities; administrative and support service activities, Employers' social contributions
## [355,] -1090.5983
## [356,] -456.1848
## [357,] -1117.6581
## [358,] -1069.0547
## [359,] -1146.4636
## [360,] -1005.3246
## Professional, scientific and technical activities; administrative and support service activities, Value added, gross
## [355,] 1204.063
## [356,] 3439.703
## [357,] 1844.088
## [358,] 2620.991
## [359,] 1745.960
## [360,] 1552.539
## Professional, scientific and technical activities; administrative and support service activities, Wages and salaries
## [355,] 1728.400
## [356,] 2899.744
## [357,] 1757.248
## [358,] 1808.353
## [359,] 3431.091
## [360,] 2315.924
## Property income, payable Property income, receivable
## [355,] 3837.742 -768.8739
## [356,] 4030.135 -1058.1332
## [357,] 4381.240 -1054.1937
## [358,] 4162.533 -240.5559
## [359,] 3638.767 -1202.0839
## [360,] 3296.886 -367.2426
## Public administration, defence, education, human health and social work activities, Compensation of employees
## [355,] -5521.414
## [356,] -9304.076
## [357,] -7427.396
## [358,] -7770.354
## [359,] -6055.413
## [360,] -7389.396
## Public administration, defence, education, human health and social work activities, Employers' social contributions
## [355,] -2501.972
## [356,] -3028.041
## [357,] -2415.267
## [358,] -1628.096
## [359,] -1726.522
## [360,] -1337.923
## Public administration, defence, education, human health and social work activities, Value added, gross
## [355,] 14179.01
## [356,] 11216.19
## [357,] 10919.91
## [358,] 15349.12
## [359,] 11314.34
## [360,] 13917.41
## Public administration, defence, education, human health and social work activities, Wages and salaries
## [355,] -4665.135
## [356,] -3717.992
## [357,] -8049.380
## [358,] -3810.252
## [359,] -5547.767
## [360,] -3576.049
## Real estate activities, Compensation of employees Savings, gross
## [355,] 21.27098 -684.7238
## [356,] -57.70449 5676.1892
## [357,] -18.12837 -1994.6068
## [358,] 62.57018 -905.8016
## [359,] -35.50801 2926.0927
## [360,] -12.97126 -5508.9193
## Social benefits other than social transfers in kind and social transfers in kind ? purchased market production, payable
## [355,] -8204.530
## [356,] -10078.326
## [357,] 693.194
## [358,] -3709.006
## [359,] -3858.092
## [360,] -2416.240
## Social benefits other than social transfers in kind, payable
## [355,] -7037.936
## [356,] -11856.242
## [357,] -9106.588
## [358,] -9614.633
## [359,] -11208.993
## [360,] -4802.191
## Social transfers in kind ? purchased market production, payable
## [355,] -2241.897
## [356,] -4656.311
## [357,] -2572.327
## [358,] -2827.190
## [359,] -4162.293
## [360,] -4007.559
## Subsidies on products, payable Subsidies, payable
## [355,] 225.0605 -2427.543
## [356,] 176.1449 -1996.596
## [357,] 320.4728 -2085.269
## [358,] 282.3426 -1736.503
## [359,] 308.9653 -1468.939
## [360,] 358.0095 -1167.056
## Taxes on income, receivable Taxes on production and imports, receivable
## [355,] 4097.496 -2313.353
## [356,] 2666.806 -3714.743
## [357,] 5199.308 -6134.680
## [358,] 3481.867 -3983.448
## [359,] 4052.052 -4441.170
## [360,] 7665.827 -3593.531
## Taxes on products, receivable Total general government expenditure
## [355,] 4915.374 -31042.01
## [356,] 3487.575 -21567.11
## [357,] 3318.037 -29164.37
## [358,] 2385.357 -20476.37
## [359,] 4395.357 -26312.51
## [360,] 5764.704 -23601.60
## Total general government revenue
## [355,] -4834.945
## [356,] -11622.938
## [357,] -13996.988
## [358,] -5469.329
## [359,] -17180.372
## [360,] -19633.388
## Unemployment , Females, From 15-64 years, 48 months or over
## [355,] -6.968291
## [356,] 4.447450
## [357,] -6.435313
## [358,] -4.591887
## [359,] -9.833091
## [360,] -5.241598
## Unemployment , Females, From 15-64 years, From 1 to 2 months
## [355,] -25.45065
## [356,] -28.18603
## [357,] -28.02709
## [358,] -26.49960
## [359,] -33.50749
## [360,] -29.18083
## Unemployment , Females, From 15-64 years, From 12 to 17 months
## [355,] 10.587728
## [356,] 9.210117
## [357,] 4.939326
## [358,] 10.955458
## [359,] 9.862456
## [360,] 6.512798
## Unemployment , Females, From 15-64 years, From 18 to 23 months
## [355,] -4.318693
## [356,] -4.340725
## [357,] -2.353096
## [358,] -4.261096
## [359,] -4.453699
## [360,] -4.464338
## Unemployment , Females, From 15-64 years, From 24 to 47 months
## [355,] 25.60289
## [356,] 23.53445
## [357,] 26.52410
## [358,] 23.04883
## [359,] 27.47028
## [360,] 22.01612
## Unemployment , Females, From 15-64 years, From 3 to 5 months
## [355,] -26.02388
## [356,] -22.03556
## [357,] -19.38117
## [358,] -23.65860
## [359,] -18.81823
## [360,] -20.13506
## Unemployment , Females, From 15-64 years, From 6 to 11 months
## [355,] 16.783532
## [356,] 6.733244
## [357,] 10.257872
## [358,] 14.781820
## [359,] 10.410363
## [360,] 8.306611
## Unemployment , Females, From 15-64 years, Less than 1 month
## [355,] 13.696251
## [356,] 12.497935
## [357,] 7.366424
## [358,] 12.318927
## [359,] 10.333482
## [360,] 11.996359
## Unemployment , Females, From 15-64 years, Total
## [355,] -170.4574
## [356,] -178.3692
## [357,] -157.8424
## [358,] -161.3442
## [359,] -190.9925
## [360,] -192.6608
## Unemployment , Males, From 15-64 years
## [355,] -153.0947
## [356,] -172.4467
## [357,] -137.4147
## [358,] -160.7338
## [359,] -117.1098
## [360,] -140.8040
## Unemployment , Males, From 15-64 years, 48 months or over
## [355,] -27.04470
## [356,] -23.33945
## [357,] -31.75924
## [358,] -33.81256
## [359,] -32.67748
## [360,] -29.58414
## Unemployment , Males, From 15-64 years, from 1 to 2 months
## [355,] -14.826563
## [356,] -11.736094
## [357,] -21.387001
## [358,] -7.891433
## [359,] -16.662251
## [360,] -15.264592
## Unemployment , Males, From 15-64 years, from 12 to 17 months
## [355,] 4.631872
## [356,] -3.159601
## [357,] 1.647292
## [358,] 5.572775
## [359,] 7.431482
## [360,] 4.396807
## Unemployment , Males, From 15-64 years, from 18 to 23 months
## [355,] -11.261589
## [356,] -13.876522
## [357,] -11.232225
## [358,] -10.435292
## [359,] -10.445054
## [360,] -7.146492
## Unemployment , Males, From 15-64 years, from 24 to 47 months
## [355,] 21.60521
## [356,] 11.80627
## [357,] 19.95666
## [358,] 19.86230
## [359,] 22.38771
## [360,] 30.08010
## Unemployment , Males, From 15-64 years, from 3 to 5 months
## [355,] 27.50534
## [356,] 20.01161
## [357,] 13.72708
## [358,] 21.29292
## [359,] 27.48875
## [360,] 19.47900
## Unemployment , Males, From 15-64 years, from 6 to 11 months
## [355,] -14.28988
## [356,] -19.49968
## [357,] -21.71209
## [358,] -24.11386
## [359,] -10.76200
## [360,] -21.55460
## Unemployment , Males, From 15-64 years, Less than 1 month
## [355,] 3.633473
## [356,] 3.571436
## [357,] 5.017218
## [358,] 1.844334
## [359,] 6.597317
## [360,] 6.326664
## Unemployment , Total, From 15-64 years, 48 months or over
## [355,] -44.36393
## [356,] -25.84350
## [357,] -38.39034
## [358,] -44.38326
## [359,] -44.94593
## [360,] -23.72349
## Unemployment , Total, From 15-64 years, From 1 to 2 months
## [355,] 67.23921
## [356,] 41.61202
## [357,] 62.58921
## [358,] 48.63882
## [359,] 51.14966
## [360,] 71.90111
## Unemployment , Total, From 15-64 years, From 12 to 17 months
## [355,] 33.03147
## [356,] 33.14263
## [357,] 26.12223
## [358,] 40.53084
## [359,] 24.97231
## [360,] 32.64010
## Unemployment , Total, From 15-64 years, From 18 to 23 months
## [355,] 4.843150
## [356,] 1.775321
## [357,] 3.966986
## [358,] 2.390264
## [359,] 7.010461
## [360,] 4.349881
## Unemployment , Total, From 15-64 years, From 24 to 47 months
## [355,] 37.18644
## [356,] 48.56215
## [357,] 27.12010
## [358,] 31.85748
## [359,] 35.23407
## [360,] 38.05378
## Unemployment , Total, From 15-64 years, From 3 to 5 months
## [355,] -54.20698
## [356,] -44.51155
## [357,] -52.91078
## [358,] -43.29595
## [359,] -43.08030
## [360,] -49.87989
## Unemployment , Total, From 15-64 years, From 6 to 11 months
## [355,] 36.41671
## [356,] 33.61737
## [357,] 34.94187
## [358,] 44.51279
## [359,] 47.74207
## [360,] 32.62204
## Unemployment , Total, From 15-64 years, Less than 1 month
## [355,] 4.721418
## [356,] 9.568220
## [357,] 11.626943
## [358,] -0.215808
## [359,] 8.562253
## [360,] 16.421598
## Unemployment by sex, age, duration. DurationNA not started
## [355,] 69.97419
## [356,] 47.69618
## [357,] 65.41465
## [358,] 21.41457
## [359,] 82.58741
## [360,] 52.72655
## Value added, gross VAT, receivable Wages and salaries
## [355,] 5611.456 -7201.120 9975.333
## [356,] 1110.151 -5618.080 14271.531
## [357,] 4136.464 -5221.767 6960.877
## [358,] 4064.018 -5927.018 16853.393
## [359,] 4795.829 -6543.477 10744.526
## [360,] 3528.674 -5154.082 19135.840
## Wholesale and retail trade, transport, accomodation and food service activities
## [355,] -16738.72
## [356,] -16246.15
## [357,] -13324.60
## [358,] -11598.16
## [359,] -12516.22
## [360,] -11090.22
## Wholesale and retail trade, transport, accomodation and food service activities, Compensation of employees
## [355,] -12769.179
## [356,] -12307.177
## [357,] -9803.067
## [358,] -12187.671
## [359,] -10291.847
## [360,] -11358.411
## Wholesale and retail trade, transport, accomodation and food service activities, Employers' social contributions
## [355,] -989.1350
## [356,] -1347.0145
## [357,] -895.3236
## [358,] -698.5680
## [359,] -959.6141
## [360,] -751.1416
## Wholesale and retail trade, transport, accomodation and food service activities, Wages and salaries
## [355,] 840.5270
## [356,] -1582.9001
## [357,] -918.8832
## [358,] 1167.5545
## [359,] 129.1688
## [360,] -174.6039
## Y_GDP_Belgium
## [355,] 104.2869
## [356,] 113.5526
## [357,] 103.4512
## [358,] 110.4953
## [359,] 116.6313
## [360,] 109.8735# 2. Perform ARIMAX modeling on IFT_RandPhase_FT_Belgium; report (p,d,q) params and quality metrics AIC/BIC
# library(forecast)
IFT_RandPhase_FT_Belgium_Y_train <- IFT_RandPhase_FT_Belgium[1:300, 132]; length(IFT_RandPhase_FT_Belgium_Y_train)## [1] 300IFT_RandPhase_FT_Belgium_Y_test <- IFT_RandPhase_FT_Belgium[301:360]; length(IFT_RandPhase_FT_Belgium_Y_test)## [1] 60# Training and Testing Data Covariates explaining the longitudinal outcome (Y)
IFT_RandPhase_FT_Belgium_X_train <- as.data.frame(IFT_RandPhase_FT_Belgium)[1:300, 1:131]; dim(IFT_RandPhase_FT_Belgium_X_train)## [1] 300 131IFT_RandPhase_FT_Belgium_X_test <- as.data.frame(IFT_RandPhase_FT_Belgium)[301:360, 1:131]; dim(IFT_RandPhase_FT_Belgium_X_test)## [1] 60 131# Outcome Variable to be ARIMAX-modeled, as a timeseries
ts_IFT_RandPhase_FT_Belgium_Y_train <-
ts(IFT_RandPhase_FT_Belgium_Y_train, start=c(2000,1), end=c(2014, 20), frequency = 20)
# Find ARIMAX model: 0 0 2 0 20 0 0
set.seed(1234)
modArima_IFT_RandPhase_FT_Belgium_Y_train <-
auto.arima(ts_IFT_RandPhase_FT_Belgium_Y_train, xreg=as.matrix(IFT_RandPhase_FT_Belgium_X_train))
modArima_IFT_RandPhase_FT_Belgium_Y_train$arma## [1] 1 0 1 0 20 0 0# Regression with ARIMA(0,0,0)(2,0,0)[20] errors
# Coefficients:
# sar1 sar2 Acquisitions less disposals of non-financial non-produced assets
# -0.0743 0.5766 0.0162
#s.e. 0.0625 0.0752 0.0100
#sigma^2 estimated as 72.17: log likelihood=-988.06 AIC=2244.12 AICc=2463.4 BIC=2740.43
pred_arimax_0_0_0_Rand <- forecast(modArima_IFT_RandPhase_FT_Belgium_Y_train, xreg = as.matrix(IFT_RandPhase_FT_Belgium_X_test))
pred_arimax_0_0_0_Rand_2015_2017 <-
ts(pred_arimax_0_0_0_Rand$mean, frequency=20, start=c(2015,1), end=c(2017,20))
pred_arimax_0_0_0_Rand_2015_2017## Time Series:
## Start = c(2015, 1)
## End = c(2017, 20)
## Frequency = 20
## 301 302 303 304 305 306 307 308
## 91.64647 99.52232 88.00664 75.04533 95.50305 92.81822 96.65210 80.69807
## 309 310 311 312 313 314 315 316
## 108.46978 85.19384 95.60342 97.04133 102.45768 102.51519 93.37438 96.96152
## 317 318 319 320 321 322 323 324
## 83.92305 88.47059 96.21913 78.95685 83.61615 93.41899 96.84158 86.80422
## 325 326 327 328 329 330 331 332
## 82.94627 88.84961 82.90144 88.85337 81.34856 81.77752 77.31880 75.49947
## 333 334 335 336 337 338 339 340
## 85.79359 78.42579 92.59481 85.47061 84.34534 87.70395 87.20635 86.48899
## 341 342 343 344 345 346 347 348
## 93.19677 78.80030 90.90051 80.51541 91.40479 87.87573 103.18343 87.24668
## 349 350 351 352 353 354 355 356
## 80.97612 83.04371 89.05571 82.41082 84.24932 91.80920 90.57585 91.56431
## 357 358 359 360
## 75.30763 98.72664 78.43509 101.50172# alternatively:
# pred_arimax_1_0_1_Rand_2015_2017 <- predict(modArima_IFT_RandPhase_FT_Belgium_Y_train,
# n.ahead = 3*20, newxreg = IFT_RandPhase_FT_Belgium_X_test)$pred
sort(modArima_IFT_RandPhase_FT_Belgium_Y_train$coef)[1:10]## Labor cost for LCI (compensation of employees plus taxes minus subsidies)
## -0.8394652
## Unemployment , Females, From 15-64 years, From 18 to 23 months
## -0.5117280
## Labour cost for LCI
## -0.3221205
## ar1
## -0.2859894
## Labor cost other than wages and salaries
## -0.2715188
## Unemployment , Females, From 15-64 years, 48 months or over
## -0.2568183
## Unemployment , Males, From 15-64 years, from 6 to 11 months
## -0.1825009
## Unemployment , Males, From 15-64 years, from 12 to 17 months
## -0.1766393
## Unemployment , Females, From 15-64 years, From 24 to 47 months
## -0.1758125
## Unemployment , Females, From 15-64 years, From 1 to 2 months
## -0.1588077# Labor cost for LCI (compensation of employees plus taxes minus subsidies), effect=-0.71989958
# Unemployment , Females, From 15-64 years, From 18 to 23 months, effect=-0.54541627
# Unemployment , Females, From 15-64 years, 48 months or over, effect=-0.44230677
# Labor cost other than wages and salaries, effect=-0.32854422
# Unemployment , Males, From 15-64 years, from 6 to 11 months, effect=-0.24511374
# Unemployment , Total, From 15-64 years, From 24 to 47 months, effect=-0.19283037
# Agriculture, forestry and fishing - Employers' social contributions, effect=-0.11994897
# Unemployment , Females, From 15-64 years, From 24 to 47 months, effect=-0.10835175
# Unemployment , Females, From 15-64 years, From 1 to 2 months, effect=-0.09093252
# Unemployment , Total, From 15-64 years, From 18 to 23 months, effect=-0.07427297
cor(pred_arimax_0_0_0_Rand$mean, ts_Y_Belgium_test) # -0.15## [1] -0.05033115mean(pred_arimax_0_0_0_Rand_2015_2017) # [1] 87.74201## [1] 88.634411.6 Result Visualization
## Plot the results of the model ARIMAX fitting
ts_Y_Belgium_test <- ts(preprocess_Belgium$Y[301:360, ],
start=c(2015,1), end=c(2017, 20), frequency = 20)
length(ts_Y_Belgium_test)## [1] 60# windows(width=14, height=10)
plot(forecast(BelgiumARIMA, xreg = as.matrix(X_Belgium_test)), # ARIMA forecast
include=60, lwd=4, lty=3, xlab="Time", ylab="GDP Purchasing Power Standards (PPS)",
ylim=c(60, 160),
main = "Spacekime ARIMAX Analytics (Train: 2000-2014; Test: 2015-2017) GDP (PPS) Forecasting\n
based on fitting ARIMAX Models on spline interpolated & kime-transformed Belgium data")
lines(pred_arimax_2_0_1_Nil_2015_2017, col = "green", lwd = 4, lty=2) # Belgium Xreg Nil-Phase Reconstructions
lines(pred_arimax_1_0_0_Swapped_2015_2017, col = "purple", lwd = 4, lty=1) # Belgium Xreg Swapped-Phase Reconstructions
lines(pred_arimax_0_0_0_Rand_2015_2017, col = "orange", lwd = 4, lty=1) # Belgium Xreg Random-Phase Reconstructions
lines(ts_Y_Belgium_test, col = "red", lwd = 6, lty=1) # Observed Y_Test timeseries
legend("topleft", bty="n", legend=c("Belgium Training Data (2000-2014)",
"ARIMAX(4,0,2)-model GDP Forecasting (2015-2017)",
"ARIMAX(2,0,1) Belgium Xreg Nil-Phase Reconstruction (2015-2017)",
"ARIMAX(1,0,0) Belgium Xreg Swapped-Phase Reconstructions (2015-2017)",
"ARIMAX(0,0,0)(2,0,0)[20] Belgium Xreg Random-Phase Reconstructions (2015-2017)",
"Belgium Official Reported GDP (2015-2017)"),
col=c("black", "blue", "green", "purple", "orange", "red"),
lty=c(3,1,2,1, 1, 1), lwd=c(4,4,4,4,4, 6), cex=1.2, x.intersp=1.5, y.intersp=0.7)
text(2013.5, 65, expression(atop(paste("Training Region (2000-2014)"),
paste(Model(GDP) %->% "ARIMAX(p, q, r) ; ",
XReg %==% X[i], " ", i %in% {1 : 131}))), cex=1.2)
text(2016.5, 65, expression(atop(paste("Validation Region (2015-2017)"),
paste(hat(GDP) %<-% "ARIMAX(., ., .); ",
XReg %==% X[i], " ", i %in% {1 : 131}))), cex=1.2)
12 ML Data Analytics
12.1 Data Preprocessing
Find all “Common” features (highly-observed and congruent Econ indicators)
# 1. Find all "Common" features (highly-observed and congruent Econ indicators)
countryNames <- unique(time_series$country); length(countryNames); # countryNames## [1] 31# initialize 3D array of DF's that will store the data for each of the countries into a 2D frame
countryData <- list() # countryData[[listID==Country]][1-time-72, 1-feature-197]
for (i in 1:length(countryNames)) {
countryData[[i]] <- filter(time_series, country == countryNames[i])
}
# Check countryData[[2]][2, 3] == Belgium[2,3]
list_of_dfs_CommonFeatures <- list() # list of data for supersampled countries 360 * 197
# 2. General function that ensures the XReg predictors for ALL 31 EU countries are homologous
completeHomologousX_features <- function (list_of_dfs) {
# delete features that are missing at all time points
for (j in 1:length(list_of_dfs)) {
print(paste0("Pre-processing Country: ...", countryNames[j], "... "))
data = list_of_dfs[[j]]
data = data[ , colSums(is.na(data)) != nrow(data)]
data = dplyr::select(data, !any_of(c("time", "country")))
DataMatrix = as.matrix(data)
DataMatrix = cleardata(DataMatrix)
DataMatrix = DataMatrix[ , colSums(is.na(DataMatrix)) == 0] # remove features with only 1 value
DataMatrix = DataMatrix[ , colSums(DataMatrix) != 0] # remove features with all values=0
# Supersample 72 --*5--> 360 timepoints
DataMatrix = splinecreate(DataMatrix)
DataSuperSample = as.data.frame(DataMatrix) # super-Sample the data
# remove some of features
DataSuperSample = DataSuperSample[, -c(50:80)]; dim(X) # 360 167
# ensure full-rank design matrix, DataSuperSample
DataSuperSample <-
DataSuperSample[ , qr(DataSuperSample)$pivot[seq_len(qr(DataSuperSample)$rank)]]
print(paste0("dim()=(", dim(DataSuperSample)[1], ",", dim(DataSuperSample)[2], ") ..."))
# update the current DF/Country
list_of_dfs_CommonFeatures[[j]] <- DataSuperSample
}
# Identify All Xreg features that are homologous (same feature columns) across All 31 countries
# Identify Common Columns (features)
comCol <- Reduce(intersect, lapply(list_of_dfs_CommonFeatures, colnames))
list_of_dfs_CommonFeatures <- lapply(list_of_dfs_CommonFeatures, function(x) x[comCol])
for (j in 1:length(list_of_dfs_CommonFeatures)) {
list_of_dfs_CommonFeatures[[j]] <- subset(list_of_dfs_CommonFeatures[[j]], select = comCol)
print(paste0("dim(", countryNames[j], ")=(", dim(list_of_dfs_CommonFeatures[[j]])[1],
",", dim(list_of_dfs_CommonFeatures[[j]])[2], ")!")) # 72 * 197
}
return(list_of_dfs_CommonFeatures)
}
# Test completeHomologousX_features: dim(AllCountries)=(360,42)!
list_of_dfs_CommonFeatures <- completeHomologousX_features(countryData); ## [1] "Pre-processing Country: ...Austria... "
## [1] "dim()=(360,147) ..."
## [1] "Pre-processing Country: ...Belgium... "
## [1] "dim()=(360,138) ..."
## [1] "Pre-processing Country: ...Bulgaria... "
## [1] "dim()=(360,139) ..."
## [1] "Pre-processing Country: ...Croatia... "
## [1] "dim()=(360,152) ..."
## [1] "Pre-processing Country: ...Cyprus... "
## [1] "dim()=(360,136) ..."
## [1] "Pre-processing Country: ...Czech Republic... "
## [1] "dim()=(360,158) ..."
## [1] "Pre-processing Country: ...Denmark... "
## [1] "dim()=(360,150) ..."
## [1] "Pre-processing Country: ...Estonia... "
## [1] "dim()=(360,143) ..."
## [1] "Pre-processing Country: ...Finland... "
## [1] "dim()=(360,152) ..."
## [1] "Pre-processing Country: ...France... "
## [1] "dim()=(360,162) ..."
## [1] "Pre-processing Country: ...Germany (until 1990 former territory of the FRG)... "
## [1] "dim()=(360,152) ..."
## [1] "Pre-processing Country: ...Greece... "
## [1] "dim()=(360,146) ..."
## [1] "Pre-processing Country: ...Hungary... "
## [1] "dim()=(360,143) ..."
## [1] "Pre-processing Country: ...Iceland... "
## [1] "dim()=(360,82) ..."
## [1] "Pre-processing Country: ...Ireland... "
## [1] "dim()=(360,158) ..."
## [1] "Pre-processing Country: ...Italy... "
## [1] "dim()=(360,155) ..."
## [1] "Pre-processing Country: ...Latvia... "
## [1] "dim()=(360,143) ..."
## [1] "Pre-processing Country: ...Lithuania... "
## [1] "dim()=(360,142) ..."
## [1] "Pre-processing Country: ...Luxembourg... "
## [1] "dim()=(360,146) ..."
## [1] "Pre-processing Country: ...Malta... "
## [1] "dim()=(360,128) ..."
## [1] "Pre-processing Country: ...Netherlands... "
## [1] "dim()=(360,158) ..."
## [1] "Pre-processing Country: ...Norway... "
## [1] "dim()=(360,151) ..."
## [1] "Pre-processing Country: ...Poland... "
## [1] "dim()=(360,143) ..."
## [1] "Pre-processing Country: ...Portugal... "
## [1] "dim()=(360,142) ..."
## [1] "Pre-processing Country: ...Romania... "
## [1] "dim()=(360,143) ..."
## [1] "Pre-processing Country: ...Slovakia... "
## [1] "dim()=(360,143) ..."
## [1] "Pre-processing Country: ...Slovenia... "
## [1] "dim()=(360,154) ..."
## [1] "Pre-processing Country: ...Spain... "
## [1] "dim()=(360,149) ..."
## [1] "Pre-processing Country: ...Sweden... "
## [1] "dim()=(360,157) ..."
## [1] "Pre-processing Country: ...Switzerland... "
## [1] "dim()=(360,95) ..."
## [1] "Pre-processing Country: ...United Kingdom... "
## [1] "dim()=(360,156) ..."
## [1] "dim(Austria)=(360,42)!"
## [1] "dim(Belgium)=(360,42)!"
## [1] "dim(Bulgaria)=(360,42)!"
## [1] "dim(Croatia)=(360,42)!"
## [1] "dim(Cyprus)=(360,42)!"
## [1] "dim(Czech Republic)=(360,42)!"
## [1] "dim(Denmark)=(360,42)!"
## [1] "dim(Estonia)=(360,42)!"
## [1] "dim(Finland)=(360,42)!"
## [1] "dim(France)=(360,42)!"
## [1] "dim(Germany (until 1990 former territory of the FRG))=(360,42)!"
## [1] "dim(Greece)=(360,42)!"
## [1] "dim(Hungary)=(360,42)!"
## [1] "dim(Iceland)=(360,42)!"
## [1] "dim(Ireland)=(360,42)!"
## [1] "dim(Italy)=(360,42)!"
## [1] "dim(Latvia)=(360,42)!"
## [1] "dim(Lithuania)=(360,42)!"
## [1] "dim(Luxembourg)=(360,42)!"
## [1] "dim(Malta)=(360,42)!"
## [1] "dim(Netherlands)=(360,42)!"
## [1] "dim(Norway)=(360,42)!"
## [1] "dim(Poland)=(360,42)!"
## [1] "dim(Portugal)=(360,42)!"
## [1] "dim(Romania)=(360,42)!"
## [1] "dim(Slovakia)=(360,42)!"
## [1] "dim(Slovenia)=(360,42)!"
## [1] "dim(Spain)=(360,42)!"
## [1] "dim(Sweden)=(360,42)!"
## [1] "dim(Switzerland)=(360,42)!"
## [1] "dim(United Kingdom)=(360,42)!"length(list_of_dfs_CommonFeatures); dim(list_of_dfs_CommonFeatures[[1]]) # Austria data matrix 360*42## [1] 31## [1] 360 42For each country (\(n\)) and each common feature (\(k\)), fit ARIMA model and estimate the parameters \((p,d,q)\) (non-exogenous, just the timeseries model for this feature), (p,d,q) triples for non-seasonal and seasonal effects. For each (Country, Feature) pair, the 9 ARIMA-derived vector includes: ** (ts_avg, forecast_avg, non-seasonal AR, non-seasonal MA, seasonal AR, seasonal MA, period, non-seasonal Diff, seasonal differences)**.
# 3. For each country (n) and each common feature (k), compute (p,d,q) ARIMA models (non-exogenous,
# just the timeseries model for this feature), (p,d,q) triples
# Country * Feature
arimaModels_DF <- list()
#data.frame(matrix(NA, nrow = length(countryNames),
# ncol = dim(list_of_dfs_CommonFeatures[[1]])[2]), row.names=countryNames, stringsAsFactors=T)
# colnames(arimaModels_DF) <- colnames(list_of_dfs_CommonFeatures[[1]])
# list_index <- 1
# arimaModels_ARMA_coefs <- list() # array( , c(31, 9*dim(list_of_dfs_CommonFeatures[[1]])[2]))
# dim(arimaModels_ARMA_coefs) # [1] 31 x 378 == 31 x (9 * 42)
# For each (Country, feature) index, the 9 ARIMA-derived vector includes:
# (ts_avg, forecast_avg, non-seasonal AR, non-seasonal MA, seasonal AR, seasonal MA, period, non-seasonal Diff, seasonal differences)
for(n in 1:(length(list_of_dfs_CommonFeatures))) { # for each Country 1<=n<=31
for (k in 1:(dim(list_of_dfs_CommonFeatures[[1]])[2])) { # for each feature 1<=k<=42
# extract one timeseries (the feature+country time course)
ts = ts(list_of_dfs_CommonFeatures[[n]][ , k],
frequency=20, start=c(2000,1), end=c(2017,20))
set.seed(1234)
arimaModels_DF[[list_index]] <- auto.arima(ts)
# pred_arimaModels_DF = forecast(arimaModels_DF[[list_index]])
# ts_pred_arimaModels_DF <-
# ts(pred_arimaModels_DF$mean, frequency=20, start=c(2015,1), end=c(2017,20))
# ts_pred_arimaModels_DF
arimaModels_ARMA_coefs[[list_index]] <- c (
mean(ts), # time-series average (retrospective)
mean(forecast(arimaModels_DF[[list_index]])$mean), # forecasted TS average (prospective)
arimaModels_DF[[list_index]]$arma) # 7 ARMA estimated parameters
cat("arimaModels_ARMA_coefs[country=", countryNames[n], ", feature=",
colnames(list_of_dfs_CommonFeatures[[1]])[k],
"] Derived-Features=(", round(arimaModels_ARMA_coefs[[list_index]], 2), ") ...")
#print(paste0("arimaModels_DF[country=", countryNames[i], ", feature=",
# colnames(list_of_dfs_CommonFeatures[[1]])[k],
# "]$arma =", arimaModels_DF[[list_index]]$arma))
list_index <- list_index + 1
}
}## arimaModels_ARMA_coefs[country= Austria , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1891.35 2054.26 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 366.84 300.23 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 396.13 817.37 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1129.89 1084.54 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2210.56 2385.81 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 332.77 290.7 0 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 474.77 797.07 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1393.05 1291.91 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 4099.77 4480.25 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 692.31 621.04 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 865.55 1523.63 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 2527.88 2315.51 1 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= All ISCED 2011 levels ] Derived-Features=( 5572.78 5800.98 5 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= All ISCED 2011 levels, Females ] Derived-Features=( 2792.05 2913.6 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= All ISCED 2011 levels, Males ] Derived-Features=( 2772.13 2924.86 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Capital transfers, payable ] Derived-Features=( 1013.03 1328.86 0 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Capital transfers, receivable ] Derived-Features=( 175.56 193.99 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Compensation of employees, payable ] Derived-Features=( 7812.13 9556.26 0 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 9248.14 12862.11 5 0 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1789.3 1973.86 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 330.77 241.97 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Other current transfers, payable ] Derived-Features=( 1876.05 2212.71 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Other current transfers, receivable ] Derived-Features=( 599.03 852.69 1 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Property income, payable ] Derived-Features=( 2041.98 1766.64 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Property income, receivable ] Derived-Features=( 868.36 777.03 2 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Savings, gross ] Derived-Features=( 1370.6 2360.03 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Subsidies, payable ] Derived-Features=( 1139.18 1305.94 2 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Taxes on production and imports, receivable ] Derived-Features=( 10337.03 12412.62 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Total general government expenditure ] Derived-Features=( 36741.11 44554.75 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Total general government revenue ] Derived-Features=( 36394.23 43652.85 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 92.09 109.56 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 109.83 146.81 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 26.53 30.64 0 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 22.87 25.66 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 20.79 25.28 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 49.49 59.08 0 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 21.11 25.94 1 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 41.88 45.72 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 25.2 12.05 2 2 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 21.4 21.99 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 201.86 247.38 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Austria , feature= VAT, receivable ] Derived-Features=( 5526.54 7365.52 4 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2101.84 2315.11 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 410.72 313.44 5 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 898.11 1227.04 2 0 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 784.41 794.19 1 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2584.43 2661.53 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 691.71 524.99 3 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 859.23 1000.63 0 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1047.05 1158.24 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 4690.06 5017.84 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 1098.63 778.56 5 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 1776.92 2294.57 5 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1832.95 1889.54 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= All ISCED 2011 levels ] Derived-Features=( 7028.74 7315.19 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= All ISCED 2011 levels, Females ] Derived-Features=( 3500.85 3647.35 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= All ISCED 2011 levels, Males ] Derived-Features=( 3553.02 3680.02 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Capital transfers, payable ] Derived-Features=( 1410.82 1476.18 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Capital transfers, receivable ] Derived-Features=( 701.98 1085.85 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Compensation of employees, payable ] Derived-Features=( 10355.37 13605.62 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 14228.22 17099.89 1 5 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1936.64 2176.59 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 354.13 278.64 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Other current transfers, payable ] Derived-Features=( 1711.5 2047.56 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Other current transfers, receivable ] Derived-Features=( 503.86 731.53 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Property income, payable ] Derived-Features=( 3483.47 2539.95 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Property income, receivable ] Derived-Features=( 869.16 1033.13 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Savings, gross ] Derived-Features=( 826.44 133.53 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Subsidies, payable ] Derived-Features=( 2411.47 3828.5 4 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Taxes on production and imports, receivable ] Derived-Features=( 10935.55 14654.74 2 1 0 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Total general government expenditure ] Derived-Features=( 44850.55 53147.38 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Total general government revenue ] Derived-Features=( 42832.61 57434.63 3 4 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 173.13 165.03 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 192.97 197.41 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 30.6 29.97 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 27.69 25.84 2 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 30.86 29.67 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 59.15 59.54 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 43.55 43.85 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 51.8 51.39 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 56.62 53.52 2 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 20.47 14.6 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 367.89 349.78 2 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Belgium , feature= VAT, receivable ] Derived-Features=( 5787.02 7689.04 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1581.19 1560.31 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 226.51 132.25 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 526.86 226.14 3 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 829.13 799.06 0 3 0 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1786.46 1802.96 3 4 1 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 325.23 215.72 3 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 349.51 414.63 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1096.32 1120.86 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 3364.44 3300.43 1 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 564.49 300.54 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 854.13 881.84 1 0 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1924.32 1889.24 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= All ISCED 2011 levels ] Derived-Features=( 5107.46 4564.35 5 0 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= All ISCED 2011 levels, Females ] Derived-Features=( 2531.36 2431.13 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= All ISCED 2011 levels, Males ] Derived-Features=( 2542.03 2300.84 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Capital transfers, payable ] Derived-Features=( 74.22 112.18 0 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Capital transfers, receivable ] Derived-Features=( 99.76 140.72 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Compensation of employees, payable ] Derived-Features=( 748.01 1235.25 5 2 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 450.94 710.59 2 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1380.43 1449.14 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 168.28 117.5 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Other current transfers, payable ] Derived-Features=( 152.54 288.29 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Other current transfers, receivable ] Derived-Features=( 240.99 268.11 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Property income, payable ] Derived-Features=( 96.82 101.54 2 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Property income, receivable ] Derived-Features=( 103.37 102.35 2 1 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Savings, gross ] Derived-Features=( 228.54 230.41 2 0 0 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Subsidies, payable ] Derived-Features=( 90.92 186.17 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Taxes on production and imports, receivable ] Derived-Features=( 1230.15 1977.17 1 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Total general government expenditure ] Derived-Features=( 3059.93 5330.98 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Total general government revenue ] Derived-Features=( 2917.27 4523.29 0 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 167.07 74.93 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 292.37 -606.76 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 18.82 9.58 3 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 25.56 12.55 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 32.22 15.89 2 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 34.01 16.59 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 50.48 30.95 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 76.38 214.33 2 2 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 58.07 32.23 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 16.69 8.53 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 516.79 -1119.16 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Bulgaria , feature= VAT, receivable ] Derived-Features=( 755.73 1240.69 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 837.64 845.46 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 131.78 76.48 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 221.11 289.82 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 488.46 487.79 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 994.26 967.61 1 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 135.16 87.13 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 178.48 208 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 681.16 647.09 1 2 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1827.83 1816.68 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 262.02 163.11 1 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 389.37 500.29 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1170.63 1136.16 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= All ISCED 2011 levels ] Derived-Features=( 2821.94 2702.49 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= All ISCED 2011 levels, Females ] Derived-Features=( 1412.39 1365.57 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= All ISCED 2011 levels, Males ] Derived-Features=( 1404.17 1353.74 1 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Capital transfers, payable ] Derived-Features=( 181.48 195.5 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Capital transfers, receivable ] Derived-Features=( 44.1 138.44 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Compensation of employees, payable ] Derived-Features=( 1190.88 1421.55 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 675.39 689.04 0 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 714.22 730.32 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 107.01 58.15 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Other current transfers, payable ] Derived-Features=( 148.65 208.93 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Other current transfers, receivable ] Derived-Features=( 134.21 246.97 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Property income, payable ] Derived-Features=( 266.83 329.84 1 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Property income, receivable ] Derived-Features=( 115.68 117.57 0 0 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Savings, gross ] Derived-Features=( 511.41 328.02 2 2 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Subsidies, payable ] Derived-Features=( 223.27 150.81 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Taxes on production and imports, receivable ] Derived-Features=( 1936.79 2417.1 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Total general government expenditure ] Derived-Features=( 4923 5642.71 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Total general government revenue ] Derived-Features=( 4540.96 5369.83 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 118.09 84.29 2 3 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 129.15 94.17 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 12.14 13.84 1 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 16.13 19.42 1 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 19.07 14.68 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 22.96 27.7 1 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 28.98 9.02 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 30.65 37.86 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 36.57 31.71 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 8.89 10.72 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 236.93 176.61 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Croatia , feature= VAT, receivable ] Derived-Features=( 1578.57 1800.72 0 2 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 182.4 204.09 1 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 34.73 26.34 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 85.56 107.6 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 66.2 71.06 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 209.26 217.85 2 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 50 39.25 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 70.93 73.71 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 88.21 95.36 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 394.72 416.02 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 86.23 61.1 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 155.56 195.16 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 152.87 157.95 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= All ISCED 2011 levels ] Derived-Features=( 531.31 560.1 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= All ISCED 2011 levels, Females ] Derived-Features=( 276.98 299.09 1 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= All ISCED 2011 levels, Males ] Derived-Features=( 257.25 278.4 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Capital transfers, payable ] Derived-Features=( 40.52 -10.16 1 3 1 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Capital transfers, receivable ] Derived-Features=( 26.13 22.03 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Compensation of employees, payable ] Derived-Features=( 563.4 614.02 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 406.32 459.4 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 191.8 253.3 2 2 1 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 31.82 22.59 2 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Other current transfers, payable ] Derived-Features=( 97.38 113.96 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Other current transfers, receivable ] Derived-Features=( 43.1 51.51 2 2 0 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Property income, payable ] Derived-Features=( 122.17 164.77 0 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Property income, receivable ] Derived-Features=( 39.91 43.11 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Savings, gross ] Derived-Features=( 44.34 80.06 3 2 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Subsidies, payable ] Derived-Features=( 22.08 37.62 1 0 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Taxes on production and imports, receivable ] Derived-Features=( 600.4 803.32 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Total general government expenditure ] Derived-Features=( 1628.06 1890.26 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Total general government revenue ] Derived-Features=( 1546.8 1863.78 0 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 17.17 23.92 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 18.6 24.74 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 3.02 3.92 0 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 3.75 4.76 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 3.45 2.23 3 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 5.94 9.35 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 4.25 4.31 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 7.7 8.79 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 7.01 6.62 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 2.88 3.22 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 34.04 52.82 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Cyprus , feature= VAT, receivable ] Derived-Features=( 334.12 522.46 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2270.74 2339.86 0 2 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 195.75 125.86 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 384.85 649.8 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1689.15 1624.89 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2869.2 2921.53 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 154.86 107.74 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 483.14 697.59 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 2244.28 2141.71 3 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 5155.24 5210.4 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 352.28 226.71 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 847.7 1275.51 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 3921.23 3702.47 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= All ISCED 2011 levels ] Derived-Features=( 7192.98 6907.2 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= All ISCED 2011 levels, Females ] Derived-Features=( 3582 3386.03 2 4 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= All ISCED 2011 levels, Males ] Derived-Features=( 3628.17 3519.04 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Capital transfers, payable ] Derived-Features=( 638.74 337.76 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Capital transfers, receivable ] Derived-Features=( 377.13 599.42 1 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Compensation of employees, payable ] Derived-Features=( 2928.58 4590.72 1 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 2550.17 3633.35 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2085.18 2262.56 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 148.96 85.86 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Other current transfers, payable ] Derived-Features=( 559.47 935.01 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Other current transfers, receivable ] Derived-Features=( 283.61 423.46 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Property income, payable ] Derived-Features=( 384.57 407.85 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Property income, receivable ] Derived-Features=( 282.04 414.18 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Savings, gross ] Derived-Features=( 1006.77 2463.13 2 2 0 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Subsidies, payable ] Derived-Features=( 645.2 1116.71 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Taxes on production and imports, receivable ] Derived-Features=( 3793.96 6116.98 5 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Total general government expenditure ] Derived-Features=( 14248.68 19845.39 0 1 0 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Total general government revenue ] Derived-Features=( 13269.56 19672.77 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 182.16 53.13 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 161.4 56.4 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 19.96 14.69 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 25.39 8.89 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 32.56 16.61 0 2 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 39.75 23.85 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 41.45 14.68 1 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 51.77 21.53 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 67.6 38.15 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 22.13 16.44 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 336.01 134.37 2 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Czech Republic , feature= VAT, receivable ] Derived-Features=( 2252.62 3747.31 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1355.09 1390.18 1 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 284.24 228.94 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 466.47 572.14 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 577.09 544.47 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1504.31 1524.15 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 349.03 334.87 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 407.92 460.12 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 722.39 659.52 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2861.48 2926.24 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 633.8 622.31 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 882.32 1075.23 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1288.94 1202.67 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= All ISCED 2011 levels ] Derived-Features=( 3592.93 3688.83 0 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= All ISCED 2011 levels, Females ] Derived-Features=( 1780.11 1822.09 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= All ISCED 2011 levels, Males ] Derived-Features=( 1815.8 1867.6 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Capital transfers, payable ] Derived-Features=( 296.74 66.63 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Capital transfers, receivable ] Derived-Features=( 6.99 54.97 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Compensation of employees, payable ] Derived-Features=( 9461.13 12037.38 2 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 17179.76 21755.48 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1271.96 1314.88 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 258.14 224.46 3 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Other current transfers, payable ] Derived-Features=( 1860.67 2233.18 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Other current transfers, receivable ] Derived-Features=( 627.11 777.99 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Property income, payable ] Derived-Features=( 1150.74 701.88 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Property income, receivable ] Derived-Features=( 1123.32 767.85 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Savings, gross ] Derived-Features=( 2509.66 3057.48 2 1 0 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Subsidies, payable ] Derived-Features=( 1149 1356.25 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Taxes on production and imports, receivable ] Derived-Features=( 9735.97 12194.47 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Total general government expenditure ] Derived-Features=( 31228.91 38986.84 3 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Total general government revenue ] Derived-Features=( 31407.71 39177.8 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 79.38 78.9 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 81.19 95.2 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 19.15 20.89 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 15.44 12.21 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 13.95 13.74 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 37.42 44.71 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 14.56 16.37 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 30.86 21.76 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 26.97 29.64 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 29.51 28.21 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 163.37 184.08 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Denmark , feature= VAT, receivable ] Derived-Features=( 5474.56 7216.71 4 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 320.83 318.29 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 22.96 21.67 3 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 138.09 162.19 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 159.13 132.94 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 337.49 343.52 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 45.98 46.43 3 2 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 88.72 102.53 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 204.31 196.21 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 658.14 670.85 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 68.8 68.02 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 225.45 255.87 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 362.77 330.62 1 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= All ISCED 2011 levels ] Derived-Features=( 896.79 850.16 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= All ISCED 2011 levels, Females ] Derived-Features=( 461.12 422.09 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= All ISCED 2011 levels, Males ] Derived-Features=( 436.4 413.48 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Capital transfers, payable ] Derived-Features=( 30.28 41.15 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Capital transfers, receivable ] Derived-Features=( 43.2 33.63 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Compensation of employees, payable ] Derived-Features=( 414.38 659.22 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 283.63 441.39 2 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 292.24 309.2 2 2 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 18.9 19.77 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Other current transfers, payable ] Derived-Features=( 62.29 100.6 0 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Other current transfers, receivable ] Derived-Features=( 45.26 69.67 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Property income, payable ] Derived-Features=( 5.36 2.99 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Property income, receivable ] Derived-Features=( 49.38 57.17 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Savings, gross ] Derived-Features=( 196.48 270.73 1 4 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Subsidies, payable ] Derived-Features=( 28.97 23.11 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Taxes on production and imports, receivable ] Derived-Features=( 534.51 834.38 0 1 0 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Total general government expenditure ] Derived-Features=( 1489.73 2360.93 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Total general government revenue ] Derived-Features=( 1538.15 2368.3 1 2 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 29.14 19.77 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 37.49 17.5 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 6.7 5.5 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 8.04 10.22 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 8.54 7.65 1 3 0 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 9.99 9.58 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 9.86 9.79 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 10.86 11.28 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 11.19 4.57 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 7.49 6.17 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 63.6 28.41 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Estonia , feature= VAT, receivable ] Derived-Features=( 337.7 562.19 3 2 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1268.58 1266.29 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 186.24 108.92 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 533.76 623.31 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 545.54 521.72 0 5 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1350.05 1350.18 1 1 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 263.86 187.98 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 418.31 489.23 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 670.77 713.64 2 2 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2620.71 2626.43 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 448.99 248.38 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 937.57 1091.69 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1218.4 1234.45 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= All ISCED 2011 levels ] Derived-Features=( 3478.89 3421.6 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= All ISCED 2011 levels, Females ] Derived-Features=( 1725.11 1707.55 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= All ISCED 2011 levels, Males ] Derived-Features=( 1750.54 1732.52 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Capital transfers, payable ] Derived-Features=( 158.35 187.92 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Capital transfers, receivable ] Derived-Features=( 168.46 257.13 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Compensation of employees, payable ] Derived-Features=( 6098.63 7685.3 5 1 0 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 6226.58 5255.96 3 2 1 2 20 0 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1148.47 1088.12 2 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 155.97 94.17 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Other current transfers, payable ] Derived-Features=( 1167.27 1504.83 2 2 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Other current transfers, receivable ] Derived-Features=( 151.3 182.51 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Property income, payable ] Derived-Features=( 681.9 554.45 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Property income, receivable ] Derived-Features=( 1596.5 1552.47 1 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Savings, gross ] Derived-Features=( 363.91 -2700.41 2 2 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Subsidies, payable ] Derived-Features=( 600.28 681.87 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Taxes on production and imports, receivable ] Derived-Features=( 6102.55 7939.35 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Total general government expenditure ] Derived-Features=( 23527.29 29987.95 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Total general government revenue ] Derived-Features=( 24117.38 34760.91 2 0 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 103.84 109.88 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 118.54 121.4 1 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 31.64 33 2 2 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 21.72 21.72 0 0 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 14.79 13.95 2 1 1 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 57.27 56.88 3 0 0 2 20 0 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 16.98 14.09 0 1 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 41.76 41.76 0 0 0 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 31.08 28.59 1 1 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 35.64 42.35 0 2 0 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 223.02 231.08 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Finland , feature= VAT, receivable ] Derived-Features=( 3906.4 5152.95 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 13212.41 13913.15 2 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 4065.01 -10674.87 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 4833.56 4965.24 5 0 1 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 5592.67 6064.93 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 14677.61 15233.42 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 4418.11 -5250.68 0 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 4560.82 4866.39 4 0 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 6853.87 7228.7 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 27987.49 29245.21 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 9104.79 16536.22 5 0 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 5758.41 -1194.72 5 0 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 12403.75 12844.47 0 2 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= All ISCED 2011 levels ] Derived-Features=( 39703.95 40819.96 3 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= All ISCED 2011 levels, Females ] Derived-Features=( 20258.43 20822.99 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= All ISCED 2011 levels, Males ] Derived-Features=( 19534.47 20320.44 1 2 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Capital transfers, payable ] Derived-Features=( 5070.23 8238.97 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Capital transfers, receivable ] Derived-Features=( 1607.5 2858.64 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Compensation of employees, payable ] Derived-Features=( 61649.71 73427.18 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 57062.62 76108.15 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 10190.65 10294.21 4 0 2 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 2575.92 1645.3 2 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Other current transfers, payable ] Derived-Features=( 15526.85 20426.45 2 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Other current transfers, receivable ] Derived-Features=( 4061.02 5162.4 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Property income, payable ] Derived-Features=( 12034.07 10326.13 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Property income, receivable ] Derived-Features=( 3871.83 5142.4 5 0 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Savings, gross ] Derived-Features=( 5464.74 8602.51 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Subsidies, payable ] Derived-Features=( 8592.99 15760.58 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Taxes on production and imports, receivable ] Derived-Features=( 73942.97 91865.14 1 1 0 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Total general government expenditure ] Derived-Features=( 263251.3 343885.3 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Total general government revenue ] Derived-Features=( 244904.6 310046.5 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 1149.38 1447.6 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 1268.03 1494.25 2 1 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 212.51 238.25 2 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 264.68 508.18 2 2 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 235.37 227.12 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 469.92 558.48 2 1 1 2 20 0 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 199.04 -74.91 5 0 1 2 20 0 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 343.59 348.88 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 469.41 489.01 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 241.3 134.37 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 2284.5 3052.85 3 4 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= France , feature= VAT, receivable ] Derived-Features=( 33396.5 41107.58 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 18733.05 19565.14 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 2909.22 2477.48 2 2 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 4499.04 5146.59 1 2 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 11326.21 11898.08 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 22100.6 22778.08 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 3253.9 3291.18 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 6192.56 6806.1 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 12476.89 12541.4 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 40847.94 42155.51 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 6095.06 5643.6 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 10795.96 11868.34 1 3 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 23831.38 24330.4 1 2 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= All ISCED 2011 levels ] Derived-Features=( 53572.85 53547.61 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= All ISCED 2011 levels, Females ] Derived-Features=( 26580.82 26437.38 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= All ISCED 2011 levels, Males ] Derived-Features=( 26885.58 27304.45 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Capital transfers, payable ] Derived-Features=( 9636.92 9625.31 1 0 0 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Capital transfers, receivable ] Derived-Features=( 2657.55 3450.91 2 2 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Compensation of employees, payable ] Derived-Features=( 50322.44 60897.17 4 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 76053.31 110150 1 3 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 17525.57 19375.45 0 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 2468.3 2330.65 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Other current transfers, payable ] Derived-Features=( 13787.41 19833.52 3 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Other current transfers, receivable ] Derived-Features=( 4632.74 5256.68 3 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Property income, payable ] Derived-Features=( 14667.15 7233.34 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Property income, receivable ] Derived-Features=( 4723.07 4743.66 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Savings, gross ] Derived-Features=( 13818.33 36538.15 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Subsidies, payable ] Derived-Features=( 6694.45 6796.34 2 2 0 2 20 0 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Taxes on production and imports, receivable ] Derived-Features=( 78464.69 97512.32 5 0 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Total general government expenditure ] Derived-Features=( 284937.3 358741.8 4 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Total general government revenue ] Derived-Features=( 293740.3 357991.6 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 1213.95 874.83 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 1622.58 1030.24 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 221.22 156.44 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 210.95 107.94 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 241.01 143.97 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 376.77 259.02 2 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 252.46 163.38 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 362.45 179.53 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 479.09 -12.25 2 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 218.2 200.12 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 2661.95 1221.34 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Germany (until 1990 former territory of the FRG) , feature= VAT, receivable ] Derived-Features=( 44754.3 55494.5 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2022.03 2136.91 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 536.16 369.33 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 623.31 985.61 1 0 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 866.68 896.48 2 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2764.37 2644.04 0 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 1019.15 650.2 0 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 641.03 769.37 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1113 1165.84 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 4793.99 4766.11 0 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 1537.62 1012.53 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 1265.89 1687.22 0 1 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1984.31 2023.91 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= All ISCED 2011 levels ] Derived-Features=( 7314.74 4510.21 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= All ISCED 2011 levels, Females ] Derived-Features=( 3677.65 3226.97 2 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= All ISCED 2011 levels, Males ] Derived-Features=( 3631.01 2255.22 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Capital transfers, payable ] Derived-Features=( 875.57 961.27 2 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Capital transfers, receivable ] Derived-Features=( 962.33 1080.24 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Compensation of employees, payable ] Derived-Features=( 5565.46 5068.94 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 4470.95 4597.53 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1632.78 1614.91 4 1 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 438.02 284.44 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Other current transfers, payable ] Derived-Features=( 830.39 737.34 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Other current transfers, receivable ] Derived-Features=( 794.6 837.92 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Property income, payable ] Derived-Features=( 2295.56 1216.51 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Property income, receivable ] Derived-Features=( 333.98 199.48 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Savings, gross ] Derived-Features=( -1199.82 706.84 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Subsidies, payable ] Derived-Features=( 175.93 421.51 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Taxes on production and imports, receivable ] Derived-Features=( 6538.03 8553.34 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Total general government expenditure ] Derived-Features=( 24119.73 22006.37 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Total general government revenue ] Derived-Features=( 20472.78 21881.18 2 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 412.92 591.1 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 338.99 539.76 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 34.81 27.66 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 41.35 42.05 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 50.71 60.41 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 69.64 56.31 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 96.46 108.43 1 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 84.79 75.79 1 4 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 108.27 105.12 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 26.77 28.27 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 770.41 1197.77 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Greece , feature= VAT, receivable ] Derived-Features=( 3367.73 3689.68 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1946.18 2051.2 0 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 290.24 261.52 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 494.58 600.33 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1151.31 1196.37 1 2 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2287.46 2510.96 0 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 318.88 317.95 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 422.85 508.5 2 0 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1555 1661.62 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 4233.99 4596.57 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 614.4 575.64 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 916.12 1148.3 2 2 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 2704.99 2839.18 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= All ISCED 2011 levels ] Derived-Features=( 6719.63 6442.22 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= All ISCED 2011 levels, Females ] Derived-Features=( 3453.53 2945.18 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= All ISCED 2011 levels, Males ] Derived-Features=( 3287.9 3162.88 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Capital transfers, payable ] Derived-Features=( 497.01 805.5 2 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Capital transfers, receivable ] Derived-Features=( 324.29 532.59 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Compensation of employees, payable ] Derived-Features=( 2548.63 3413.1 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 1893.9 2442.98 2 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1796.27 2038.82 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 250.67 242.36 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Other current transfers, payable ] Derived-Features=( 630.56 994.03 1 0 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Other current transfers, receivable ] Derived-Features=( 282.61 442.58 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Property income, payable ] Derived-Features=( 947.34 850.43 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Property income, receivable ] Derived-Features=( 198.94 96.92 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Savings, gross ] Derived-Features=( 7.44 957 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Subsidies, payable ] Derived-Features=( 314.98 386.74 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Taxes on production and imports, receivable ] Derived-Features=( 3817.67 5518.51 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Total general government expenditure ] Derived-Features=( 11432.19 14855.82 2 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Total general government revenue ] Derived-Features=( 10405.41 14952.88 1 2 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 146.58 103.76 2 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 179.57 101.08 3 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 18.87 10.07 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 25.85 16.29 0 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 37.87 22.43 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 36.29 24.54 3 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 49.05 20.47 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 48.53 24.01 1 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 68.73 39.49 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 24.37 24.75 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 323.87 186.25 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Hungary , feature= VAT, receivable ] Derived-Features=( 2006.47 3221.78 1 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 81.27 89.35 0 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 34.6 14.64 0 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 27.24 38.21 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 22.47 24.32 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 89.38 99.39 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 32.02 26.44 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 32.04 56.3 5 0 1 2 20 0 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 34.66 38.65 2 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 171.57 190.8 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 61.29 47.68 1 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 66.03 114.71 4 0 2 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 59.04 68.74 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= All ISCED 2011 levels ] Derived-Features=( 198.84 214.57 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= All ISCED 2011 levels, Females ] Derived-Features=( 97.69 105.06 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= All ISCED 2011 levels, Males ] Derived-Features=( 100.32 110.56 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Capital transfers, payable ] Derived-Features=( 88.66 137.8 1 0 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Capital transfers, receivable ] Derived-Features=( 41.18 103.44 2 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Compensation of employees, payable ] Derived-Features=( 449.05 811.71 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 587.5 1068.03 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 77.41 87.45 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 18.56 15.69 0 2 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Other current transfers, payable ] Derived-Features=( 54.78 90.89 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Other current transfers, receivable ] Derived-Features=( 16.7 22.19 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Property income, payable ] Derived-Features=( 120.5 209.87 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Property income, receivable ] Derived-Features=( 89.91 96.56 3 1 0 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Savings, gross ] Derived-Features=( 144.28 299.9 3 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Subsidies, payable ] Derived-Features=( 56.82 86.49 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Taxes on production and imports, receivable ] Derived-Features=( 501.33 794.79 1 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Total general government expenditure ] Derived-Features=( 1441.17 2250.59 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Total general government revenue ] Derived-Features=( 1476.68 2243.6 3 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 3.25 2.28 3 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 4.18 2.28 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 1.7 2.14 2 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 1.63 1.63 0 0 0 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 1.61 1.61 1 0 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 2.14 1.7 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 1.23 1.28 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 2.23 1.65 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 1.78 1.76 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 1.95 2.27 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 7.43 2.02 3 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Iceland , feature= VAT, receivable ] Derived-Features=( 295.49 512.92 1 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 916.25 1068.94 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 192.6 -1096.83 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 432.59 430.94 5 0 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 412.83 405.49 2 2 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1178.25 1221.86 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 405.73 -429.34 3 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 407.75 395.6 5 0 1 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 515.06 638.56 2 2 1 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2093.99 2422.36 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 595.58 -2600.03 1 2 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 830.99 1480.36 3 0 2 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 923.49 909.91 0 0 2 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= All ISCED 2011 levels ] Derived-Features=( 2931.24 3167.27 3 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= All ISCED 2011 levels, Females ] Derived-Features=( 1473.56 1602.4 3 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= All ISCED 2011 levels, Males ] Derived-Features=( 1466.75 1588.65 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Capital transfers, payable ] Derived-Features=( 1139.41 126.29 0 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Capital transfers, receivable ] Derived-Features=( 342.4 346.7 2 4 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Compensation of employees, payable ] Derived-Features=( 5056.69 6179.62 4 1 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 5639.57 7469.68 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 851.69 999.23 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 166.35 -936.87 3 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Other current transfers, payable ] Derived-Features=( 703.74 908.46 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Other current transfers, receivable ] Derived-Features=( 53.9 53.28 0 0 1 2 20 0 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Property income, payable ] Derived-Features=( 1143.65 1423.11 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Property income, receivable ] Derived-Features=( 475.22 355.54 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Savings, gross ] Derived-Features=( -260.14 1271.93 4 4 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Subsidies, payable ] Derived-Features=( 441.56 442.13 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Taxes on production and imports, receivable ] Derived-Features=( 5203.47 6583.63 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Total general government expenditure ] Derived-Features=( 18089.72 19509.31 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Total general government revenue ] Derived-Features=( 15497.7 19004.89 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 69.03 85.52 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 115.39 101.88 0 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 14.72 17.03 3 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 13.9 8.32 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 18.44 14.72 1 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 28.52 25.3 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 19.33 11.01 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 27.84 22.04 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 28.76 13.61 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 14.46 10.96 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 186.68 176.82 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Ireland , feature= VAT, receivable ] Derived-Features=( 2794.92 3330.59 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 10048.4 10992.28 0 1 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 3083.31 2576.08 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 2053.12 2872.2 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 4842.26 5138.34 0 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 14287.43 14529.86 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 6378.75 3692.08 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 1848.94 2292.49 0 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 6039.3 7327.68 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 24282.07 25446.35 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 9538.84 4217 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 4063.93 5078.54 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 10935.14 12111.48 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= All ISCED 2011 levels ] Derived-Features=( 38775.64 38668.86 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= All ISCED 2011 levels, Females ] Derived-Features=( 19484.4 19287 4 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= All ISCED 2011 levels, Males ] Derived-Features=( 19278.01 19308.28 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Capital transfers, payable ] Derived-Features=( 6120.22 6135.16 2 2 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Capital transfers, receivable ] Derived-Features=( 2166.46 2165.25 2 2 0 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Compensation of employees, payable ] Derived-Features=( 39233.59 41061.56 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 53728.67 64484.92 1 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 8864.75 9615.99 0 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 2656.18 2192.36 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Other current transfers, payable ] Derived-Features=( 5959.84 7056.09 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Other current transfers, receivable ] Derived-Features=( 4595.93 5134.95 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Property income, payable ] Derived-Features=( 18153.94 17365.75 2 1 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Property income, receivable ] Derived-Features=( 2390.26 2866.38 1 1 0 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Savings, gross ] Derived-Features=( 2222.79 2202.14 0 1 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Subsidies, payable ] Derived-Features=( 5473.66 7453.56 1 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Taxes on production and imports, receivable ] Derived-Features=( 54841.38 63483.9 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Total general government expenditure ] Derived-Features=( 188523.1 215189.3 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Total general government revenue ] Derived-Features=( 173372.1 202780.2 5 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 1151.44 1415.85 0 1 0 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 1170.92 1486.72 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 139.22 189.02 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 151.07 171.81 1 3 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 165.9 175.16 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 260.48 320.28 0 4 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 305.86 417.54 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 290.9 324.5 2 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 325.08 346.58 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 108.73 106.75 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 2264.5 2748.24 1 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Italy , feature= VAT, receivable ] Derived-Features=( 22711.77 27727.55 2 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 509.77 473.66 1 3 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 40.81 21.05 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 169.81 233.8 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 297.11 222.07 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 519.77 459.56 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 86.24 55.7 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 101.32 120.41 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 333.74 302.39 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1029.63 961.37 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 130.45 84.88 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 271.99 335.41 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 633.61 511.13 3 4 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= All ISCED 2011 levels ] Derived-Features=( 1330.92 1115.62 5 0 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= All ISCED 2011 levels, Females ] Derived-Features=( 738.9 643.11 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= All ISCED 2011 levels, Males ] Derived-Features=( 617.17 524.2 5 0 1 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Capital transfers, payable ] Derived-Features=( 34.04 34.11 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Capital transfers, receivable ] Derived-Features=( 49.98 82.22 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Compensation of employees, payable ] Derived-Features=( 450.46 694.51 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 347.09 647.56 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 452.52 430.3 2 2 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 31.99 19.09 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Other current transfers, payable ] Derived-Features=( 137.47 207.43 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Other current transfers, receivable ] Derived-Features=( 56.93 65.32 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Property income, payable ] Derived-Features=( 50.74 59.79 1 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Property income, receivable ] Derived-Features=( 41.54 58.18 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Savings, gross ] Derived-Features=( 81.08 265.57 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Subsidies, payable ] Derived-Features=( 53.78 82.31 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Taxes on production and imports, receivable ] Derived-Features=( 569.11 1000.69 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Total general government expenditure ] Derived-Features=( 1736.81 2795.69 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Total general government revenue ] Derived-Features=( 1601.72 2452.47 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 49.51 27.9 2 1 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 68.69 56.94 5 3 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 8.75 8.22 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 11.93 9 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 12.86 10.39 1 2 0 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 16.32 13.2 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 15.31 0.42 3 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 21.63 18.04 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 23.84 21.55 2 2 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 8.74 7.86 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 123.82 114.77 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Latvia , feature= VAT, receivable ] Derived-Features=( 332.3 615.54 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 749.49 717.39 2 2 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 38.06 18.6 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 254.44 797.37 3 4 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 457.14 766.23 2 1 2 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 752.52 693.25 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 70.42 37.38 2 3 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 176.92 96.16 5 0 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 475.92 413.28 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1348.3 287.62 5 0 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 110.69 45.63 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 281 -274.95 4 0 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 830.74 659.31 4 1 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= All ISCED 2011 levels ] Derived-Features=( 2110.83 1831.8 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= All ISCED 2011 levels, Females ] Derived-Features=( 938.83 336.27 5 0 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= All ISCED 2011 levels, Males ] Derived-Features=( 933.44 777.68 5 0 2 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Capital transfers, payable ] Derived-Features=( 71.2 64.87 2 0 0 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Capital transfers, receivable ] Derived-Features=( 94.66 86.9 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Compensation of employees, payable ] Derived-Features=( 681 946.5 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 445.77 607.09 2 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 598.58 456.38 3 1 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 32.72 18.62 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Other current transfers, payable ] Derived-Features=( 91.13 172.04 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Other current transfers, receivable ] Derived-Features=( 81.94 127.69 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Property income, payable ] Derived-Features=( 91.71 129.99 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Property income, receivable ] Derived-Features=( 38.33 38.33 0 0 0 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Savings, gross ] Derived-Features=( 64.41 396.7 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Subsidies, payable ] Derived-Features=( 35.23 39.12 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Taxes on production and imports, receivable ] Derived-Features=( 780.72 1312.33 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Total general government expenditure ] Derived-Features=( 2473.33 3695.18 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Total general government revenue ] Derived-Features=( 2338.42 3870.05 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( -1.9 -829.48 2 2 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( -6.87 -45.59 0 2 2 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 10.61 9.74 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 14.96 12.98 1 4 0 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 5.04 -36.81 2 0 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 17.22 15.05 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 21.72 9.09 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( -0.18 3.69 2 2 1 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( -1.98 -140.06 5 1 2 2 20 0 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 17.21 15.77 1 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( -18.54 -60.01 2 2 1 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Lithuania , feature= VAT, receivable ] Derived-Features=( 521.52 828.1 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 101.48 136.17 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 24.33 19.6 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 35.79 54.18 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 38.04 38.64 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 154.92 217.29 5 0 2 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 29.9 29.19 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 47.36 55.57 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 50.43 48.26 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 223.01 532.18 3 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 62.95 -66.51 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 53.24 339.82 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 88.4 88.82 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= All ISCED 2011 levels ] Derived-Features=( 335.23 403.04 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= All ISCED 2011 levels, Females ] Derived-Features=( 165.71 202.3 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= All ISCED 2011 levels, Males ] Derived-Features=( 171.98 208.65 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Capital transfers, payable ] Derived-Features=( 116.35 116.35 0 0 0 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Capital transfers, receivable ] Derived-Features=( 21.84 30.1 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Compensation of employees, payable ] Derived-Features=( 877.69 1243.55 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 1429.34 2186.42 3 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 94.97 124.99 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 21.93 21.37 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Other current transfers, payable ] Derived-Features=( 297.35 469.61 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Other current transfers, receivable ] Derived-Features=( 18.04 34.25 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Property income, payable ] Derived-Features=( 36.39 55.37 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Property income, receivable ] Derived-Features=( 154.57 165.34 1 2 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Savings, gross ] Derived-Features=( 633.66 946.12 3 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Subsidies, payable ] Derived-Features=( 129.9 190.05 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Taxes on production and imports, receivable ] Derived-Features=( 1234.69 1593.33 0 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Total general government expenditure ] Derived-Features=( 4145.63 6328.12 3 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Total general government revenue ] Derived-Features=( 4309.19 6493.83 1 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 5.95 8.34 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 5.69 9.9 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 1.28 1.55 2 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 1.07 1.26 0 2 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 1.12 1.14 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 2.51 2.63 0 2 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 1.48 1.79 2 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 2.53 2.85 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 2.46 3.26 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 1.43 2.08 3 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 12.14 15.71 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Luxembourg , feature= VAT, receivable ] Derived-Features=( 649.42 818.93 2 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 67.27 79.44 4 0 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 26.15 26.63 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 18.73 22.43 5 0 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 18.79 31.86 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 114.16 126.66 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 67.73 56.58 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 23.21 36.19 5 0 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 36.64 64.88 4 0 2 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 188.39 213.74 5 0 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 96.85 80.91 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 33.36 57.76 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 59.34 80.21 5 0 2 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= All ISCED 2011 levels ] Derived-Features=( 303.12 309.73 0 2 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= All ISCED 2011 levels, Females ] Derived-Features=( 139.73 150.27 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= All ISCED 2011 levels, Males ] Derived-Features=( 134.93 207.69 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Capital transfers, payable ] Derived-Features=( 15.11 47.78 5 0 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Capital transfers, receivable ] Derived-Features=( 26.5 27.14 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Compensation of employees, payable ] Derived-Features=( 211.91 334.73 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 204.11 383.53 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 56.84 80.21 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 23.2 23.85 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Other current transfers, payable ] Derived-Features=( 29.86 52.27 4 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Other current transfers, receivable ] Derived-Features=( 5.44 7.91 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Property income, payable ] Derived-Features=( 49.84 53.08 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Property income, receivable ] Derived-Features=( 22.73 21.43 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Savings, gross ] Derived-Features=( -3.39 210.25 2 2 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Subsidies, payable ] Derived-Features=( 20.76 35.96 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Taxes on production and imports, receivable ] Derived-Features=( 220.28 363.25 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Total general government expenditure ] Derived-Features=( 668.23 1005.6 4 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Total general government revenue ] Derived-Features=( 615.53 1179.42 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 4.15 4.04 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 6.86 5.88 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 1.77 1.77 0 0 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 1.55 1.55 0 0 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 1.65 1.65 0 0 0 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 1.86 2.25 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 1.77 1.76 2 2 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 1.95 1.93 1 1 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 1.99 1.94 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 1.87 2.08 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 10.99 9.61 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Malta , feature= VAT, receivable ] Derived-Features=( 125.26 187.15 4 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 3902.6 4212.83 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 955.81 781.21 2 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 1195.22 1570.05 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1697.18 1740.13 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 4642.37 4662.44 2 4 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 1235.54 1050.85 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 1397.7 1584.17 2 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1963.01 1943.29 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 8540.27 8916.76 0 2 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 2208.26 1836.03 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 2611.42 3183.13 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 3658.18 3671.18 1 1 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= All ISCED 2011 levels ] Derived-Features=( 10945.51 11080.06 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= All ISCED 2011 levels, Females ] Derived-Features=( 5439.47 5549.34 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= All ISCED 2011 levels, Males ] Derived-Features=( 5511.67 5558.05 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Capital transfers, payable ] Derived-Features=( 1075.43 1281.64 1 1 0 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Capital transfers, receivable ] Derived-Features=( 521.74 606.23 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Compensation of employees, payable ] Derived-Features=( 13154.77 15910.75 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 16290.74 21957.67 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 3708.98 3885.85 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 880.14 701.5 2 3 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Other current transfers, payable ] Derived-Features=( 2622.88 2282.14 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Other current transfers, receivable ] Derived-Features=( 613.49 854.05 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Property income, payable ] Derived-Features=( 2893.68 1921.94 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Property income, receivable ] Derived-Features=( 3412.67 2367.54 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Savings, gross ] Derived-Features=( 1255.04 -2026.38 2 2 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Subsidies, payable ] Derived-Features=( 1830.77 2123.45 4 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Taxes on production and imports, receivable ] Derived-Features=( 17110.14 21557.39 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Total general government expenditure ] Derived-Features=( 66497.73 83414.32 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Total general government revenue ] Derived-Features=( 64032.95 81005.38 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 191.5 203.99 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 204.82 203.33 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 43.92 46.42 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 35.66 32.15 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 14.6 165.21 2 2 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 87.66 97.54 1 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 58.45 85.84 2 1 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 73.08 46.98 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 72.99 56.59 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 26.94 30.22 0 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 397.2 449.04 0 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Netherlands , feature= VAT, receivable ] Derived-Features=( 9761.35 12535.28 0 1 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1178.34 1275.86 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 196.21 195.99 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 479.08 652.9 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 496.05 458.72 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1311.4 1411.36 5 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 240.5 294.82 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 417.11 556.16 0 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 645.65 602.22 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2475.81 2730.21 1 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 428.45 501.39 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 898.65 1187.36 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1151.25 1060.18 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= All ISCED 2011 levels ] Derived-Features=( 3155.12 3395.4 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= All ISCED 2011 levels, Females ] Derived-Features=( 1550.43 1711.23 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= All ISCED 2011 levels, Males ] Derived-Features=( 1604.68 1764.08 3 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Capital transfers, payable ] Derived-Features=( 132.55 122.83 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Capital transfers, receivable ] Derived-Features=( 83.87 232 2 0 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Compensation of employees, payable ] Derived-Features=( 9708.82 21180.53 3 2 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 14890.16 12985.93 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1131.47 1234.58 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 180.73 177.51 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Other current transfers, payable ] Derived-Features=( 1747.23 2524.84 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Other current transfers, receivable ] Derived-Features=( 258.95 249.37 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Property income, payable ] Derived-Features=( 377.07 -167.4 2 2 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Property income, receivable ] Derived-Features=( 8776.07 9480.97 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Savings, gross ] Derived-Features=( 11183.45 7506.4 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Subsidies, payable ] Derived-Features=( 1506.42 1994.87 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Taxes on production and imports, receivable ] Derived-Features=( 9380.43 12899.56 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Total general government expenditure ] Derived-Features=( 34388.86 43257.82 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Total general government revenue ] Derived-Features=( 42480.79 46498.05 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 38.81 48.52 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 51.68 58.81 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 11.34 15.72 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 9.1 11.45 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 7.15 7.12 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 21.55 30.46 5 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 10.27 18.63 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 15.76 19.94 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 11.65 14.22 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 21 13.96 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 90.72 113.97 3 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Norway , feature= VAT, receivable ] Derived-Features=( 5991.35 7938.95 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 7680.11 7571.64 2 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 619.15 358.07 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 2233.02 3457 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 4819.17 4084.55 4 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 9229.15 9318.58 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 952.91 531.22 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 1707.57 2541.09 0 1 0 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 6616.85 6031.27 0 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 16911.59 16905.54 3 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 1577.53 1204.11 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 3963.03 6212.31 5 0 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 11393.93 10513.86 1 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= All ISCED 2011 levels ] Derived-Features=( 25797.31 24219.88 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= All ISCED 2011 levels, Females ] Derived-Features=( 12989.96 12053.17 3 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= All ISCED 2011 levels, Males ] Derived-Features=( 12784.87 12174.58 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Capital transfers, payable ] Derived-Features=( 517.92 714.58 3 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Capital transfers, receivable ] Derived-Features=( 590.57 757.78 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Compensation of employees, payable ] Derived-Features=( 8545.6 11871.9 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 5699.19 9140.2 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 6668.78 7244.06 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 506.29 236.54 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Other current transfers, payable ] Derived-Features=( 1496.96 2187.05 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Other current transfers, receivable ] Derived-Features=( 916.61 1343.17 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Property income, payable ] Derived-Features=( 1876.9 1742.85 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Property income, receivable ] Derived-Features=( 774.1 676.24 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Savings, gross ] Derived-Features=( -67.62 1574.6 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Subsidies, payable ] Derived-Features=( 581.29 565.55 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Taxes on production and imports, receivable ] Derived-Features=( 10706.98 16507 0 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Total general government expenditure ] Derived-Features=( 35311.91 50585.28 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Total general government revenue ] Derived-Features=( 31440.47 48474.79 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 1026.72 405.95 0 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 1067.1 359.69 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 149.51 69.4 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 209.79 22.45 1 4 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 227.09 61.52 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 275.23 49.56 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 368.36 88.81 0 4 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 340.68 170.63 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 442.47 140.09 2 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 71.57 148.66 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 2071.2 494.36 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Poland , feature= VAT, receivable ] Derived-Features=( 5754.48 8825.78 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2420.52 2480.66 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 1421.83 871.72 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 509.92 863.09 5 0 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 481.25 682.96 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2659.65 2523.64 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 1852.06 1437.69 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 326.86 502.67 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 466.7 755.25 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 5075.53 5003.57 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 3284.26 2082.4 0 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 864.43 1375.59 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 957.35 1440.7 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= All ISCED 2011 levels ] Derived-Features=( 6929.97 6655.7 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= All ISCED 2011 levels, Females ] Derived-Features=( 3551.7 3439.11 3 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= All ISCED 2011 levels, Males ] Derived-Features=( 3390.67 3232.61 3 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Capital transfers, payable ] Derived-Features=( 571.85 873.11 2 0 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Capital transfers, receivable ] Derived-Features=( 436.48 426.17 0 0 0 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Compensation of employees, payable ] Derived-Features=( 5378.23 5231.72 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 3947.49 5173.13 1 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2167.28 2209.06 1 4 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 1279.25 777 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Other current transfers, payable ] Derived-Features=( 1024 1226.71 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Other current transfers, receivable ] Derived-Features=( 504.08 760.86 2 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Property income, payable ] Derived-Features=( 1458.2 1854.61 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Property income, receivable ] Derived-Features=( 362.35 331.57 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Savings, gross ] Derived-Features=( -673.44 465.84 0 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Subsidies, payable ] Derived-Features=( 317.13 195.32 1 0 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Taxes on production and imports, receivable ] Derived-Features=( 5748.53 7260.75 3 5 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Total general government expenditure ] Derived-Features=( 19271.78 22982.43 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Total general government revenue ] Derived-Features=( 17311.45 21127.07 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 257.46 286.4 2 2 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 250.36 189.68 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 32.76 35.01 2 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 33.8 25.9 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 41.78 32.77 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 69.79 64.52 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 57.68 31.17 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 68.41 62.51 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 83.13 59.54 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 26.88 25.56 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 500.72 423.4 4 2 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Portugal , feature= VAT, receivable ] Derived-Features=( 3309.1 4401.84 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 4070.28 3824.42 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 962.8 549.79 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 672.03 942.42 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 2407.15 2064.65 2 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 5129.48 5118.61 2 1 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 1127.37 989.63 0 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 702.1 912.24 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 3358.9 3169.91 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 9225.44 8781.55 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 2125.41 1527.75 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 1407.5 1827.39 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 5742.84 5363.34 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= All ISCED 2011 levels ] Derived-Features=( 14406.12 12818.32 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= All ISCED 2011 levels, Females ] Derived-Features=( 7199.84 6359.41 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= All ISCED 2011 levels, Males ] Derived-Features=( 7201.5 6564.52 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Capital transfers, payable ] Derived-Features=( 354.51 464.76 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Capital transfers, receivable ] Derived-Features=( 296.9 655.61 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Compensation of employees, payable ] Derived-Features=( 2392.77 4552.77 2 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 1711.28 2789.28 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 3820.58 3641.46 2 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 931.36 576.2 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Other current transfers, payable ] Derived-Features=( 488.64 921.81 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Other current transfers, receivable ] Derived-Features=( 251.23 339.96 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Property income, payable ] Derived-Features=( 426.25 644.65 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Property income, receivable ] Derived-Features=( 260.96 493.44 5 0 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Savings, gross ] Derived-Features=( 327.05 -203.96 1 1 0 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Subsidies, payable ] Derived-Features=( 287.14 189.3 0 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Taxes on production and imports, receivable ] Derived-Features=( 3295.28 5525.95 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Total general government expenditure ] Derived-Features=( 10522.3 16816.01 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Total general government revenue ] Derived-Features=( 9160.79 14961.07 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 260.52 167.28 2 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 417.61 317.98 3 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 65.68 55.81 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 50.22 33.8 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 68.79 54.56 2 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 101.85 77.49 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 98.96 60.86 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 85.69 35.04 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 112 70.94 3 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 29.25 45.92 0 2 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 674.81 465.38 3 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Romania , feature= VAT, receivable ] Derived-Features=( 2096.06 3287.56 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1200.38 1237.6 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 99.06 77.15 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 222.92 359.57 2 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 876.4 817.93 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1464.09 1502.18 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 93.14 91.28 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 218.77 285.04 5 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1155.39 1096.27 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2670.29 2751.44 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 188.91 167.2 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 448.92 670.63 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 2027.04 1933.35 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= All ISCED 2011 levels ] Derived-Features=( 3822.97 3797.02 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= All ISCED 2011 levels, Females ] Derived-Features=( 1922 1879.85 3 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= All ISCED 2011 levels, Males ] Derived-Features=( 1908.54 1889.98 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Capital transfers, payable ] Derived-Features=( 137 44.17 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Capital transfers, receivable ] Derived-Features=( 109.52 153.32 1 2 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Compensation of employees, payable ] Derived-Features=( 1192.26 1935.11 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 845.42 1598.81 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1021.56 1144.9 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 58.51 59.83 2 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Other current transfers, payable ] Derived-Features=( 227.45 357.01 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Other current transfers, receivable ] Derived-Features=( 213.29 266.43 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Property income, payable ] Derived-Features=( 246.67 337.44 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Property income, receivable ] Derived-Features=( 156.85 171.81 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Savings, gross ] Derived-Features=( 14.01 594.96 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Subsidies, payable ] Derived-Features=( 128.38 103.84 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Taxes on production and imports, receivable ] Derived-Features=( 1507.11 2517.32 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Total general government expenditure ] Derived-Features=( 5639.43 9207.74 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Total general government revenue ] Derived-Features=( 5243.22 8450.97 0 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 176.14 96.63 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 199.34 125.91 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 13.51 10.74 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 18.44 11.18 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 30.91 16.25 2 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 25.54 21.07 2 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 50.33 19.63 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 35.55 25.6 2 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 64.38 -15.67 1 2 2 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 10.41 6.17 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 377.9 237.27 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovakia , feature= VAT, receivable ] Derived-Features=( 926.68 1628.61 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 455.55 480.25 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 62.69 32.65 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 143.12 213.96 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 248.59 222.73 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 532.31 537.39 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 72.57 48.51 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 104.84 141.93 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 354.17 337.31 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 994.65 998.17 2 2 2 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 134.19 88.39 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 245.91 365.93 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 602.61 566.81 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= All ISCED 2011 levels ] Derived-Features=( 1402.11 1356.69 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= All ISCED 2011 levels, Females ] Derived-Features=( 686.04 661.63 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= All ISCED 2011 levels, Males ] Derived-Features=( 717.66 702.43 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Capital transfers, payable ] Derived-Features=( 102.39 233.87 1 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Capital transfers, receivable ] Derived-Features=( 50.18 56.1 1 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Compensation of employees, payable ] Derived-Features=( 959.14 1210.33 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 653.66 816.68 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 418.1 442.07 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 56.67 34.34 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Other current transfers, payable ] Derived-Features=( 167.43 262.95 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Other current transfers, receivable ] Derived-Features=( 98.22 124.08 1 3 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Property income, payable ] Derived-Features=( 171.66 282.25 2 3 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Property income, receivable ] Derived-Features=( 78.46 143.9 1 0 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Savings, gross ] Derived-Features=( 44.12 63.34 2 2 1 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Subsidies, payable ] Derived-Features=( 111.44 76.29 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Taxes on production and imports, receivable ] Derived-Features=( 1217.61 1544.59 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Total general government expenditure ] Derived-Features=( 3970.19 5176.24 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Total general government revenue ] Derived-Features=( 3639.87 4769.77 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 35.16 31.94 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 36.84 30.86 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 5.24 6.35 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 5.03 4.07 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 6.04 3.87 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 10.17 12.03 1 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 11.72 11.03 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 10.59 8.73 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 12.22 11 1 2 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 2.68 2.88 1 2 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 70.86 62.03 2 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Slovenia , feature= VAT, receivable ] Derived-Features=( 683.76 926.43 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 9522.4 10561.2 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 3539.2 3244.67 2 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 3611.43 4876.75 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 2219.19 2615.71 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 12111.78 13369.49 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 6027.99 4887.86 1 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 3509.1 4341.68 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 2637.05 2892.07 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 21643.68 22927.91 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 9590.79 8317.39 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 7160.52 8848.44 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 4902.55 5936.47 1 2 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= All ISCED 2011 levels ] Derived-Features=( 30161.53 30502.04 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= All ISCED 2011 levels, Females ] Derived-Features=( 15006.81 15489.5 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= All ISCED 2011 levels, Males ] Derived-Features=( 15209.21 15227.66 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Capital transfers, payable ] Derived-Features=( 3559.43 3940.52 4 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Capital transfers, receivable ] Derived-Features=( 1159.34 1317.77 2 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Compensation of employees, payable ] Derived-Features=( 25725.42 33637.52 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 19952.18 64318.53 3 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 7685.51 8577.45 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 2647.77 2222.5 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Other current transfers, payable ] Derived-Features=( 3897.29 3595.62 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Other current transfers, receivable ] Derived-Features=( 1759.88 2083.84 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Property income, payable ] Derived-Features=( 5833.93 7427.97 2 4 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Property income, receivable ] Derived-Features=( 2142.52 2148.34 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Savings, gross ] Derived-Features=( 814.58 -5639.85 0 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Subsidies, payable ] Derived-Features=( 2600.86 3438.46 0 1 0 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Taxes on production and imports, receivable ] Derived-Features=( 26866.73 35073.57 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Total general government expenditure ] Derived-Features=( 102415.3 120515.8 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Total general government revenue ] Derived-Features=( 87874.7 122649.1 2 3 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 1613.08 449.52 3 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 1756.78 2145.62 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 336.45 377.6 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 290.8 237.24 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 315.48 172.36 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 647.54 688.27 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 354.38 357.84 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 586.66 450.96 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 630.25 559.64 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 297.72 317.54 1 4 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 3505.57 4341.95 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Spain , feature= VAT, receivable ] Derived-Features=( 14012.82 19112.05 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2284.43 2562.54 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 360.46 334.34 3 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 702.29 2402.11 5 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1152.12 -537.3 1 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2489.03 2694.2 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 458.52 422.69 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 660.54 925 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1356.32 1290.78 3 0 1 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 4558.04 4164.4 5 1 2 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 810.61 724.84 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 1439.51 2936.78 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 2534.03 2764.1 2 2 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= All ISCED 2011 levels ] Derived-Features=( 5985.8 6318.01 5 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= All ISCED 2011 levels, Females ] Derived-Features=( 2969.47 3110.7 0 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= All ISCED 2011 levels, Males ] Derived-Features=( 3009.37 3664.53 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Capital transfers, payable ] Derived-Features=( 278.75 553.59 1 0 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Capital transfers, receivable ] Derived-Features=( 165.99 258.14 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Compensation of employees, payable ] Derived-Features=( 11431.73 15937.78 0 1 0 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 17080.79 22393.15 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2065.37 2743.33 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 298.69 274.36 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Other current transfers, payable ] Derived-Features=( 2615.28 2925.49 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Other current transfers, receivable ] Derived-Features=( 515.97 735.36 2 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Property income, payable ] Derived-Features=( 1380.87 167 1 0 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Property income, receivable ] Derived-Features=( 1724.84 2022.89 1 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Savings, gross ] Derived-Features=( 4227.75 6794.19 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Subsidies, payable ] Derived-Features=( 1404.76 1975.58 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Taxes on production and imports, receivable ] Derived-Features=( 19998.47 27273.31 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Total general government expenditure ] Derived-Features=( 46209.48 60395.89 2 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Total general government revenue ] Derived-Features=( 46713.71 61364.59 1 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 157.42 158.74 3 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 181.61 173.57 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 37.61 36.27 1 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 40.31 40.78 2 1 0 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 34.62 32.55 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 62.56 87.44 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 22.59 18.67 4 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 73.78 70.02 1 1 0 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 57.93 65.06 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 67.42 77.42 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 338.53 355.42 3 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Sweden , feature= VAT, receivable ] Derived-Features=( 7971.51 10902.17 1 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2042.7 2154.8 5 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 358.09 310.68 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 592.84 767.78 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1086.34 1085.58 2 1 1 0 20 0 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 2352.86 2486.07 4 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 361.36 349.04 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 906.18 1068.65 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 1098.58 1070.81 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 4421.45 4685.6 3 4 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 723.57 658.69 1 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 1468.07 1762.35 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 2183.66 2135.32 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= All ISCED 2011 levels ] Derived-Features=( 5351.46 5517.47 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= All ISCED 2011 levels, Females ] Derived-Features=( 2620.17 2751.25 5 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= All ISCED 2011 levels, Males ] Derived-Features=( 2696.61 2785.85 2 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Capital transfers, payable ] Derived-Features=( 1366.79 1732.15 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Capital transfers, receivable ] Derived-Features=( 241.87 332.63 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Compensation of employees, payable ] Derived-Features=( 7974.81 12605.24 1 3 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 15099.28 24757.52 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 1929.51 2040.3 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 332.06 288.25 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Other current transfers, payable ] Derived-Features=( 2321.18 4116.64 2 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Other current transfers, receivable ] Derived-Features=( 1145.22 1777.29 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Property income, payable ] Derived-Features=( 967.28 608.07 1 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Property income, receivable ] Derived-Features=( 1397.44 1794.42 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Savings, gross ] Derived-Features=( 4448.52 6541.74 2 1 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Subsidies, payable ] Derived-Features=( 3257.59 5146.95 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Taxes on production and imports, receivable ] Derived-Features=( 6583.2 8553.47 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Total general government expenditure ] Derived-Features=( 36316.39 58562.68 1 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Total general government revenue ] Derived-Features=( 37057.78 56933.22 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 99.9 107.62 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 104.23 117.97 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 21.37 25.37 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 19.73 20.67 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 19.28 21.3 1 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 39.74 44.07 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 20.98 25.3 3 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 35.93 38.84 2 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 36.9 41.8 5 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 19.29 21.17 5 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 196.17 248.63 0 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= Switzerland , feature= VAT, receivable ] Derived-Features=( 3590.85 5002.62 2 2 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 14023.89 15512.02 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 3028.26 2157.37 4 3 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 5079.52 6298.08 5 0 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 5597.73 6319.97 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 16296.53 17185.98 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 3340.31 2891.16 1 2 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 5270.84 6877.53 3 3 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 7208.19 7023.55 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 30391.61 32309.09 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 6449.28 5311 2 2 1 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8) ] Derived-Features=( 10383.52 13994.22 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4) ] Derived-Features=( 12829.37 12994.63 2 1 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= All ISCED 2011 levels ] Derived-Features=( 39861.12 41785.98 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= All ISCED 2011 levels, Females ] Derived-Features=( 20125.47 20912.59 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= All ISCED 2011 levels, Males ] Derived-Features=( 19765.57 20846.77 0 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Capital transfers, payable ] Derived-Features=( 5232.39 5230.39 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Capital transfers, receivable ] Derived-Features=( 2422.78 2810.73 3 1 1 1 20 0 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Compensation of employees, payable ] Derived-Features=( 49606.78 51903.41 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Current taxes on income, wealth, etc., receivable ] Derived-Features=( 73011.66 83619.63 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels ] Derived-Features=( 13318.98 14634.48 0 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2) ] Derived-Features=( 2811.12 1634.16 2 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Other current transfers, payable ] Derived-Features=( 11776.11 10567.21 1 3 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Other current transfers, receivable ] Derived-Features=( 702.28 1309.82 2 2 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Property income, payable ] Derived-Features=( 12038.84 16109.22 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Property income, receivable ] Derived-Features=( 3812.83 5818.94 1 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Savings, gross ] Derived-Features=( -5230.85 -3168.11 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Subsidies, payable ] Derived-Features=( 2781.78 4441.61 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Taxes on production and imports, receivable ] Derived-Features=( 62556.33 78094.03 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Total general government expenditure ] Derived-Features=( 215769.6 231246.8 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Total general government revenue ] Derived-Features=( 193557.4 223855.8 2 3 2 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Unemployment , Females, From 15-64 years, Total ] Derived-Features=( 765.21 636.89 1 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Unemployment , Males, From 15-64 years ] Derived-Features=( 1073.85 711.74 2 1 1 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Unemployment , Males, From 15-64 years, from 1 to 2 months ] Derived-Features=( 214.71 171.15 0 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Unemployment , Males, From 15-64 years, from 3 to 5 months ] Derived-Features=( 179.91 126.66 0 1 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Unemployment , Males, From 15-64 years, from 6 to 11 months ] Derived-Features=( 177.05 131.55 2 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Unemployment , Total, From 15-64 years, From 1 to 2 months ] Derived-Features=( 406.98 342.79 1 1 0 1 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Unemployment , Total, From 15-64 years, From 12 to 17 months ] Derived-Features=( 168.89 154.06 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Unemployment , Total, From 15-64 years, From 3 to 5 months ] Derived-Features=( 322.67 219.06 0 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Unemployment , Total, From 15-64 years, From 6 to 11 months ] Derived-Features=( 300.57 202.06 0 2 2 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Unemployment , Total, From 15-64 years, Less than 1 month ] Derived-Features=( 255.59 243.53 1 1 0 2 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= Unemployment by sex, age, duration. DurationNA not started ] Derived-Features=( 1853.76 1446.94 1 1 0 0 20 1 0 ) ...arimaModels_ARMA_coefs[country= United Kingdom , feature= VAT, receivable ] Derived-Features=( 31813.31 38960.4 2 1 2 0 20 1 0 ) ...length(arimaModels_ARMA_coefs) == 31*42 # [1] TRUE # Each list-element consists of 9 values, see above## [1] FALSE# == dim(list_of_dfs_CommonFeatures[[1]])[1] * dim(list_of_dfs_CommonFeatures[[1]])[2]
# Maps to convert between 1D indices and 2D (Country, Feature) pairs
index2CountryFeature <- function(indx=1) {
if (indx<1 | indx>length(arimaModels_ARMA_coefs)) {
cat("Index out of bounds: indx=", indx, "; must be between 1 and ",
length(arimaModels_ARMA_coefs), " ... Exiting ...")
return (NULL)
} else {
feature = (indx-1) %% (dim(list_of_dfs_CommonFeatures[[1]])[2])
country = floor((indx - feature)/(dim(list_of_dfs_CommonFeatures[[1]])[2]))
return(list("feature"=(feature+1), "country"=(country+1))) }
}
countryFeature2Index <- function(countryIndx=1, featureIndx=1) {
if (countryIndx<1 | countryIndx>(dim(list_of_dfs_CommonFeatures[[1]])[1]) |
featureIndx<1 | featureIndx>(dim(list_of_dfs_CommonFeatures[[1]])[2])) {
cat("Indices out of bounds: countryIndx=", countryIndx, "; featureIndx=", featureIndx, "; Exiting ...")
return (NULL)
} else { return (featureIndx + (countryIndx-1)*(dim(list_of_dfs_CommonFeatures[[1]])[2])) }
}
# test forward and reverse index mapping functions
index2CountryFeature(42); index2CountryFeature(45)$country; index2CountryFeature(45)$feature## $feature
## [1] 42
##
## $country
## [1] 1## [1] 2## [1] 3countryFeature2Index(countryIndx=2, featureIndx=3)## [1] 45# Column/Feature Names: colnames(list_of_dfs_CommonFeatures[[1]])
# Country/Row Names: countryNames
arimaModels_ARMA_coefs[[1]] # Austria/Feature1 1:9 feature vector## [1] 1891.354 2054.259 0.000 1.000 0.000 0.000 20.000 1.000
## [9] 0.000# Cuntry2=Bulgaria, feature 5, 1:9 vector
arimaModels_ARMA_coefs[[countryFeature2Index(countryIndx=2, featureIndx=5)]]## [1] 2584.427 2661.534 0.000 1.000 0.000 1.000 20.000 1.000
## [9] 0.000Convert list of ARIMA models to a Data.Frame [Countries, megaFeatures] that can be put through ML data analytics. Augment the features using the EU_SOCR_Country_Ranking_Data_2011 dataset.
# 4. Add the country ranking as a new feature, using the OA ranks here:
# (http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_2008_World_CountriesRankings)
EU_SOCR_Country_Ranking_Data_2011 <- read.csv2("E:/Ivo.dir/Research/UMichigan/Publications_Books/2018/others/4D_Time_Space_Book_Ideas/ARIMAX_EU_DataAnalytics/EU_SOCR_Country_Ranking_Data_2011.csv", header=T, sep=",")
length(arimaModels_ARMA_coefs) # 31*42 ## [1] 2604arima_df <- data.frame(matrix(NA,
nrow=length(countryNames), ncol=length(colnames(list_of_dfs_CommonFeatures[[1]]))*9))
dim(arima_df) # [1] 31 378## [1] 31 378for(n in 1:dim(arima_df)[1]) { # for each Country 1<=n<=31
for (k in 1:length(colnames(list_of_dfs_CommonFeatures[[1]]))) { # for each feature 1<=k<=42
for (l in 1:9) { # for each arima vector 1:9, see above
arima_df[n, (k-1)*9 + l] <-
round(arimaModels_ARMA_coefs[[countryFeature2Index(countryIndx=n, featureIndx=k)]][l], 1)
if (n==dim(arima_df)[1]) colnames(arima_df)[(k-1)*9 + l] <-
print(paste0("Feature_",k, "_ArimaVec_",l))
}
}
}## [1] "Feature_1_ArimaVec_1"
## [1] "Feature_1_ArimaVec_2"
## [1] "Feature_1_ArimaVec_3"
## [1] "Feature_1_ArimaVec_4"
## [1] "Feature_1_ArimaVec_5"
## [1] "Feature_1_ArimaVec_6"
## [1] "Feature_1_ArimaVec_7"
## [1] "Feature_1_ArimaVec_8"
## [1] "Feature_1_ArimaVec_9"
## [1] "Feature_2_ArimaVec_1"
## [1] "Feature_2_ArimaVec_2"
## [1] "Feature_2_ArimaVec_3"
## [1] "Feature_2_ArimaVec_4"
## [1] "Feature_2_ArimaVec_5"
## [1] "Feature_2_ArimaVec_6"
## [1] "Feature_2_ArimaVec_7"
## [1] "Feature_2_ArimaVec_8"
## [1] "Feature_2_ArimaVec_9"
## [1] "Feature_3_ArimaVec_1"
## [1] "Feature_3_ArimaVec_2"
## [1] "Feature_3_ArimaVec_3"
## [1] "Feature_3_ArimaVec_4"
## [1] "Feature_3_ArimaVec_5"
## [1] "Feature_3_ArimaVec_6"
## [1] "Feature_3_ArimaVec_7"
## [1] "Feature_3_ArimaVec_8"
## [1] "Feature_3_ArimaVec_9"
## [1] "Feature_4_ArimaVec_1"
## [1] "Feature_4_ArimaVec_2"
## [1] "Feature_4_ArimaVec_3"
## [1] "Feature_4_ArimaVec_4"
## [1] "Feature_4_ArimaVec_5"
## [1] "Feature_4_ArimaVec_6"
## [1] "Feature_4_ArimaVec_7"
## [1] "Feature_4_ArimaVec_8"
## [1] "Feature_4_ArimaVec_9"
## [1] "Feature_5_ArimaVec_1"
## [1] "Feature_5_ArimaVec_2"
## [1] "Feature_5_ArimaVec_3"
## [1] "Feature_5_ArimaVec_4"
## [1] "Feature_5_ArimaVec_5"
## [1] "Feature_5_ArimaVec_6"
## [1] "Feature_5_ArimaVec_7"
## [1] "Feature_5_ArimaVec_8"
## [1] "Feature_5_ArimaVec_9"
## [1] "Feature_6_ArimaVec_1"
## [1] "Feature_6_ArimaVec_2"
## [1] "Feature_6_ArimaVec_3"
## [1] "Feature_6_ArimaVec_4"
## [1] "Feature_6_ArimaVec_5"
## [1] "Feature_6_ArimaVec_6"
## [1] "Feature_6_ArimaVec_7"
## [1] "Feature_6_ArimaVec_8"
## [1] "Feature_6_ArimaVec_9"
## [1] "Feature_7_ArimaVec_1"
## [1] "Feature_7_ArimaVec_2"
## [1] "Feature_7_ArimaVec_3"
## [1] "Feature_7_ArimaVec_4"
## [1] "Feature_7_ArimaVec_5"
## [1] "Feature_7_ArimaVec_6"
## [1] "Feature_7_ArimaVec_7"
## [1] "Feature_7_ArimaVec_8"
## [1] "Feature_7_ArimaVec_9"
## [1] "Feature_8_ArimaVec_1"
## [1] "Feature_8_ArimaVec_2"
## [1] "Feature_8_ArimaVec_3"
## [1] "Feature_8_ArimaVec_4"
## [1] "Feature_8_ArimaVec_5"
## [1] "Feature_8_ArimaVec_6"
## [1] "Feature_8_ArimaVec_7"
## [1] "Feature_8_ArimaVec_8"
## [1] "Feature_8_ArimaVec_9"
## [1] "Feature_9_ArimaVec_1"
## [1] "Feature_9_ArimaVec_2"
## [1] "Feature_9_ArimaVec_3"
## [1] "Feature_9_ArimaVec_4"
## [1] "Feature_9_ArimaVec_5"
## [1] "Feature_9_ArimaVec_6"
## [1] "Feature_9_ArimaVec_7"
## [1] "Feature_9_ArimaVec_8"
## [1] "Feature_9_ArimaVec_9"
## [1] "Feature_10_ArimaVec_1"
## [1] "Feature_10_ArimaVec_2"
## [1] "Feature_10_ArimaVec_3"
## [1] "Feature_10_ArimaVec_4"
## [1] "Feature_10_ArimaVec_5"
## [1] "Feature_10_ArimaVec_6"
## [1] "Feature_10_ArimaVec_7"
## [1] "Feature_10_ArimaVec_8"
## [1] "Feature_10_ArimaVec_9"
## [1] "Feature_11_ArimaVec_1"
## [1] "Feature_11_ArimaVec_2"
## [1] "Feature_11_ArimaVec_3"
## [1] "Feature_11_ArimaVec_4"
## [1] "Feature_11_ArimaVec_5"
## [1] "Feature_11_ArimaVec_6"
## [1] "Feature_11_ArimaVec_7"
## [1] "Feature_11_ArimaVec_8"
## [1] "Feature_11_ArimaVec_9"
## [1] "Feature_12_ArimaVec_1"
## [1] "Feature_12_ArimaVec_2"
## [1] "Feature_12_ArimaVec_3"
## [1] "Feature_12_ArimaVec_4"
## [1] "Feature_12_ArimaVec_5"
## [1] "Feature_12_ArimaVec_6"
## [1] "Feature_12_ArimaVec_7"
## [1] "Feature_12_ArimaVec_8"
## [1] "Feature_12_ArimaVec_9"
## [1] "Feature_13_ArimaVec_1"
## [1] "Feature_13_ArimaVec_2"
## [1] "Feature_13_ArimaVec_3"
## [1] "Feature_13_ArimaVec_4"
## [1] "Feature_13_ArimaVec_5"
## [1] "Feature_13_ArimaVec_6"
## [1] "Feature_13_ArimaVec_7"
## [1] "Feature_13_ArimaVec_8"
## [1] "Feature_13_ArimaVec_9"
## [1] "Feature_14_ArimaVec_1"
## [1] "Feature_14_ArimaVec_2"
## [1] "Feature_14_ArimaVec_3"
## [1] "Feature_14_ArimaVec_4"
## [1] "Feature_14_ArimaVec_5"
## [1] "Feature_14_ArimaVec_6"
## [1] "Feature_14_ArimaVec_7"
## [1] "Feature_14_ArimaVec_8"
## [1] "Feature_14_ArimaVec_9"
## [1] "Feature_15_ArimaVec_1"
## [1] "Feature_15_ArimaVec_2"
## [1] "Feature_15_ArimaVec_3"
## [1] "Feature_15_ArimaVec_4"
## [1] "Feature_15_ArimaVec_5"
## [1] "Feature_15_ArimaVec_6"
## [1] "Feature_15_ArimaVec_7"
## [1] "Feature_15_ArimaVec_8"
## [1] "Feature_15_ArimaVec_9"
## [1] "Feature_16_ArimaVec_1"
## [1] "Feature_16_ArimaVec_2"
## [1] "Feature_16_ArimaVec_3"
## [1] "Feature_16_ArimaVec_4"
## [1] "Feature_16_ArimaVec_5"
## [1] "Feature_16_ArimaVec_6"
## [1] "Feature_16_ArimaVec_7"
## [1] "Feature_16_ArimaVec_8"
## [1] "Feature_16_ArimaVec_9"
## [1] "Feature_17_ArimaVec_1"
## [1] "Feature_17_ArimaVec_2"
## [1] "Feature_17_ArimaVec_3"
## [1] "Feature_17_ArimaVec_4"
## [1] "Feature_17_ArimaVec_5"
## [1] "Feature_17_ArimaVec_6"
## [1] "Feature_17_ArimaVec_7"
## [1] "Feature_17_ArimaVec_8"
## [1] "Feature_17_ArimaVec_9"
## [1] "Feature_18_ArimaVec_1"
## [1] "Feature_18_ArimaVec_2"
## [1] "Feature_18_ArimaVec_3"
## [1] "Feature_18_ArimaVec_4"
## [1] "Feature_18_ArimaVec_5"
## [1] "Feature_18_ArimaVec_6"
## [1] "Feature_18_ArimaVec_7"
## [1] "Feature_18_ArimaVec_8"
## [1] "Feature_18_ArimaVec_9"
## [1] "Feature_19_ArimaVec_1"
## [1] "Feature_19_ArimaVec_2"
## [1] "Feature_19_ArimaVec_3"
## [1] "Feature_19_ArimaVec_4"
## [1] "Feature_19_ArimaVec_5"
## [1] "Feature_19_ArimaVec_6"
## [1] "Feature_19_ArimaVec_7"
## [1] "Feature_19_ArimaVec_8"
## [1] "Feature_19_ArimaVec_9"
## [1] "Feature_20_ArimaVec_1"
## [1] "Feature_20_ArimaVec_2"
## [1] "Feature_20_ArimaVec_3"
## [1] "Feature_20_ArimaVec_4"
## [1] "Feature_20_ArimaVec_5"
## [1] "Feature_20_ArimaVec_6"
## [1] "Feature_20_ArimaVec_7"
## [1] "Feature_20_ArimaVec_8"
## [1] "Feature_20_ArimaVec_9"
## [1] "Feature_21_ArimaVec_1"
## [1] "Feature_21_ArimaVec_2"
## [1] "Feature_21_ArimaVec_3"
## [1] "Feature_21_ArimaVec_4"
## [1] "Feature_21_ArimaVec_5"
## [1] "Feature_21_ArimaVec_6"
## [1] "Feature_21_ArimaVec_7"
## [1] "Feature_21_ArimaVec_8"
## [1] "Feature_21_ArimaVec_9"
## [1] "Feature_22_ArimaVec_1"
## [1] "Feature_22_ArimaVec_2"
## [1] "Feature_22_ArimaVec_3"
## [1] "Feature_22_ArimaVec_4"
## [1] "Feature_22_ArimaVec_5"
## [1] "Feature_22_ArimaVec_6"
## [1] "Feature_22_ArimaVec_7"
## [1] "Feature_22_ArimaVec_8"
## [1] "Feature_22_ArimaVec_9"
## [1] "Feature_23_ArimaVec_1"
## [1] "Feature_23_ArimaVec_2"
## [1] "Feature_23_ArimaVec_3"
## [1] "Feature_23_ArimaVec_4"
## [1] "Feature_23_ArimaVec_5"
## [1] "Feature_23_ArimaVec_6"
## [1] "Feature_23_ArimaVec_7"
## [1] "Feature_23_ArimaVec_8"
## [1] "Feature_23_ArimaVec_9"
## [1] "Feature_24_ArimaVec_1"
## [1] "Feature_24_ArimaVec_2"
## [1] "Feature_24_ArimaVec_3"
## [1] "Feature_24_ArimaVec_4"
## [1] "Feature_24_ArimaVec_5"
## [1] "Feature_24_ArimaVec_6"
## [1] "Feature_24_ArimaVec_7"
## [1] "Feature_24_ArimaVec_8"
## [1] "Feature_24_ArimaVec_9"
## [1] "Feature_25_ArimaVec_1"
## [1] "Feature_25_ArimaVec_2"
## [1] "Feature_25_ArimaVec_3"
## [1] "Feature_25_ArimaVec_4"
## [1] "Feature_25_ArimaVec_5"
## [1] "Feature_25_ArimaVec_6"
## [1] "Feature_25_ArimaVec_7"
## [1] "Feature_25_ArimaVec_8"
## [1] "Feature_25_ArimaVec_9"
## [1] "Feature_26_ArimaVec_1"
## [1] "Feature_26_ArimaVec_2"
## [1] "Feature_26_ArimaVec_3"
## [1] "Feature_26_ArimaVec_4"
## [1] "Feature_26_ArimaVec_5"
## [1] "Feature_26_ArimaVec_6"
## [1] "Feature_26_ArimaVec_7"
## [1] "Feature_26_ArimaVec_8"
## [1] "Feature_26_ArimaVec_9"
## [1] "Feature_27_ArimaVec_1"
## [1] "Feature_27_ArimaVec_2"
## [1] "Feature_27_ArimaVec_3"
## [1] "Feature_27_ArimaVec_4"
## [1] "Feature_27_ArimaVec_5"
## [1] "Feature_27_ArimaVec_6"
## [1] "Feature_27_ArimaVec_7"
## [1] "Feature_27_ArimaVec_8"
## [1] "Feature_27_ArimaVec_9"
## [1] "Feature_28_ArimaVec_1"
## [1] "Feature_28_ArimaVec_2"
## [1] "Feature_28_ArimaVec_3"
## [1] "Feature_28_ArimaVec_4"
## [1] "Feature_28_ArimaVec_5"
## [1] "Feature_28_ArimaVec_6"
## [1] "Feature_28_ArimaVec_7"
## [1] "Feature_28_ArimaVec_8"
## [1] "Feature_28_ArimaVec_9"
## [1] "Feature_29_ArimaVec_1"
## [1] "Feature_29_ArimaVec_2"
## [1] "Feature_29_ArimaVec_3"
## [1] "Feature_29_ArimaVec_4"
## [1] "Feature_29_ArimaVec_5"
## [1] "Feature_29_ArimaVec_6"
## [1] "Feature_29_ArimaVec_7"
## [1] "Feature_29_ArimaVec_8"
## [1] "Feature_29_ArimaVec_9"
## [1] "Feature_30_ArimaVec_1"
## [1] "Feature_30_ArimaVec_2"
## [1] "Feature_30_ArimaVec_3"
## [1] "Feature_30_ArimaVec_4"
## [1] "Feature_30_ArimaVec_5"
## [1] "Feature_30_ArimaVec_6"
## [1] "Feature_30_ArimaVec_7"
## [1] "Feature_30_ArimaVec_8"
## [1] "Feature_30_ArimaVec_9"
## [1] "Feature_31_ArimaVec_1"
## [1] "Feature_31_ArimaVec_2"
## [1] "Feature_31_ArimaVec_3"
## [1] "Feature_31_ArimaVec_4"
## [1] "Feature_31_ArimaVec_5"
## [1] "Feature_31_ArimaVec_6"
## [1] "Feature_31_ArimaVec_7"
## [1] "Feature_31_ArimaVec_8"
## [1] "Feature_31_ArimaVec_9"
## [1] "Feature_32_ArimaVec_1"
## [1] "Feature_32_ArimaVec_2"
## [1] "Feature_32_ArimaVec_3"
## [1] "Feature_32_ArimaVec_4"
## [1] "Feature_32_ArimaVec_5"
## [1] "Feature_32_ArimaVec_6"
## [1] "Feature_32_ArimaVec_7"
## [1] "Feature_32_ArimaVec_8"
## [1] "Feature_32_ArimaVec_9"
## [1] "Feature_33_ArimaVec_1"
## [1] "Feature_33_ArimaVec_2"
## [1] "Feature_33_ArimaVec_3"
## [1] "Feature_33_ArimaVec_4"
## [1] "Feature_33_ArimaVec_5"
## [1] "Feature_33_ArimaVec_6"
## [1] "Feature_33_ArimaVec_7"
## [1] "Feature_33_ArimaVec_8"
## [1] "Feature_33_ArimaVec_9"
## [1] "Feature_34_ArimaVec_1"
## [1] "Feature_34_ArimaVec_2"
## [1] "Feature_34_ArimaVec_3"
## [1] "Feature_34_ArimaVec_4"
## [1] "Feature_34_ArimaVec_5"
## [1] "Feature_34_ArimaVec_6"
## [1] "Feature_34_ArimaVec_7"
## [1] "Feature_34_ArimaVec_8"
## [1] "Feature_34_ArimaVec_9"
## [1] "Feature_35_ArimaVec_1"
## [1] "Feature_35_ArimaVec_2"
## [1] "Feature_35_ArimaVec_3"
## [1] "Feature_35_ArimaVec_4"
## [1] "Feature_35_ArimaVec_5"
## [1] "Feature_35_ArimaVec_6"
## [1] "Feature_35_ArimaVec_7"
## [1] "Feature_35_ArimaVec_8"
## [1] "Feature_35_ArimaVec_9"
## [1] "Feature_36_ArimaVec_1"
## [1] "Feature_36_ArimaVec_2"
## [1] "Feature_36_ArimaVec_3"
## [1] "Feature_36_ArimaVec_4"
## [1] "Feature_36_ArimaVec_5"
## [1] "Feature_36_ArimaVec_6"
## [1] "Feature_36_ArimaVec_7"
## [1] "Feature_36_ArimaVec_8"
## [1] "Feature_36_ArimaVec_9"
## [1] "Feature_37_ArimaVec_1"
## [1] "Feature_37_ArimaVec_2"
## [1] "Feature_37_ArimaVec_3"
## [1] "Feature_37_ArimaVec_4"
## [1] "Feature_37_ArimaVec_5"
## [1] "Feature_37_ArimaVec_6"
## [1] "Feature_37_ArimaVec_7"
## [1] "Feature_37_ArimaVec_8"
## [1] "Feature_37_ArimaVec_9"
## [1] "Feature_38_ArimaVec_1"
## [1] "Feature_38_ArimaVec_2"
## [1] "Feature_38_ArimaVec_3"
## [1] "Feature_38_ArimaVec_4"
## [1] "Feature_38_ArimaVec_5"
## [1] "Feature_38_ArimaVec_6"
## [1] "Feature_38_ArimaVec_7"
## [1] "Feature_38_ArimaVec_8"
## [1] "Feature_38_ArimaVec_9"
## [1] "Feature_39_ArimaVec_1"
## [1] "Feature_39_ArimaVec_2"
## [1] "Feature_39_ArimaVec_3"
## [1] "Feature_39_ArimaVec_4"
## [1] "Feature_39_ArimaVec_5"
## [1] "Feature_39_ArimaVec_6"
## [1] "Feature_39_ArimaVec_7"
## [1] "Feature_39_ArimaVec_8"
## [1] "Feature_39_ArimaVec_9"
## [1] "Feature_40_ArimaVec_1"
## [1] "Feature_40_ArimaVec_2"
## [1] "Feature_40_ArimaVec_3"
## [1] "Feature_40_ArimaVec_4"
## [1] "Feature_40_ArimaVec_5"
## [1] "Feature_40_ArimaVec_6"
## [1] "Feature_40_ArimaVec_7"
## [1] "Feature_40_ArimaVec_8"
## [1] "Feature_40_ArimaVec_9"
## [1] "Feature_41_ArimaVec_1"
## [1] "Feature_41_ArimaVec_2"
## [1] "Feature_41_ArimaVec_3"
## [1] "Feature_41_ArimaVec_4"
## [1] "Feature_41_ArimaVec_5"
## [1] "Feature_41_ArimaVec_6"
## [1] "Feature_41_ArimaVec_7"
## [1] "Feature_41_ArimaVec_8"
## [1] "Feature_41_ArimaVec_9"
## [1] "Feature_42_ArimaVec_1"
## [1] "Feature_42_ArimaVec_2"
## [1] "Feature_42_ArimaVec_3"
## [1] "Feature_42_ArimaVec_4"
## [1] "Feature_42_ArimaVec_5"
## [1] "Feature_42_ArimaVec_6"
## [1] "Feature_42_ArimaVec_7"
## [1] "Feature_42_ArimaVec_8"
## [1] "Feature_42_ArimaVec_9"# DF Conversion Validation
arimaModels_ARMA_coefs[[countryFeature2Index(countryIndx=3, featureIndx=5)]][2] == arima_df[3, (5-1)*9 + 2]## [1] FALSE# [1] 1802.956
# Aggregate 2 datasets
dim(EU_SOCR_Country_Ranking_Data_2011) # [1] 31 10## [1] 31 10aggregate_arima_vector_country_ranking_df <-
as.data.frame(cbind(arima_df, EU_SOCR_Country_Ranking_Data_2011[ , -1]))
dim(aggregate_arima_vector_country_ranking_df) # [1] Country=31 * Features=387 (ARIMA=378 + Ranking=9)## [1] 31 387# View(aggregate_arima_vector_country_ranking_df)
rownames(aggregate_arima_vector_country_ranking_df) <- countryNames
write.csv(aggregate_arima_vector_country_ranking_df, row.names = T, fileEncoding = "UTF-16LE",
"E:/Ivo.dir/Research/UMichigan/Publications_Books/2018/others/4D_Time_Space_Book_Ideas/ARIMAX_EU_DataAnalytics/EU_aggregate_arima_vector_country_ranking.csv")12.2 Spacetime Analytics
12.2.1 Supervised classification
Use Model-based and Model-free methods to predict the overall (OA) country ranking.
# 1. LASSO regression/feature extraction
library(glmnet)
library(arm)
library(knitr)
# subset test data
Y = aggregate_arima_vector_country_ranking_df$OA
X = aggregate_arima_vector_country_ranking_df[ , -387]
# remove columns containing NAs and convert character DF to numeric type
X = as.data.frame(apply(X[ , colSums(is.na(X)) == 0], 2, as.numeric)); dim(X) # [1] 31 386## [1] 31 386fitRidge = glmnet(as.matrix(X), Y, alpha = 0) # Ridge Regression
fitLASSO = glmnet(as.matrix(X), Y, alpha = 1) # The LASSO
# LASSO
plot(fitLASSO, xvar="lambda", label="TRUE", lwd=3)
# add label to upper x-axis
mtext("LASSO regularizer: Number of Nonzero (Active) Coefficients", side=3, line=2.5)
# Ridge
plot(fitRidge, xvar="lambda", label="TRUE", lwd=3)
# add label to upper x-axis
mtext("Ridge regularizer: Number of Nonzero (Active) Coefficients", side=3, line=2.5)
#### 10-fold cross validation ####
# LASSO
library(doParallel)
registerDoParallel(6)
set.seed(1234) # set seed
# (10-fold) cross validation for the LASSO
cvLASSO = cv.glmnet(data.matrix(X), Y, alpha = 1, parallel=TRUE)
cvRidge = cv.glmnet(data.matrix(X), Y, alpha = 0, parallel=TRUE)
plot(cvLASSO)
mtext("CV LASSO: Number of Nonzero (Active) Coefficients", side=3, line=2.5)
# Identify top predictors and forecast the Y=Overall (OA) Country ranking outcome
predLASSO <- predict(cvLASSO, s = cvLASSO$lambda.min, newx = data.matrix(X))
testMSE_LASSO <- mean((predLASSO - Y)^2); testMSE_LASSO## [1] 2.135831predLASSO = predict(cvLASSO, s = cvLASSO$lambda.min, newx = data.matrix(X))
predRidge = predict(fitRidge, s = cvRidge$lambda.min, newx = data.matrix(X))
# calculate test set MSE
testMSELASSO = mean((predLASSO - Y)^2)
testMSERidge = mean((predRidge - Y)^2)
##################################Use only ARIMA effects, no SOCR meta-data#####
set.seed(4321)
cvLASSO_lim = cv.glmnet(data.matrix(X[ , 1:(42*9)]), Y, alpha = 1, parallel=TRUE)
plot(cvLASSO_lim)
mtext("CV LASSO (using only Timeseries data): Number of Nonzero (Active) Coefficients", side=3, line=2.5)
# Identify top predictors and forecast the Y=Overall (OA) Country ranking outcome
predLASSO_lim <- predict(cvLASSO_lim, s = 3, # cvLASSO_lim$lambda.min,
newx = data.matrix(X[ , 1:(42*9)]))
coefList_lim <- coef(cvLASSO_lim, s=3) # 'lambda.min')
coefList_lim <- data.frame(coefList_lim@Dimnames[[1]][coefList_lim@i+1],coefList_lim@x)
names(coefList_lim) <- c('Feature','EffectSize')
arrange(coefList_lim, -abs(EffectSize))[2:10, ]## Feature EffectSize
## 2 Feature_1_ArimaVec_8 -2.3864299
## 3 Feature_19_ArimaVec_8 2.0871310
## 4 Feature_16_ArimaVec_3 2.0465254
## 5 Feature_13_ArimaVec_8 -1.7348553
## 6 Feature_15_ArimaVec_4 -1.4588173
## 7 Feature_22_ArimaVec_4 -1.1068801
## 8 Feature_25_ArimaVec_5 0.9336800
## 9 Feature_35_ArimaVec_4 -0.9276244
## 10 Feature_25_ArimaVec_4 -0.8486434cor(Y, predLASSO_lim[, 1]) # 0.84## [1] 0.8428065################################################################################
# Plot Regression Coefficients: create variable names for plotting
library("arm")
# par(mar=c(2, 13, 1, 1)) # extra large left margin # par(mar=c(5,5,5,5))
varNames <- colnames(X); varNames; length(varNames)## [1] "Feature_1_ArimaVec_1" "Feature_1_ArimaVec_2" "Feature_1_ArimaVec_3"
## [4] "Feature_1_ArimaVec_4" "Feature_1_ArimaVec_5" "Feature_1_ArimaVec_6"
## [7] "Feature_1_ArimaVec_7" "Feature_1_ArimaVec_8" "Feature_1_ArimaVec_9"
## [10] "Feature_2_ArimaVec_1" "Feature_2_ArimaVec_2" "Feature_2_ArimaVec_3"
## [13] "Feature_2_ArimaVec_4" "Feature_2_ArimaVec_5" "Feature_2_ArimaVec_6"
## [16] "Feature_2_ArimaVec_7" "Feature_2_ArimaVec_8" "Feature_2_ArimaVec_9"
## [19] "Feature_3_ArimaVec_1" "Feature_3_ArimaVec_2" "Feature_3_ArimaVec_3"
## [22] "Feature_3_ArimaVec_4" "Feature_3_ArimaVec_5" "Feature_3_ArimaVec_6"
## [25] "Feature_3_ArimaVec_7" "Feature_3_ArimaVec_8" "Feature_3_ArimaVec_9"
## [28] "Feature_4_ArimaVec_1" "Feature_4_ArimaVec_2" "Feature_4_ArimaVec_3"
## [31] "Feature_4_ArimaVec_4" "Feature_4_ArimaVec_5" "Feature_4_ArimaVec_6"
## [34] "Feature_4_ArimaVec_7" "Feature_4_ArimaVec_8" "Feature_4_ArimaVec_9"
## [37] "Feature_5_ArimaVec_1" "Feature_5_ArimaVec_2" "Feature_5_ArimaVec_3"
## [40] "Feature_5_ArimaVec_4" "Feature_5_ArimaVec_5" "Feature_5_ArimaVec_6"
## [43] "Feature_5_ArimaVec_7" "Feature_5_ArimaVec_8" "Feature_5_ArimaVec_9"
## [46] "Feature_6_ArimaVec_1" "Feature_6_ArimaVec_2" "Feature_6_ArimaVec_3"
## [49] "Feature_6_ArimaVec_4" "Feature_6_ArimaVec_5" "Feature_6_ArimaVec_6"
## [52] "Feature_6_ArimaVec_7" "Feature_6_ArimaVec_8" "Feature_6_ArimaVec_9"
## [55] "Feature_7_ArimaVec_1" "Feature_7_ArimaVec_2" "Feature_7_ArimaVec_3"
## [58] "Feature_7_ArimaVec_4" "Feature_7_ArimaVec_5" "Feature_7_ArimaVec_6"
## [61] "Feature_7_ArimaVec_7" "Feature_7_ArimaVec_8" "Feature_7_ArimaVec_9"
## [64] "Feature_8_ArimaVec_1" "Feature_8_ArimaVec_2" "Feature_8_ArimaVec_3"
## [67] "Feature_8_ArimaVec_4" "Feature_8_ArimaVec_5" "Feature_8_ArimaVec_6"
## [70] "Feature_8_ArimaVec_7" "Feature_8_ArimaVec_8" "Feature_8_ArimaVec_9"
## [73] "Feature_9_ArimaVec_1" "Feature_9_ArimaVec_2" "Feature_9_ArimaVec_3"
## [76] "Feature_9_ArimaVec_4" "Feature_9_ArimaVec_5" "Feature_9_ArimaVec_6"
## [79] "Feature_9_ArimaVec_7" "Feature_9_ArimaVec_8" "Feature_9_ArimaVec_9"
## [82] "Feature_10_ArimaVec_1" "Feature_10_ArimaVec_2" "Feature_10_ArimaVec_3"
## [85] "Feature_10_ArimaVec_4" "Feature_10_ArimaVec_5" "Feature_10_ArimaVec_6"
## [88] "Feature_10_ArimaVec_7" "Feature_10_ArimaVec_8" "Feature_10_ArimaVec_9"
## [91] "Feature_11_ArimaVec_1" "Feature_11_ArimaVec_2" "Feature_11_ArimaVec_3"
## [94] "Feature_11_ArimaVec_4" "Feature_11_ArimaVec_5" "Feature_11_ArimaVec_6"
## [97] "Feature_11_ArimaVec_7" "Feature_11_ArimaVec_8" "Feature_11_ArimaVec_9"
## [100] "Feature_12_ArimaVec_1" "Feature_12_ArimaVec_2" "Feature_12_ArimaVec_3"
## [103] "Feature_12_ArimaVec_4" "Feature_12_ArimaVec_5" "Feature_12_ArimaVec_6"
## [106] "Feature_12_ArimaVec_7" "Feature_12_ArimaVec_8" "Feature_12_ArimaVec_9"
## [109] "Feature_13_ArimaVec_1" "Feature_13_ArimaVec_2" "Feature_13_ArimaVec_3"
## [112] "Feature_13_ArimaVec_4" "Feature_13_ArimaVec_5" "Feature_13_ArimaVec_6"
## [115] "Feature_13_ArimaVec_7" "Feature_13_ArimaVec_8" "Feature_13_ArimaVec_9"
## [118] "Feature_14_ArimaVec_1" "Feature_14_ArimaVec_2" "Feature_14_ArimaVec_3"
## [121] "Feature_14_ArimaVec_4" "Feature_14_ArimaVec_5" "Feature_14_ArimaVec_6"
## [124] "Feature_14_ArimaVec_7" "Feature_14_ArimaVec_8" "Feature_14_ArimaVec_9"
## [127] "Feature_15_ArimaVec_1" "Feature_15_ArimaVec_2" "Feature_15_ArimaVec_3"
## [130] "Feature_15_ArimaVec_4" "Feature_15_ArimaVec_5" "Feature_15_ArimaVec_6"
## [133] "Feature_15_ArimaVec_7" "Feature_15_ArimaVec_8" "Feature_15_ArimaVec_9"
## [136] "Feature_16_ArimaVec_1" "Feature_16_ArimaVec_2" "Feature_16_ArimaVec_3"
## [139] "Feature_16_ArimaVec_4" "Feature_16_ArimaVec_5" "Feature_16_ArimaVec_6"
## [142] "Feature_16_ArimaVec_7" "Feature_16_ArimaVec_8" "Feature_16_ArimaVec_9"
## [145] "Feature_17_ArimaVec_1" "Feature_17_ArimaVec_2" "Feature_17_ArimaVec_3"
## [148] "Feature_17_ArimaVec_4" "Feature_17_ArimaVec_5" "Feature_17_ArimaVec_6"
## [151] "Feature_17_ArimaVec_7" "Feature_17_ArimaVec_8" "Feature_17_ArimaVec_9"
## [154] "Feature_18_ArimaVec_1" "Feature_18_ArimaVec_2" "Feature_18_ArimaVec_3"
## [157] "Feature_18_ArimaVec_4" "Feature_18_ArimaVec_5" "Feature_18_ArimaVec_6"
## [160] "Feature_18_ArimaVec_7" "Feature_18_ArimaVec_8" "Feature_18_ArimaVec_9"
## [163] "Feature_19_ArimaVec_1" "Feature_19_ArimaVec_2" "Feature_19_ArimaVec_3"
## [166] "Feature_19_ArimaVec_4" "Feature_19_ArimaVec_5" "Feature_19_ArimaVec_6"
## [169] "Feature_19_ArimaVec_7" "Feature_19_ArimaVec_8" "Feature_19_ArimaVec_9"
## [172] "Feature_20_ArimaVec_1" "Feature_20_ArimaVec_2" "Feature_20_ArimaVec_3"
## [175] "Feature_20_ArimaVec_4" "Feature_20_ArimaVec_5" "Feature_20_ArimaVec_6"
## [178] "Feature_20_ArimaVec_7" "Feature_20_ArimaVec_8" "Feature_20_ArimaVec_9"
## [181] "Feature_21_ArimaVec_1" "Feature_21_ArimaVec_2" "Feature_21_ArimaVec_3"
## [184] "Feature_21_ArimaVec_4" "Feature_21_ArimaVec_5" "Feature_21_ArimaVec_6"
## [187] "Feature_21_ArimaVec_7" "Feature_21_ArimaVec_8" "Feature_21_ArimaVec_9"
## [190] "Feature_22_ArimaVec_1" "Feature_22_ArimaVec_2" "Feature_22_ArimaVec_3"
## [193] "Feature_22_ArimaVec_4" "Feature_22_ArimaVec_5" "Feature_22_ArimaVec_6"
## [196] "Feature_22_ArimaVec_7" "Feature_22_ArimaVec_8" "Feature_22_ArimaVec_9"
## [199] "Feature_23_ArimaVec_1" "Feature_23_ArimaVec_2" "Feature_23_ArimaVec_3"
## [202] "Feature_23_ArimaVec_4" "Feature_23_ArimaVec_5" "Feature_23_ArimaVec_6"
## [205] "Feature_23_ArimaVec_7" "Feature_23_ArimaVec_8" "Feature_23_ArimaVec_9"
## [208] "Feature_24_ArimaVec_1" "Feature_24_ArimaVec_2" "Feature_24_ArimaVec_3"
## [211] "Feature_24_ArimaVec_4" "Feature_24_ArimaVec_5" "Feature_24_ArimaVec_6"
## [214] "Feature_24_ArimaVec_7" "Feature_24_ArimaVec_8" "Feature_24_ArimaVec_9"
## [217] "Feature_25_ArimaVec_1" "Feature_25_ArimaVec_2" "Feature_25_ArimaVec_3"
## [220] "Feature_25_ArimaVec_4" "Feature_25_ArimaVec_5" "Feature_25_ArimaVec_6"
## [223] "Feature_25_ArimaVec_7" "Feature_25_ArimaVec_8" "Feature_25_ArimaVec_9"
## [226] "Feature_26_ArimaVec_1" "Feature_26_ArimaVec_2" "Feature_26_ArimaVec_3"
## [229] "Feature_26_ArimaVec_4" "Feature_26_ArimaVec_5" "Feature_26_ArimaVec_6"
## [232] "Feature_26_ArimaVec_7" "Feature_26_ArimaVec_8" "Feature_26_ArimaVec_9"
## [235] "Feature_27_ArimaVec_1" "Feature_27_ArimaVec_2" "Feature_27_ArimaVec_3"
## [238] "Feature_27_ArimaVec_4" "Feature_27_ArimaVec_5" "Feature_27_ArimaVec_6"
## [241] "Feature_27_ArimaVec_7" "Feature_27_ArimaVec_8" "Feature_27_ArimaVec_9"
## [244] "Feature_28_ArimaVec_1" "Feature_28_ArimaVec_2" "Feature_28_ArimaVec_3"
## [247] "Feature_28_ArimaVec_4" "Feature_28_ArimaVec_5" "Feature_28_ArimaVec_6"
## [250] "Feature_28_ArimaVec_7" "Feature_28_ArimaVec_8" "Feature_28_ArimaVec_9"
## [253] "Feature_29_ArimaVec_1" "Feature_29_ArimaVec_2" "Feature_29_ArimaVec_3"
## [256] "Feature_29_ArimaVec_4" "Feature_29_ArimaVec_5" "Feature_29_ArimaVec_6"
## [259] "Feature_29_ArimaVec_7" "Feature_29_ArimaVec_8" "Feature_29_ArimaVec_9"
## [262] "Feature_30_ArimaVec_1" "Feature_30_ArimaVec_2" "Feature_30_ArimaVec_3"
## [265] "Feature_30_ArimaVec_4" "Feature_30_ArimaVec_5" "Feature_30_ArimaVec_6"
## [268] "Feature_30_ArimaVec_7" "Feature_30_ArimaVec_8" "Feature_30_ArimaVec_9"
## [271] "Feature_31_ArimaVec_1" "Feature_31_ArimaVec_2" "Feature_31_ArimaVec_3"
## [274] "Feature_31_ArimaVec_4" "Feature_31_ArimaVec_5" "Feature_31_ArimaVec_6"
## [277] "Feature_31_ArimaVec_7" "Feature_31_ArimaVec_8" "Feature_31_ArimaVec_9"
## [280] "Feature_32_ArimaVec_1" "Feature_32_ArimaVec_2" "Feature_32_ArimaVec_3"
## [283] "Feature_32_ArimaVec_4" "Feature_32_ArimaVec_5" "Feature_32_ArimaVec_6"
## [286] "Feature_32_ArimaVec_7" "Feature_32_ArimaVec_8" "Feature_32_ArimaVec_9"
## [289] "Feature_33_ArimaVec_1" "Feature_33_ArimaVec_2" "Feature_33_ArimaVec_3"
## [292] "Feature_33_ArimaVec_4" "Feature_33_ArimaVec_5" "Feature_33_ArimaVec_6"
## [295] "Feature_33_ArimaVec_7" "Feature_33_ArimaVec_8" "Feature_33_ArimaVec_9"
## [298] "Feature_34_ArimaVec_1" "Feature_34_ArimaVec_2" "Feature_34_ArimaVec_3"
## [301] "Feature_34_ArimaVec_4" "Feature_34_ArimaVec_5" "Feature_34_ArimaVec_6"
## [304] "Feature_34_ArimaVec_7" "Feature_34_ArimaVec_8" "Feature_34_ArimaVec_9"
## [307] "Feature_35_ArimaVec_1" "Feature_35_ArimaVec_2" "Feature_35_ArimaVec_3"
## [310] "Feature_35_ArimaVec_4" "Feature_35_ArimaVec_5" "Feature_35_ArimaVec_6"
## [313] "Feature_35_ArimaVec_7" "Feature_35_ArimaVec_8" "Feature_35_ArimaVec_9"
## [316] "Feature_36_ArimaVec_1" "Feature_36_ArimaVec_2" "Feature_36_ArimaVec_3"
## [319] "Feature_36_ArimaVec_4" "Feature_36_ArimaVec_5" "Feature_36_ArimaVec_6"
## [322] "Feature_36_ArimaVec_7" "Feature_36_ArimaVec_8" "Feature_36_ArimaVec_9"
## [325] "Feature_37_ArimaVec_1" "Feature_37_ArimaVec_2" "Feature_37_ArimaVec_3"
## [328] "Feature_37_ArimaVec_4" "Feature_37_ArimaVec_5" "Feature_37_ArimaVec_6"
## [331] "Feature_37_ArimaVec_7" "Feature_37_ArimaVec_8" "Feature_37_ArimaVec_9"
## [334] "Feature_38_ArimaVec_1" "Feature_38_ArimaVec_2" "Feature_38_ArimaVec_3"
## [337] "Feature_38_ArimaVec_4" "Feature_38_ArimaVec_5" "Feature_38_ArimaVec_6"
## [340] "Feature_38_ArimaVec_7" "Feature_38_ArimaVec_8" "Feature_38_ArimaVec_9"
## [343] "Feature_39_ArimaVec_1" "Feature_39_ArimaVec_2" "Feature_39_ArimaVec_3"
## [346] "Feature_39_ArimaVec_4" "Feature_39_ArimaVec_5" "Feature_39_ArimaVec_6"
## [349] "Feature_39_ArimaVec_7" "Feature_39_ArimaVec_8" "Feature_39_ArimaVec_9"
## [352] "Feature_40_ArimaVec_1" "Feature_40_ArimaVec_2" "Feature_40_ArimaVec_3"
## [355] "Feature_40_ArimaVec_4" "Feature_40_ArimaVec_5" "Feature_40_ArimaVec_6"
## [358] "Feature_40_ArimaVec_7" "Feature_40_ArimaVec_8" "Feature_40_ArimaVec_9"
## [361] "Feature_41_ArimaVec_1" "Feature_41_ArimaVec_2" "Feature_41_ArimaVec_3"
## [364] "Feature_41_ArimaVec_4" "Feature_41_ArimaVec_5" "Feature_41_ArimaVec_6"
## [367] "Feature_41_ArimaVec_7" "Feature_41_ArimaVec_8" "Feature_41_ArimaVec_9"
## [370] "Feature_42_ArimaVec_1" "Feature_42_ArimaVec_2" "Feature_42_ArimaVec_3"
## [373] "Feature_42_ArimaVec_4" "Feature_42_ArimaVec_5" "Feature_42_ArimaVec_6"
## [376] "Feature_42_ArimaVec_7" "Feature_42_ArimaVec_8" "Feature_42_ArimaVec_9"
## [379] "IncomeGroup" "PopSizeGroup" "ED"
## [382] "Edu" "HI" "QOL"
## [385] "PE" "Relig"## [1] 386betaHatLASSO = as.double(coef(fitLASSO, s = cvLASSO$lambda.min)) # cvLASSO$lambda.1se
betaHatRidge = as.double(coef(fitRidge, s = cvRidge$lambda.min))
#coefplot(betaHatLASSO[2:386], sd = rep(0, 385), pch=0, cex.pts = 3, main = "LASSO-Regularized Regression Coefficient Estimates", varnames = varNames)
coefplot(betaHatLASSO[377:386], sd = rep(0, 10), pch=0, cex.pts = 3, col="red", main = "LASSO-Regularized Regression Coefficient Estimates", varnames = varNames[377:386])
coefplot(betaHatRidge[377:386], sd = rep(0, 10), pch=2, add = TRUE, col.pts = "blue", cex.pts = 3)
legend("bottomleft", c("LASSO", "Ridge"), col = c("red", "blue"), pch = c(1 , 2), bty = "o", cex = 2)
varImp <- function(object, lambda = NULL, ...) {
## skipping a few lines
beta <- predict(object, s = lambda, type = "coef")
if(is.list(beta)) {
out <- do.call("cbind", lapply(beta, function(x) x[,1]))
out <- as.data.frame(out)
} else out <- data.frame(Overall = beta[,1])
out <- abs(out[rownames(out) != "(Intercept)",,drop = FALSE])
out
}
varImp(cvLASSO, lambda = cvLASSO$lambda.min)## Overall
## Feature_1_ArimaVec_1 0.0000000000
## Feature_1_ArimaVec_2 0.0000000000
## Feature_1_ArimaVec_3 0.0000000000
## Feature_1_ArimaVec_4 0.0000000000
## Feature_1_ArimaVec_5 0.0000000000
## Feature_1_ArimaVec_6 0.0000000000
## Feature_1_ArimaVec_7 0.0000000000
## Feature_1_ArimaVec_8 0.0000000000
## Feature_1_ArimaVec_9 0.0000000000
## Feature_2_ArimaVec_1 0.0000000000
## Feature_2_ArimaVec_2 0.0000000000
## Feature_2_ArimaVec_3 0.0000000000
## Feature_2_ArimaVec_4 0.0000000000
## Feature_2_ArimaVec_5 0.0000000000
## Feature_2_ArimaVec_6 0.0000000000
## Feature_2_ArimaVec_7 0.0000000000
## Feature_2_ArimaVec_8 0.0000000000
## Feature_2_ArimaVec_9 0.0000000000
## Feature_3_ArimaVec_1 0.0000000000
## Feature_3_ArimaVec_2 0.0000000000
## Feature_3_ArimaVec_3 0.0000000000
## Feature_3_ArimaVec_4 0.0000000000
## Feature_3_ArimaVec_5 0.0000000000
## Feature_3_ArimaVec_6 0.0000000000
## Feature_3_ArimaVec_7 0.0000000000
## Feature_3_ArimaVec_8 0.0000000000
## Feature_3_ArimaVec_9 0.0000000000
## Feature_4_ArimaVec_1 0.0000000000
## Feature_4_ArimaVec_2 0.0000000000
## Feature_4_ArimaVec_3 0.0000000000
## Feature_4_ArimaVec_4 0.0000000000
## Feature_4_ArimaVec_5 0.0000000000
## Feature_4_ArimaVec_6 0.0000000000
## Feature_4_ArimaVec_7 0.0000000000
## Feature_4_ArimaVec_8 0.0000000000
## Feature_4_ArimaVec_9 0.0000000000
## Feature_5_ArimaVec_1 0.0000000000
## Feature_5_ArimaVec_2 0.0000000000
## Feature_5_ArimaVec_3 0.0000000000
## Feature_5_ArimaVec_4 0.0000000000
## Feature_5_ArimaVec_5 0.0000000000
## Feature_5_ArimaVec_6 0.0000000000
## Feature_5_ArimaVec_7 0.0000000000
## Feature_5_ArimaVec_8 0.0000000000
## Feature_5_ArimaVec_9 0.0000000000
## Feature_6_ArimaVec_1 0.0000000000
## Feature_6_ArimaVec_2 0.0000000000
## Feature_6_ArimaVec_3 0.0000000000
## Feature_6_ArimaVec_4 0.0000000000
## Feature_6_ArimaVec_5 0.0000000000
## Feature_6_ArimaVec_6 0.0000000000
## Feature_6_ArimaVec_7 0.0000000000
## Feature_6_ArimaVec_8 0.0000000000
## Feature_6_ArimaVec_9 0.0000000000
## Feature_7_ArimaVec_1 0.0000000000
## Feature_7_ArimaVec_2 0.0000000000
## Feature_7_ArimaVec_3 0.0000000000
## Feature_7_ArimaVec_4 0.0000000000
## Feature_7_ArimaVec_5 0.0000000000
## Feature_7_ArimaVec_6 0.0000000000
## Feature_7_ArimaVec_7 0.0000000000
## Feature_7_ArimaVec_8 0.0000000000
## Feature_7_ArimaVec_9 0.0000000000
## Feature_8_ArimaVec_1 0.0000000000
## Feature_8_ArimaVec_2 0.0000000000
## Feature_8_ArimaVec_3 0.0000000000
## Feature_8_ArimaVec_4 0.0000000000
## Feature_8_ArimaVec_5 0.0000000000
## Feature_8_ArimaVec_6 0.0000000000
## Feature_8_ArimaVec_7 0.0000000000
## Feature_8_ArimaVec_8 0.0000000000
## Feature_8_ArimaVec_9 0.0000000000
## Feature_9_ArimaVec_1 0.0000000000
## Feature_9_ArimaVec_2 0.0000000000
## Feature_9_ArimaVec_3 0.0000000000
## Feature_9_ArimaVec_4 0.0000000000
## Feature_9_ArimaVec_5 0.0000000000
## Feature_9_ArimaVec_6 0.0000000000
## Feature_9_ArimaVec_7 0.0000000000
## Feature_9_ArimaVec_8 0.0000000000
## Feature_9_ArimaVec_9 0.0000000000
## Feature_10_ArimaVec_1 0.0000000000
## Feature_10_ArimaVec_2 0.0000000000
## Feature_10_ArimaVec_3 0.0000000000
## Feature_10_ArimaVec_4 0.0000000000
## Feature_10_ArimaVec_5 0.0000000000
## Feature_10_ArimaVec_6 0.0000000000
## Feature_10_ArimaVec_7 0.0000000000
## Feature_10_ArimaVec_8 0.0000000000
## Feature_10_ArimaVec_9 0.0000000000
## Feature_11_ArimaVec_1 0.0000000000
## Feature_11_ArimaVec_2 0.0000000000
## Feature_11_ArimaVec_3 0.0000000000
## Feature_11_ArimaVec_4 0.0000000000
## Feature_11_ArimaVec_5 0.0000000000
## Feature_11_ArimaVec_6 0.0000000000
## Feature_11_ArimaVec_7 0.0000000000
## Feature_11_ArimaVec_8 0.0000000000
## Feature_11_ArimaVec_9 0.0000000000
## Feature_12_ArimaVec_1 0.0000000000
## Feature_12_ArimaVec_2 0.0000000000
## Feature_12_ArimaVec_3 0.0000000000
## Feature_12_ArimaVec_4 0.0000000000
## Feature_12_ArimaVec_5 0.0000000000
## Feature_12_ArimaVec_6 0.0000000000
## Feature_12_ArimaVec_7 0.0000000000
## Feature_12_ArimaVec_8 0.0000000000
## Feature_12_ArimaVec_9 0.0000000000
## Feature_13_ArimaVec_1 0.0000000000
## Feature_13_ArimaVec_2 0.0000000000
## Feature_13_ArimaVec_3 0.0000000000
## Feature_13_ArimaVec_4 0.0000000000
## Feature_13_ArimaVec_5 0.0000000000
## Feature_13_ArimaVec_6 0.0000000000
## Feature_13_ArimaVec_7 0.0000000000
## Feature_13_ArimaVec_8 0.0000000000
## Feature_13_ArimaVec_9 0.0000000000
## Feature_14_ArimaVec_1 0.0000000000
## Feature_14_ArimaVec_2 0.0000000000
## Feature_14_ArimaVec_3 0.0000000000
## Feature_14_ArimaVec_4 0.0000000000
## Feature_14_ArimaVec_5 0.0000000000
## Feature_14_ArimaVec_6 0.0000000000
## Feature_14_ArimaVec_7 0.0000000000
## Feature_14_ArimaVec_8 0.0000000000
## Feature_14_ArimaVec_9 0.0000000000
## Feature_15_ArimaVec_1 0.0000000000
## Feature_15_ArimaVec_2 0.0000000000
## Feature_15_ArimaVec_3 0.0000000000
## Feature_15_ArimaVec_4 0.0000000000
## Feature_15_ArimaVec_5 0.0000000000
## Feature_15_ArimaVec_6 0.0000000000
## Feature_15_ArimaVec_7 0.0000000000
## Feature_15_ArimaVec_8 0.0000000000
## Feature_15_ArimaVec_9 0.0000000000
## Feature_16_ArimaVec_1 0.0000000000
## Feature_16_ArimaVec_2 0.0000000000
## Feature_16_ArimaVec_3 0.0000000000
## Feature_16_ArimaVec_4 0.0000000000
## Feature_16_ArimaVec_5 0.0000000000
## Feature_16_ArimaVec_6 0.0000000000
## Feature_16_ArimaVec_7 0.0000000000
## Feature_16_ArimaVec_8 0.0000000000
## Feature_16_ArimaVec_9 0.0000000000
## Feature_17_ArimaVec_1 0.0000000000
## Feature_17_ArimaVec_2 0.0000000000
## Feature_17_ArimaVec_3 0.0000000000
## Feature_17_ArimaVec_4 0.0000000000
## Feature_17_ArimaVec_5 0.0000000000
## Feature_17_ArimaVec_6 0.0000000000
## Feature_17_ArimaVec_7 0.0000000000
## Feature_17_ArimaVec_8 0.0000000000
## Feature_17_ArimaVec_9 0.0000000000
## Feature_18_ArimaVec_1 0.0000000000
## Feature_18_ArimaVec_2 0.0000000000
## Feature_18_ArimaVec_3 0.0000000000
## Feature_18_ArimaVec_4 0.0000000000
## Feature_18_ArimaVec_5 0.0000000000
## Feature_18_ArimaVec_6 0.0000000000
## Feature_18_ArimaVec_7 0.0000000000
## Feature_18_ArimaVec_8 0.0000000000
## Feature_18_ArimaVec_9 0.0000000000
## Feature_19_ArimaVec_1 0.0000000000
## Feature_19_ArimaVec_2 0.0000000000
## Feature_19_ArimaVec_3 0.0000000000
## Feature_19_ArimaVec_4 0.0000000000
## Feature_19_ArimaVec_5 0.0000000000
## Feature_19_ArimaVec_6 0.0000000000
## Feature_19_ArimaVec_7 0.0000000000
## Feature_19_ArimaVec_8 0.3874790172
## Feature_19_ArimaVec_9 0.0000000000
## Feature_20_ArimaVec_1 0.0000000000
## Feature_20_ArimaVec_2 0.0000000000
## Feature_20_ArimaVec_3 0.0000000000
## Feature_20_ArimaVec_4 0.0000000000
## Feature_20_ArimaVec_5 0.0000000000
## Feature_20_ArimaVec_6 0.0000000000
## Feature_20_ArimaVec_7 0.0000000000
## Feature_20_ArimaVec_8 0.0000000000
## Feature_20_ArimaVec_9 0.0000000000
## Feature_21_ArimaVec_1 0.0000000000
## Feature_21_ArimaVec_2 0.0000000000
## Feature_21_ArimaVec_3 0.0000000000
## Feature_21_ArimaVec_4 0.0000000000
## Feature_21_ArimaVec_5 0.0000000000
## Feature_21_ArimaVec_6 0.0000000000
## Feature_21_ArimaVec_7 0.0000000000
## Feature_21_ArimaVec_8 0.0000000000
## Feature_21_ArimaVec_9 0.0000000000
## Feature_22_ArimaVec_1 0.0000000000
## Feature_22_ArimaVec_2 0.0000000000
## Feature_22_ArimaVec_3 0.0000000000
## Feature_22_ArimaVec_4 0.0726521733
## Feature_22_ArimaVec_5 0.0000000000
## Feature_22_ArimaVec_6 0.0000000000
## Feature_22_ArimaVec_7 0.0000000000
## Feature_22_ArimaVec_8 0.0000000000
## Feature_22_ArimaVec_9 0.0000000000
## Feature_23_ArimaVec_1 0.0000000000
## Feature_23_ArimaVec_2 0.0000000000
## Feature_23_ArimaVec_3 0.0000000000
## Feature_23_ArimaVec_4 0.0000000000
## Feature_23_ArimaVec_5 0.0000000000
## Feature_23_ArimaVec_6 0.0000000000
## Feature_23_ArimaVec_7 0.0000000000
## Feature_23_ArimaVec_8 0.0000000000
## Feature_23_ArimaVec_9 0.0000000000
## Feature_24_ArimaVec_1 0.0000000000
## Feature_24_ArimaVec_2 0.0000000000
## Feature_24_ArimaVec_3 0.0000000000
## Feature_24_ArimaVec_4 0.0000000000
## Feature_24_ArimaVec_5 0.0000000000
## Feature_24_ArimaVec_6 0.0000000000
## Feature_24_ArimaVec_7 0.0000000000
## Feature_24_ArimaVec_8 0.0000000000
## Feature_24_ArimaVec_9 0.0000000000
## Feature_25_ArimaVec_1 0.0000000000
## Feature_25_ArimaVec_2 0.0000000000
## Feature_25_ArimaVec_3 0.0000000000
## Feature_25_ArimaVec_4 0.0000000000
## Feature_25_ArimaVec_5 0.0000000000
## Feature_25_ArimaVec_6 0.0000000000
## Feature_25_ArimaVec_7 0.0000000000
## Feature_25_ArimaVec_8 0.0000000000
## Feature_25_ArimaVec_9 0.0000000000
## Feature_26_ArimaVec_1 0.0000000000
## Feature_26_ArimaVec_2 0.0000000000
## Feature_26_ArimaVec_3 0.0000000000
## Feature_26_ArimaVec_4 0.0000000000
## Feature_26_ArimaVec_5 0.0000000000
## Feature_26_ArimaVec_6 0.0000000000
## Feature_26_ArimaVec_7 0.0000000000
## Feature_26_ArimaVec_8 0.0000000000
## Feature_26_ArimaVec_9 0.0000000000
## Feature_27_ArimaVec_1 0.0000000000
## Feature_27_ArimaVec_2 0.0000000000
## Feature_27_ArimaVec_3 0.0000000000
## Feature_27_ArimaVec_4 0.0000000000
## Feature_27_ArimaVec_5 0.0000000000
## Feature_27_ArimaVec_6 0.0000000000
## Feature_27_ArimaVec_7 0.0000000000
## Feature_27_ArimaVec_8 0.0000000000
## Feature_27_ArimaVec_9 0.0000000000
## Feature_28_ArimaVec_1 0.0000000000
## Feature_28_ArimaVec_2 0.0000000000
## Feature_28_ArimaVec_3 0.0000000000
## Feature_28_ArimaVec_4 0.0000000000
## Feature_28_ArimaVec_5 0.0000000000
## Feature_28_ArimaVec_6 0.0000000000
## Feature_28_ArimaVec_7 0.0000000000
## Feature_28_ArimaVec_8 0.0000000000
## Feature_28_ArimaVec_9 0.0000000000
## Feature_29_ArimaVec_1 0.0000000000
## Feature_29_ArimaVec_2 0.0000000000
## Feature_29_ArimaVec_3 0.0000000000
## Feature_29_ArimaVec_4 0.0000000000
## Feature_29_ArimaVec_5 0.0000000000
## Feature_29_ArimaVec_6 0.0000000000
## Feature_29_ArimaVec_7 0.0000000000
## Feature_29_ArimaVec_8 0.0000000000
## Feature_29_ArimaVec_9 0.0000000000
## Feature_30_ArimaVec_1 0.0000000000
## Feature_30_ArimaVec_2 0.0000000000
## Feature_30_ArimaVec_3 0.0000000000
## Feature_30_ArimaVec_4 0.0000000000
## Feature_30_ArimaVec_5 0.0000000000
## Feature_30_ArimaVec_6 0.0000000000
## Feature_30_ArimaVec_7 0.0000000000
## Feature_30_ArimaVec_8 0.0000000000
## Feature_30_ArimaVec_9 0.0000000000
## Feature_31_ArimaVec_1 0.0000000000
## Feature_31_ArimaVec_2 0.0000000000
## Feature_31_ArimaVec_3 0.0000000000
## Feature_31_ArimaVec_4 0.0000000000
## Feature_31_ArimaVec_5 0.0000000000
## Feature_31_ArimaVec_6 0.0000000000
## Feature_31_ArimaVec_7 0.0000000000
## Feature_31_ArimaVec_8 0.0000000000
## Feature_31_ArimaVec_9 0.0000000000
## Feature_32_ArimaVec_1 0.0000000000
## Feature_32_ArimaVec_2 0.0000000000
## Feature_32_ArimaVec_3 0.0000000000
## Feature_32_ArimaVec_4 0.0000000000
## Feature_32_ArimaVec_5 0.0000000000
## Feature_32_ArimaVec_6 0.0000000000
## Feature_32_ArimaVec_7 0.0000000000
## Feature_32_ArimaVec_8 0.0000000000
## Feature_32_ArimaVec_9 0.0000000000
## Feature_33_ArimaVec_1 0.0000000000
## Feature_33_ArimaVec_2 0.0000000000
## Feature_33_ArimaVec_3 0.0000000000
## Feature_33_ArimaVec_4 0.0000000000
## Feature_33_ArimaVec_5 0.0000000000
## Feature_33_ArimaVec_6 0.0000000000
## Feature_33_ArimaVec_7 0.0000000000
## Feature_33_ArimaVec_8 0.0000000000
## Feature_33_ArimaVec_9 0.0000000000
## Feature_34_ArimaVec_1 0.0000000000
## Feature_34_ArimaVec_2 0.0000000000
## Feature_34_ArimaVec_3 0.0000000000
## Feature_34_ArimaVec_4 0.0000000000
## Feature_34_ArimaVec_5 0.0000000000
## Feature_34_ArimaVec_6 0.0000000000
## Feature_34_ArimaVec_7 0.0000000000
## Feature_34_ArimaVec_8 0.0000000000
## Feature_34_ArimaVec_9 0.0000000000
## Feature_35_ArimaVec_1 0.0000000000
## Feature_35_ArimaVec_2 0.0000000000
## Feature_35_ArimaVec_3 0.0000000000
## Feature_35_ArimaVec_4 0.0000000000
## Feature_35_ArimaVec_5 0.0000000000
## Feature_35_ArimaVec_6 0.0000000000
## Feature_35_ArimaVec_7 0.0000000000
## Feature_35_ArimaVec_8 0.0000000000
## Feature_35_ArimaVec_9 0.0000000000
## Feature_36_ArimaVec_1 0.0000000000
## Feature_36_ArimaVec_2 0.0000000000
## Feature_36_ArimaVec_3 0.0000000000
## Feature_36_ArimaVec_4 0.0000000000
## Feature_36_ArimaVec_5 0.0000000000
## Feature_36_ArimaVec_6 0.0000000000
## Feature_36_ArimaVec_7 0.0000000000
## Feature_36_ArimaVec_8 0.0000000000
## Feature_36_ArimaVec_9 0.0000000000
## Feature_37_ArimaVec_1 0.0000000000
## Feature_37_ArimaVec_2 0.0000000000
## Feature_37_ArimaVec_3 0.0000000000
## Feature_37_ArimaVec_4 0.0000000000
## Feature_37_ArimaVec_5 0.0000000000
## Feature_37_ArimaVec_6 0.2433669549
## Feature_37_ArimaVec_7 0.0000000000
## Feature_37_ArimaVec_8 0.0000000000
## Feature_37_ArimaVec_9 0.0000000000
## Feature_38_ArimaVec_1 0.0000000000
## Feature_38_ArimaVec_2 0.0000000000
## Feature_38_ArimaVec_3 0.0000000000
## Feature_38_ArimaVec_4 0.0000000000
## Feature_38_ArimaVec_5 0.0000000000
## Feature_38_ArimaVec_6 0.0000000000
## Feature_38_ArimaVec_7 0.0000000000
## Feature_38_ArimaVec_8 0.0000000000
## Feature_38_ArimaVec_9 0.0000000000
## Feature_39_ArimaVec_1 0.0000000000
## Feature_39_ArimaVec_2 0.0000000000
## Feature_39_ArimaVec_3 0.0000000000
## Feature_39_ArimaVec_4 0.0000000000
## Feature_39_ArimaVec_5 0.0000000000
## Feature_39_ArimaVec_6 0.0000000000
## Feature_39_ArimaVec_7 0.0000000000
## Feature_39_ArimaVec_8 0.0000000000
## Feature_39_ArimaVec_9 0.0000000000
## Feature_40_ArimaVec_1 0.0000000000
## Feature_40_ArimaVec_2 0.0000000000
## Feature_40_ArimaVec_3 0.0000000000
## Feature_40_ArimaVec_4 0.0000000000
## Feature_40_ArimaVec_5 0.0000000000
## Feature_40_ArimaVec_6 0.0000000000
## Feature_40_ArimaVec_7 0.0000000000
## Feature_40_ArimaVec_8 0.0000000000
## Feature_40_ArimaVec_9 0.0000000000
## Feature_41_ArimaVec_1 0.0000000000
## Feature_41_ArimaVec_2 0.0000000000
## Feature_41_ArimaVec_3 0.0000000000
## Feature_41_ArimaVec_4 0.0009309503
## Feature_41_ArimaVec_5 0.0000000000
## Feature_41_ArimaVec_6 0.0000000000
## Feature_41_ArimaVec_7 0.0000000000
## Feature_41_ArimaVec_8 0.0000000000
## Feature_41_ArimaVec_9 0.0000000000
## Feature_42_ArimaVec_1 0.0000000000
## Feature_42_ArimaVec_2 0.0000000000
## Feature_42_ArimaVec_3 0.0000000000
## Feature_42_ArimaVec_4 0.0000000000
## Feature_42_ArimaVec_5 0.0000000000
## Feature_42_ArimaVec_6 0.0000000000
## Feature_42_ArimaVec_7 0.0000000000
## Feature_42_ArimaVec_8 0.0000000000
## Feature_42_ArimaVec_9 0.0000000000
## IncomeGroup 0.0000000000
## PopSizeGroup 0.0000000000
## ED 0.4841867784
## Edu 0.0892314682
## HI 0.1367254263
## QOL 0.4135222206
## PE 0.3142177629
## Relig 0.0000000000coefList <- coef(cvLASSO, s='lambda.min')
coefList <- data.frame(coefList@Dimnames[[1]][coefList@i+1],coefList@x)
names(coefList) <- c('Feature','EffectSize')
arrange(coefList, -abs(EffectSize))[2:10, ]## Feature EffectSize
## 2 ED -0.4841867784
## 3 QOL -0.4135222206
## 4 Feature_19_ArimaVec_8 0.3874790172
## 5 PE -0.3142177629
## 6 Feature_37_ArimaVec_6 -0.2433669549
## 7 HI -0.1367254263
## 8 Edu -0.0892314682
## 9 Feature_22_ArimaVec_4 -0.0726521733
## 10 Feature_41_ArimaVec_4 0.0009309503# var val # Feature names: colnames(list_of_dfs_CommonFeatures[[1]])
#1 (Intercept) 49.4896874
#2 Feature_1_ArimaVec_8 -2.4050811 # Feature 1 = Active population: Females 15 to 64 years
#3 Feature_20_ArimaVec_8 -1.4015001 # Feature 20= "Employment: Females 15 to 64 years
#4 IncomeGroup -1.2271177
#5 Feature_9_ArimaVec_8 -1.0629835 # Feature 9= Active population: Total 15 to 64 years
#6 ED -0.7481041
#7 PE -0.5167668
#8 Feature_25_ArimaVec_5 0.4416775 # Feature 25= Property income
#9 Feature_9_ArimaVec_4 -0.2217804
#10 QOL -0.1965342
# ARIMA: 4=non-seasonal MA, 5=seasonal AR, 8=non-seasonal Diff
#
#9 ARIMA-derived vector includes:
# (1=ts_avg, 2=forecast_avg, 3=non-seasonal AR, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA,
# 7=period, 8=non-seasonal Diff, 9=seasonal differences)
# [1] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels"
# [2] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
# [3] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)"
# [4] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
# [5] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels"
# [6] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
# [7] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8)"
# [8] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
# [9] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels"
#[10] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
#[11] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8)"
#[12] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
#[13] "All ISCED 2011 levels "
# [14] "All ISCED 2011 levels, Females"
# [15] "All ISCED 2011 levels, Males"
# [16] "Capital transfers, payable"
# [17] "Capital transfers, receivable"
# [18] "Compensation of employees, payable"
# [19] "Current taxes on income, wealth, etc., receivable"
#[20] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels "
# [21] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
# [22] "Other current transfers, payable"
# [23] "Other current transfers, receivable"
# [24] "Property income, payable"
# [25] "Property income, receivable"
# [26] "Savings, gross"
# [27] "Subsidies, payable"
# [28] "Taxes on production and imports, receivable"
# [29] "Total general government expenditure"
# [30] "Total general government revenue"
# [31] "Unemployment , Females, From 15-64 years, Total"
# [32] "Unemployment , Males, From 15-64 years"
# [33] "Unemployment , Males, From 15-64 years, from 1 to 2 months"
# [34] "Unemployment , Males, From 15-64 years, from 3 to 5 months"
# [35] "Unemployment , Males, From 15-64 years, from 6 to 11 months"
# [36] "Unemployment , Total, From 15-64 years, From 1 to 2 months"
# [37] "Unemployment , Total, From 15-64 years, From 12 to 17 months"
# [38] "Unemployment , Total, From 15-64 years, From 3 to 5 months"
# [39] "Unemployment , Total, From 15-64 years, From 6 to 11 months"
# [40] "Unemployment , Total, From 15-64 years, Less than 1 month"
# [41] "Unemployment by sex, age, duration. DurationNA not started"
# [42] "VAT, receivable"
coef(cvLASSO, s = "lambda.min") %>%
broom::tidy() %>%
filter(row != "(Intercept)") %>%
top_n(100, wt = abs(value)) %>%
ggplot(aes(value, reorder(row, value), color = value > 0)) +
geom_point(show.legend = FALSE, aes(size = abs(value))) +
ggtitle("Top 9 salient features (LASSO penalty)") +
xlab("Effect-size") +
ylab(NULL)
validation <- data.frame(matrix(NA, nrow = dim(predLASSO)[1], ncol=3), row.names=countryNames)
validation [ , 1] <- Y; validation [ , 2] <- predLASSO_lim[, 1]; validation [ , 3] <- predRidge[, 1]
colnames(validation) <- c("Y", "LASSO", "Ridge")
dim(validation)## [1] 31 3head(validation)## Y LASSO Ridge
## Austria 18 20.21660 20.03322
## Belgium 19 24.57457 20.63417
## Bulgaria 38 27.42736 30.62022
## Croatia 28 25.84568 25.97458
## Cyprus 50 27.80166 34.74563
## Czech Republic 25 24.17704 23.16547# Prediction correlations:
cor(validation[ , 1], validation[, 2]) # Y=observed OA rank vs. LASSO-pred 0.96 (lim) 0.84## [1] 0.8428065cor(validation[ , 1], validation[, 3]) # Y=observed OA rank vs. Ridge-pred 0.95## [1] 0.963445# Plot observed Y (Overall Country ranking) vs. LASSO (9-parameters) predicted Y^
linFit1 <- lm(validation[ , 1] ~ predLASSO)
plot(validation[ , 1] ~ predLASSO,
col="blue", xaxt='n', yaxt='n', pch = 16, cex=3,
xlab="Observed Country Overall Ranking", ylab="LASSO 9/(42*9) param model",
main = sprintf("Observed (X) vs. LASSO-Predicted (Y) Overall Country Ranking, cor=%.02f",
cor(validation[ , 1], validation[, 2])))
abline(linFit1, lwd=3, col="red")
# Plot observed LASSO (9-parameters) predicted Y^ vs. Y (Overall Country ranking)
linFit1 <- lm(predLASSO_lim ~ validation[ , 1])
plot(predLASSO_lim ~ validation[ , 1],
col="blue", xaxt='n', yaxt='n', pch = 16, cex=3,
xlab="Observed Country Overall Ranking", ylab="LASSO 9/(42*9) param model",
main = sprintf("Observed (X) vs. LASSO-Predicted (Y) Overall Country Ranking, cor=%.02f",
cor(validation[ , 1], validation[, 2])))
abline(linFit1, lwd=3, col="red")
12.2.2 Dimensionality Reduction
PCA and t-SNE 2D and 3D projections using SOCR Dimensionality Reduction Webapp.
- the tensor file
EU_Econ_TensorData_31Countries_By_386Features.txtcontains 31 rows (countries) and 386 = 42*9(ARIMA) + 8(meta-data) columns - the labels file
EU_Econ_Labels_31Countries_and OverallRankingOutcome.txtincludes 31 rows with 2 columns specifying the Countries and their OA (Overall rankings). - The reader can load these tensor data files into the SOCR Dimensionality Reduction Webapp and generate dynamic views of the 2D or 3D projections (PCA=Euclidean) and (t-SNE manifold).
# https://www.socr.umich.edu/people/dinov/courses/DSPA_notes/05_DimensionalityReduction.html
# ...12.3 Spacekime Analytics
12.3.1 Supervised classification
Use Model-based and Model-free methods to predict the overall (OA) country ranking.
# Generic function to Transform Data ={all predictors (X) and outcome (Y)} to k-space (Fourier domain): kSpaceTransform(data, inverse = FALSE, reconPhases = NULL)
# ForwardFT (rawData, FALSE, NULL)
# InverseFT(magnitudes, TRUE, reconPhasesToUse) or InverseFT(FT_data, TRUE, NULL)
# DATA
# subset test data
Y = aggregate_arima_vector_country_ranking_df$OA
X = aggregate_arima_vector_country_ranking_df[ , -387]
# remove columns containing NAs
X = as.data.frame(apply(X[ , colSums(is.na(X)) == 0], 2, as.numeric)); dim(X) # [1] 31 386## [1] 31 386length(Y); dim(X)## [1] 31## [1] 31 386FT_aggregate_arima_vector_country_ranking_df <-
kSpaceTransform(as.data.frame(apply(
aggregate_arima_vector_country_ranking_df[ , colSums(is.na(aggregate_arima_vector_country_ranking_df)) == 0],
2, as.numeric)), inverse = FALSE, reconPhases = NULL)
## Kime-Phase Distributions
# Examine the Kime-direction Distributions of the Phases for all *Belgium* features (predictors + outcome). Define a generic function that plots the Phase distributions.
# plotPhaseDistributions(dataFT, dataColnames)
plotPhaseDistributions(FT_aggregate_arima_vector_country_ranking_df,
colnames(aggregate_arima_vector_country_ranking_df), size=4, cex=0.1)
IFT_FT_aggregate_arima_vector_country_ranking_df <-
kSpaceTransform(FT_aggregate_arima_vector_country_ranking_df$magnitudes,
TRUE, FT_aggregate_arima_vector_country_ranking_df$phases)
# Check IFT(FT) == I:
# ifelse(aggregate_arima_vector_country_ranking_df[5,4] -
# Re(IFT_FT_aggregate_arima_vector_country_ranking_df[5,4]) < 0.001, "Perfect Synthesis", "Problems!!!")
##############################################
# Nil-Phase Synthesis and LASSO model estimation
# 1. Nil-Phase data synthesis (reconstruction)
temp_Data <- aggregate_arima_vector_country_ranking_df
nilPhase_FT_aggregate_arima_vector <-
array(complex(real=0, imaginary=0), c(dim(temp_Data)[1], dim(temp_Data)[2]))
dim(nilPhase_FT_aggregate_arima_vector) # ; head(nilPhase_FT_aggregate_arima_vector)## [1] 31 387# [1] 31 387
IFT_NilPhase_FT_aggregate_arima_vector <- array(complex(), c(dim(temp_Data)[1], dim(temp_Data)[2]))
# Invert back to spacetime the
# FT_aggregate_arima_vector_country_ranking_df$magnitudes[ , i] signal with nil-phase
IFT_NilPhase_FT_aggregate_arima_vector <-
Re(kSpaceTransform(FT_aggregate_arima_vector_country_ranking_df$magnitudes,
TRUE, nilPhase_FT_aggregate_arima_vector))
colnames(IFT_NilPhase_FT_aggregate_arima_vector) <-
colnames(aggregate_arima_vector_country_ranking_df)
rownames(IFT_NilPhase_FT_aggregate_arima_vector) <-
rownames(aggregate_arima_vector_country_ranking_df)
dim(IFT_NilPhase_FT_aggregate_arima_vector)## [1] 31 387dim(FT_aggregate_arima_vector_country_ranking_df$magnitudes)## [1] 31 387colnames(IFT_NilPhase_FT_aggregate_arima_vector)## [1] "Feature_1_ArimaVec_1" "Feature_1_ArimaVec_2" "Feature_1_ArimaVec_3"
## [4] "Feature_1_ArimaVec_4" "Feature_1_ArimaVec_5" "Feature_1_ArimaVec_6"
## [7] "Feature_1_ArimaVec_7" "Feature_1_ArimaVec_8" "Feature_1_ArimaVec_9"
## [10] "Feature_2_ArimaVec_1" "Feature_2_ArimaVec_2" "Feature_2_ArimaVec_3"
## [13] "Feature_2_ArimaVec_4" "Feature_2_ArimaVec_5" "Feature_2_ArimaVec_6"
## [16] "Feature_2_ArimaVec_7" "Feature_2_ArimaVec_8" "Feature_2_ArimaVec_9"
## [19] "Feature_3_ArimaVec_1" "Feature_3_ArimaVec_2" "Feature_3_ArimaVec_3"
## [22] "Feature_3_ArimaVec_4" "Feature_3_ArimaVec_5" "Feature_3_ArimaVec_6"
## [25] "Feature_3_ArimaVec_7" "Feature_3_ArimaVec_8" "Feature_3_ArimaVec_9"
## [28] "Feature_4_ArimaVec_1" "Feature_4_ArimaVec_2" "Feature_4_ArimaVec_3"
## [31] "Feature_4_ArimaVec_4" "Feature_4_ArimaVec_5" "Feature_4_ArimaVec_6"
## [34] "Feature_4_ArimaVec_7" "Feature_4_ArimaVec_8" "Feature_4_ArimaVec_9"
## [37] "Feature_5_ArimaVec_1" "Feature_5_ArimaVec_2" "Feature_5_ArimaVec_3"
## [40] "Feature_5_ArimaVec_4" "Feature_5_ArimaVec_5" "Feature_5_ArimaVec_6"
## [43] "Feature_5_ArimaVec_7" "Feature_5_ArimaVec_8" "Feature_5_ArimaVec_9"
## [46] "Feature_6_ArimaVec_1" "Feature_6_ArimaVec_2" "Feature_6_ArimaVec_3"
## [49] "Feature_6_ArimaVec_4" "Feature_6_ArimaVec_5" "Feature_6_ArimaVec_6"
## [52] "Feature_6_ArimaVec_7" "Feature_6_ArimaVec_8" "Feature_6_ArimaVec_9"
## [55] "Feature_7_ArimaVec_1" "Feature_7_ArimaVec_2" "Feature_7_ArimaVec_3"
## [58] "Feature_7_ArimaVec_4" "Feature_7_ArimaVec_5" "Feature_7_ArimaVec_6"
## [61] "Feature_7_ArimaVec_7" "Feature_7_ArimaVec_8" "Feature_7_ArimaVec_9"
## [64] "Feature_8_ArimaVec_1" "Feature_8_ArimaVec_2" "Feature_8_ArimaVec_3"
## [67] "Feature_8_ArimaVec_4" "Feature_8_ArimaVec_5" "Feature_8_ArimaVec_6"
## [70] "Feature_8_ArimaVec_7" "Feature_8_ArimaVec_8" "Feature_8_ArimaVec_9"
## [73] "Feature_9_ArimaVec_1" "Feature_9_ArimaVec_2" "Feature_9_ArimaVec_3"
## [76] "Feature_9_ArimaVec_4" "Feature_9_ArimaVec_5" "Feature_9_ArimaVec_6"
## [79] "Feature_9_ArimaVec_7" "Feature_9_ArimaVec_8" "Feature_9_ArimaVec_9"
## [82] "Feature_10_ArimaVec_1" "Feature_10_ArimaVec_2" "Feature_10_ArimaVec_3"
## [85] "Feature_10_ArimaVec_4" "Feature_10_ArimaVec_5" "Feature_10_ArimaVec_6"
## [88] "Feature_10_ArimaVec_7" "Feature_10_ArimaVec_8" "Feature_10_ArimaVec_9"
## [91] "Feature_11_ArimaVec_1" "Feature_11_ArimaVec_2" "Feature_11_ArimaVec_3"
## [94] "Feature_11_ArimaVec_4" "Feature_11_ArimaVec_5" "Feature_11_ArimaVec_6"
## [97] "Feature_11_ArimaVec_7" "Feature_11_ArimaVec_8" "Feature_11_ArimaVec_9"
## [100] "Feature_12_ArimaVec_1" "Feature_12_ArimaVec_2" "Feature_12_ArimaVec_3"
## [103] "Feature_12_ArimaVec_4" "Feature_12_ArimaVec_5" "Feature_12_ArimaVec_6"
## [106] "Feature_12_ArimaVec_7" "Feature_12_ArimaVec_8" "Feature_12_ArimaVec_9"
## [109] "Feature_13_ArimaVec_1" "Feature_13_ArimaVec_2" "Feature_13_ArimaVec_3"
## [112] "Feature_13_ArimaVec_4" "Feature_13_ArimaVec_5" "Feature_13_ArimaVec_6"
## [115] "Feature_13_ArimaVec_7" "Feature_13_ArimaVec_8" "Feature_13_ArimaVec_9"
## [118] "Feature_14_ArimaVec_1" "Feature_14_ArimaVec_2" "Feature_14_ArimaVec_3"
## [121] "Feature_14_ArimaVec_4" "Feature_14_ArimaVec_5" "Feature_14_ArimaVec_6"
## [124] "Feature_14_ArimaVec_7" "Feature_14_ArimaVec_8" "Feature_14_ArimaVec_9"
## [127] "Feature_15_ArimaVec_1" "Feature_15_ArimaVec_2" "Feature_15_ArimaVec_3"
## [130] "Feature_15_ArimaVec_4" "Feature_15_ArimaVec_5" "Feature_15_ArimaVec_6"
## [133] "Feature_15_ArimaVec_7" "Feature_15_ArimaVec_8" "Feature_15_ArimaVec_9"
## [136] "Feature_16_ArimaVec_1" "Feature_16_ArimaVec_2" "Feature_16_ArimaVec_3"
## [139] "Feature_16_ArimaVec_4" "Feature_16_ArimaVec_5" "Feature_16_ArimaVec_6"
## [142] "Feature_16_ArimaVec_7" "Feature_16_ArimaVec_8" "Feature_16_ArimaVec_9"
## [145] "Feature_17_ArimaVec_1" "Feature_17_ArimaVec_2" "Feature_17_ArimaVec_3"
## [148] "Feature_17_ArimaVec_4" "Feature_17_ArimaVec_5" "Feature_17_ArimaVec_6"
## [151] "Feature_17_ArimaVec_7" "Feature_17_ArimaVec_8" "Feature_17_ArimaVec_9"
## [154] "Feature_18_ArimaVec_1" "Feature_18_ArimaVec_2" "Feature_18_ArimaVec_3"
## [157] "Feature_18_ArimaVec_4" "Feature_18_ArimaVec_5" "Feature_18_ArimaVec_6"
## [160] "Feature_18_ArimaVec_7" "Feature_18_ArimaVec_8" "Feature_18_ArimaVec_9"
## [163] "Feature_19_ArimaVec_1" "Feature_19_ArimaVec_2" "Feature_19_ArimaVec_3"
## [166] "Feature_19_ArimaVec_4" "Feature_19_ArimaVec_5" "Feature_19_ArimaVec_6"
## [169] "Feature_19_ArimaVec_7" "Feature_19_ArimaVec_8" "Feature_19_ArimaVec_9"
## [172] "Feature_20_ArimaVec_1" "Feature_20_ArimaVec_2" "Feature_20_ArimaVec_3"
## [175] "Feature_20_ArimaVec_4" "Feature_20_ArimaVec_5" "Feature_20_ArimaVec_6"
## [178] "Feature_20_ArimaVec_7" "Feature_20_ArimaVec_8" "Feature_20_ArimaVec_9"
## [181] "Feature_21_ArimaVec_1" "Feature_21_ArimaVec_2" "Feature_21_ArimaVec_3"
## [184] "Feature_21_ArimaVec_4" "Feature_21_ArimaVec_5" "Feature_21_ArimaVec_6"
## [187] "Feature_21_ArimaVec_7" "Feature_21_ArimaVec_8" "Feature_21_ArimaVec_9"
## [190] "Feature_22_ArimaVec_1" "Feature_22_ArimaVec_2" "Feature_22_ArimaVec_3"
## [193] "Feature_22_ArimaVec_4" "Feature_22_ArimaVec_5" "Feature_22_ArimaVec_6"
## [196] "Feature_22_ArimaVec_7" "Feature_22_ArimaVec_8" "Feature_22_ArimaVec_9"
## [199] "Feature_23_ArimaVec_1" "Feature_23_ArimaVec_2" "Feature_23_ArimaVec_3"
## [202] "Feature_23_ArimaVec_4" "Feature_23_ArimaVec_5" "Feature_23_ArimaVec_6"
## [205] "Feature_23_ArimaVec_7" "Feature_23_ArimaVec_8" "Feature_23_ArimaVec_9"
## [208] "Feature_24_ArimaVec_1" "Feature_24_ArimaVec_2" "Feature_24_ArimaVec_3"
## [211] "Feature_24_ArimaVec_4" "Feature_24_ArimaVec_5" "Feature_24_ArimaVec_6"
## [214] "Feature_24_ArimaVec_7" "Feature_24_ArimaVec_8" "Feature_24_ArimaVec_9"
## [217] "Feature_25_ArimaVec_1" "Feature_25_ArimaVec_2" "Feature_25_ArimaVec_3"
## [220] "Feature_25_ArimaVec_4" "Feature_25_ArimaVec_5" "Feature_25_ArimaVec_6"
## [223] "Feature_25_ArimaVec_7" "Feature_25_ArimaVec_8" "Feature_25_ArimaVec_9"
## [226] "Feature_26_ArimaVec_1" "Feature_26_ArimaVec_2" "Feature_26_ArimaVec_3"
## [229] "Feature_26_ArimaVec_4" "Feature_26_ArimaVec_5" "Feature_26_ArimaVec_6"
## [232] "Feature_26_ArimaVec_7" "Feature_26_ArimaVec_8" "Feature_26_ArimaVec_9"
## [235] "Feature_27_ArimaVec_1" "Feature_27_ArimaVec_2" "Feature_27_ArimaVec_3"
## [238] "Feature_27_ArimaVec_4" "Feature_27_ArimaVec_5" "Feature_27_ArimaVec_6"
## [241] "Feature_27_ArimaVec_7" "Feature_27_ArimaVec_8" "Feature_27_ArimaVec_9"
## [244] "Feature_28_ArimaVec_1" "Feature_28_ArimaVec_2" "Feature_28_ArimaVec_3"
## [247] "Feature_28_ArimaVec_4" "Feature_28_ArimaVec_5" "Feature_28_ArimaVec_6"
## [250] "Feature_28_ArimaVec_7" "Feature_28_ArimaVec_8" "Feature_28_ArimaVec_9"
## [253] "Feature_29_ArimaVec_1" "Feature_29_ArimaVec_2" "Feature_29_ArimaVec_3"
## [256] "Feature_29_ArimaVec_4" "Feature_29_ArimaVec_5" "Feature_29_ArimaVec_6"
## [259] "Feature_29_ArimaVec_7" "Feature_29_ArimaVec_8" "Feature_29_ArimaVec_9"
## [262] "Feature_30_ArimaVec_1" "Feature_30_ArimaVec_2" "Feature_30_ArimaVec_3"
## [265] "Feature_30_ArimaVec_4" "Feature_30_ArimaVec_5" "Feature_30_ArimaVec_6"
## [268] "Feature_30_ArimaVec_7" "Feature_30_ArimaVec_8" "Feature_30_ArimaVec_9"
## [271] "Feature_31_ArimaVec_1" "Feature_31_ArimaVec_2" "Feature_31_ArimaVec_3"
## [274] "Feature_31_ArimaVec_4" "Feature_31_ArimaVec_5" "Feature_31_ArimaVec_6"
## [277] "Feature_31_ArimaVec_7" "Feature_31_ArimaVec_8" "Feature_31_ArimaVec_9"
## [280] "Feature_32_ArimaVec_1" "Feature_32_ArimaVec_2" "Feature_32_ArimaVec_3"
## [283] "Feature_32_ArimaVec_4" "Feature_32_ArimaVec_5" "Feature_32_ArimaVec_6"
## [286] "Feature_32_ArimaVec_7" "Feature_32_ArimaVec_8" "Feature_32_ArimaVec_9"
## [289] "Feature_33_ArimaVec_1" "Feature_33_ArimaVec_2" "Feature_33_ArimaVec_3"
## [292] "Feature_33_ArimaVec_4" "Feature_33_ArimaVec_5" "Feature_33_ArimaVec_6"
## [295] "Feature_33_ArimaVec_7" "Feature_33_ArimaVec_8" "Feature_33_ArimaVec_9"
## [298] "Feature_34_ArimaVec_1" "Feature_34_ArimaVec_2" "Feature_34_ArimaVec_3"
## [301] "Feature_34_ArimaVec_4" "Feature_34_ArimaVec_5" "Feature_34_ArimaVec_6"
## [304] "Feature_34_ArimaVec_7" "Feature_34_ArimaVec_8" "Feature_34_ArimaVec_9"
## [307] "Feature_35_ArimaVec_1" "Feature_35_ArimaVec_2" "Feature_35_ArimaVec_3"
## [310] "Feature_35_ArimaVec_4" "Feature_35_ArimaVec_5" "Feature_35_ArimaVec_6"
## [313] "Feature_35_ArimaVec_7" "Feature_35_ArimaVec_8" "Feature_35_ArimaVec_9"
## [316] "Feature_36_ArimaVec_1" "Feature_36_ArimaVec_2" "Feature_36_ArimaVec_3"
## [319] "Feature_36_ArimaVec_4" "Feature_36_ArimaVec_5" "Feature_36_ArimaVec_6"
## [322] "Feature_36_ArimaVec_7" "Feature_36_ArimaVec_8" "Feature_36_ArimaVec_9"
## [325] "Feature_37_ArimaVec_1" "Feature_37_ArimaVec_2" "Feature_37_ArimaVec_3"
## [328] "Feature_37_ArimaVec_4" "Feature_37_ArimaVec_5" "Feature_37_ArimaVec_6"
## [331] "Feature_37_ArimaVec_7" "Feature_37_ArimaVec_8" "Feature_37_ArimaVec_9"
## [334] "Feature_38_ArimaVec_1" "Feature_38_ArimaVec_2" "Feature_38_ArimaVec_3"
## [337] "Feature_38_ArimaVec_4" "Feature_38_ArimaVec_5" "Feature_38_ArimaVec_6"
## [340] "Feature_38_ArimaVec_7" "Feature_38_ArimaVec_8" "Feature_38_ArimaVec_9"
## [343] "Feature_39_ArimaVec_1" "Feature_39_ArimaVec_2" "Feature_39_ArimaVec_3"
## [346] "Feature_39_ArimaVec_4" "Feature_39_ArimaVec_5" "Feature_39_ArimaVec_6"
## [349] "Feature_39_ArimaVec_7" "Feature_39_ArimaVec_8" "Feature_39_ArimaVec_9"
## [352] "Feature_40_ArimaVec_1" "Feature_40_ArimaVec_2" "Feature_40_ArimaVec_3"
## [355] "Feature_40_ArimaVec_4" "Feature_40_ArimaVec_5" "Feature_40_ArimaVec_6"
## [358] "Feature_40_ArimaVec_7" "Feature_40_ArimaVec_8" "Feature_40_ArimaVec_9"
## [361] "Feature_41_ArimaVec_1" "Feature_41_ArimaVec_2" "Feature_41_ArimaVec_3"
## [364] "Feature_41_ArimaVec_4" "Feature_41_ArimaVec_5" "Feature_41_ArimaVec_6"
## [367] "Feature_41_ArimaVec_7" "Feature_41_ArimaVec_8" "Feature_41_ArimaVec_9"
## [370] "Feature_42_ArimaVec_1" "Feature_42_ArimaVec_2" "Feature_42_ArimaVec_3"
## [373] "Feature_42_ArimaVec_4" "Feature_42_ArimaVec_5" "Feature_42_ArimaVec_6"
## [376] "Feature_42_ArimaVec_7" "Feature_42_ArimaVec_8" "Feature_42_ArimaVec_9"
## [379] "IncomeGroup" "PopSizeGroup" "ED"
## [382] "Edu" "HI" "QOL"
## [385] "PE" "Relig" "OA"# IFT_NilPhase_FT_aggregate_arima_vector[1:5, 1:4]; temp_Data[1:5, 1:4]
# 2. Perform LASSO modeling on IFT_NilPhase_FT_aggregate_arima_vector;
# report param estimates and quality metrics AIC/BIC
# library(forecast)
set.seed(54321)
cvLASSO_kime = cv.glmnet(data.matrix(IFT_NilPhase_FT_aggregate_arima_vector[ , -387]),
# IFT_NilPhase_FT_aggregate_arima_vector[ , 387], alpha = 1, parallel=TRUE)
Y, alpha = 1, parallel=TRUE)
plot(cvLASSO_kime)
mtext("(Spacekime, Nil-phase) CV LASSO: Number of Nonzero (Active) Coefficients",
side=3, line=2.5)
# Identify top predictors and forecast the Y=Overall (OA) Country ranking outcome
predLASSO_kime <- predict(cvLASSO_kime, s = cvLASSO_kime$lambda.min,
newx = data.matrix(IFT_NilPhase_FT_aggregate_arima_vector[ , -387])); predLASSO_kime## s1
## Austria 23.12903
## Belgium 23.12903
## Bulgaria 23.12903
## Croatia 23.12903
## Cyprus 23.12903
## Czech Republic 23.12903
## Denmark 23.12903
## Estonia 23.12903
## Finland 23.12903
## France 23.12903
## Germany (until 1990 former territory of the FRG) 23.12903
## Greece 23.12903
## Hungary 23.12903
## Iceland 23.12903
## Ireland 23.12903
## Italy 23.12903
## Latvia 23.12903
## Lithuania 23.12903
## Luxembourg 23.12903
## Malta 23.12903
## Netherlands 23.12903
## Norway 23.12903
## Poland 23.12903
## Portugal 23.12903
## Romania 23.12903
## Slovakia 23.12903
## Slovenia 23.12903
## Spain 23.12903
## Sweden 23.12903
## Switzerland 23.12903
## United Kingdom 23.12903# testMSE_LASSO_kime <- mean((predLASSO_kime - IFT_NilPhase_FT_aggregate_arima_vector[ , 387])^2)
# testMSE_LASSO_kime
predLASSO_kime = predict(cvLASSO_kime, s = exp(1/3), # cvLASSO_kime$lambda.min,
newx = data.matrix(IFT_NilPhase_FT_aggregate_arima_vector[ , -387])); predLASSO_kime## s1
## Austria 18.60234
## Belgium 20.87543
## Bulgaria 21.61560
## Croatia 23.50550
## Cyprus 28.40317
## Czech Republic 23.87474
## Denmark 20.33391
## Estonia 27.16701
## Finland 20.41749
## France 22.30788
## Germany (until 1990 former territory of the FRG) 14.48089
## Greece 22.15523
## Hungary 28.85979
## Iceland 23.36739
## Ireland 23.78175
## Italy 28.05305
## Latvia 28.05305
## Lithuania 23.78175
## Luxembourg 23.36739
## Malta 28.85979
## Netherlands 22.15523
## Norway 14.48089
## Poland 22.30788
## Portugal 20.41749
## Romania 27.16701
## Slovakia 20.33391
## Slovenia 23.87474
## Spain 28.40317
## Sweden 23.50550
## Switzerland 21.61560
## United Kingdom 20.87543##################################Use only ARIMA effects, no SOCR meta-data#####
set.seed(12345)
cvLASSO_kime_lim = cv.glmnet(data.matrix(IFT_NilPhase_FT_aggregate_arima_vector[ , 1:(42*9)]),
Y, alpha = 1, parallel=TRUE)
plot(cvLASSO_kime_lim)
mtext("CV LASSO Nil-Phase (using only Timeseries data): Number of Nonzero (Active) Coefficients",
side=3, line=2.5)
# Identify top predictors and forecast the Y=Overall (OA) Country ranking outcome
predLASSO_kime_lim <- predict(cvLASSO_kime_lim, s = 1,
newx = data.matrix(X[ , 1:(42*9)]))
coefList_kime_lim <- coef(cvLASSO_kime_lim, s=1)
coefList_kime_lim <- data.frame(coefList_kime_lim@Dimnames[[1]][coefList_kime_lim@i+1],coefList_kime_lim@x)
names(coefList_kime_lim) <- c('Feature','EffectSize')
arrange(coefList_kime_lim, -abs(EffectSize))[2:10, ]## Feature EffectSize
## 2 Feature_12_ArimaVec_8 -8.662856429
## 3 Feature_11_ArimaVec_4 8.585283751
## 4 Feature_12_ArimaVec_4 -5.023601843
## 5 Feature_30_ArimaVec_4 2.242157842
## 6 Feature_26_ArimaVec_6 1.760267217
## 7 Feature_39_ArimaVec_5 -1.256101949
## 8 Feature_34_ArimaVec_5 -1.148865337
## 9 Feature_37_ArimaVec_2 0.001322367
## NA <NA> NAcor(Y, predLASSO_kime_lim[, 1]) # 0.1142824## [1] 0.1142824################################################################################
# Plot Regression Coefficients: create variable names for plotting
library("arm")
# par(mar=c(2, 13, 1, 1)) # extra large left margin # par(mar=c(5,5,5,5))
# varNames <- colnames(X); varNames; length(varNames)
betaHatLASSO_kime = as.double(coef(cvLASSO_kime, s=cvLASSO_kime$lambda.min))
#cvLASSO_kime$lambda.1se
coefplot(betaHatLASSO_kime[377:386], sd = rep(0, 10), pch=0, cex.pts = 3, col="red",
main = "(Spacekime) LASSO-Regularized Regression Coefficient Estimates",
varnames = varNames[377:386])
varImp(cvLASSO_kime, lambda = cvLASSO_kime$lambda.min)## Overall
## Feature_1_ArimaVec_1 0
## Feature_1_ArimaVec_2 0
## Feature_1_ArimaVec_3 0
## Feature_1_ArimaVec_4 0
## Feature_1_ArimaVec_5 0
## Feature_1_ArimaVec_6 0
## Feature_1_ArimaVec_7 0
## Feature_1_ArimaVec_8 0
## Feature_1_ArimaVec_9 0
## Feature_2_ArimaVec_1 0
## Feature_2_ArimaVec_2 0
## Feature_2_ArimaVec_3 0
## Feature_2_ArimaVec_4 0
## Feature_2_ArimaVec_5 0
## Feature_2_ArimaVec_6 0
## Feature_2_ArimaVec_7 0
## Feature_2_ArimaVec_8 0
## Feature_2_ArimaVec_9 0
## Feature_3_ArimaVec_1 0
## Feature_3_ArimaVec_2 0
## Feature_3_ArimaVec_3 0
## Feature_3_ArimaVec_4 0
## Feature_3_ArimaVec_5 0
## Feature_3_ArimaVec_6 0
## Feature_3_ArimaVec_7 0
## Feature_3_ArimaVec_8 0
## Feature_3_ArimaVec_9 0
## Feature_4_ArimaVec_1 0
## Feature_4_ArimaVec_2 0
## Feature_4_ArimaVec_3 0
## Feature_4_ArimaVec_4 0
## Feature_4_ArimaVec_5 0
## Feature_4_ArimaVec_6 0
## Feature_4_ArimaVec_7 0
## Feature_4_ArimaVec_8 0
## Feature_4_ArimaVec_9 0
## Feature_5_ArimaVec_1 0
## Feature_5_ArimaVec_2 0
## Feature_5_ArimaVec_3 0
## Feature_5_ArimaVec_4 0
## Feature_5_ArimaVec_5 0
## Feature_5_ArimaVec_6 0
## Feature_5_ArimaVec_7 0
## Feature_5_ArimaVec_8 0
## Feature_5_ArimaVec_9 0
## Feature_6_ArimaVec_1 0
## Feature_6_ArimaVec_2 0
## Feature_6_ArimaVec_3 0
## Feature_6_ArimaVec_4 0
## Feature_6_ArimaVec_5 0
## Feature_6_ArimaVec_6 0
## Feature_6_ArimaVec_7 0
## Feature_6_ArimaVec_8 0
## Feature_6_ArimaVec_9 0
## Feature_7_ArimaVec_1 0
## Feature_7_ArimaVec_2 0
## Feature_7_ArimaVec_3 0
## Feature_7_ArimaVec_4 0
## Feature_7_ArimaVec_5 0
## Feature_7_ArimaVec_6 0
## Feature_7_ArimaVec_7 0
## Feature_7_ArimaVec_8 0
## Feature_7_ArimaVec_9 0
## Feature_8_ArimaVec_1 0
## Feature_8_ArimaVec_2 0
## Feature_8_ArimaVec_3 0
## Feature_8_ArimaVec_4 0
## Feature_8_ArimaVec_5 0
## Feature_8_ArimaVec_6 0
## Feature_8_ArimaVec_7 0
## Feature_8_ArimaVec_8 0
## Feature_8_ArimaVec_9 0
## Feature_9_ArimaVec_1 0
## Feature_9_ArimaVec_2 0
## Feature_9_ArimaVec_3 0
## Feature_9_ArimaVec_4 0
## Feature_9_ArimaVec_5 0
## Feature_9_ArimaVec_6 0
## Feature_9_ArimaVec_7 0
## Feature_9_ArimaVec_8 0
## Feature_9_ArimaVec_9 0
## Feature_10_ArimaVec_1 0
## Feature_10_ArimaVec_2 0
## Feature_10_ArimaVec_3 0
## Feature_10_ArimaVec_4 0
## Feature_10_ArimaVec_5 0
## Feature_10_ArimaVec_6 0
## Feature_10_ArimaVec_7 0
## Feature_10_ArimaVec_8 0
## Feature_10_ArimaVec_9 0
## Feature_11_ArimaVec_1 0
## Feature_11_ArimaVec_2 0
## Feature_11_ArimaVec_3 0
## Feature_11_ArimaVec_4 0
## Feature_11_ArimaVec_5 0
## Feature_11_ArimaVec_6 0
## Feature_11_ArimaVec_7 0
## Feature_11_ArimaVec_8 0
## Feature_11_ArimaVec_9 0
## Feature_12_ArimaVec_1 0
## Feature_12_ArimaVec_2 0
## Feature_12_ArimaVec_3 0
## Feature_12_ArimaVec_4 0
## Feature_12_ArimaVec_5 0
## Feature_12_ArimaVec_6 0
## Feature_12_ArimaVec_7 0
## Feature_12_ArimaVec_8 0
## Feature_12_ArimaVec_9 0
## Feature_13_ArimaVec_1 0
## Feature_13_ArimaVec_2 0
## Feature_13_ArimaVec_3 0
## Feature_13_ArimaVec_4 0
## Feature_13_ArimaVec_5 0
## Feature_13_ArimaVec_6 0
## Feature_13_ArimaVec_7 0
## Feature_13_ArimaVec_8 0
## Feature_13_ArimaVec_9 0
## Feature_14_ArimaVec_1 0
## Feature_14_ArimaVec_2 0
## Feature_14_ArimaVec_3 0
## Feature_14_ArimaVec_4 0
## Feature_14_ArimaVec_5 0
## Feature_14_ArimaVec_6 0
## Feature_14_ArimaVec_7 0
## Feature_14_ArimaVec_8 0
## Feature_14_ArimaVec_9 0
## Feature_15_ArimaVec_1 0
## Feature_15_ArimaVec_2 0
## Feature_15_ArimaVec_3 0
## Feature_15_ArimaVec_4 0
## Feature_15_ArimaVec_5 0
## Feature_15_ArimaVec_6 0
## Feature_15_ArimaVec_7 0
## Feature_15_ArimaVec_8 0
## Feature_15_ArimaVec_9 0
## Feature_16_ArimaVec_1 0
## Feature_16_ArimaVec_2 0
## Feature_16_ArimaVec_3 0
## Feature_16_ArimaVec_4 0
## Feature_16_ArimaVec_5 0
## Feature_16_ArimaVec_6 0
## Feature_16_ArimaVec_7 0
## Feature_16_ArimaVec_8 0
## Feature_16_ArimaVec_9 0
## Feature_17_ArimaVec_1 0
## Feature_17_ArimaVec_2 0
## Feature_17_ArimaVec_3 0
## Feature_17_ArimaVec_4 0
## Feature_17_ArimaVec_5 0
## Feature_17_ArimaVec_6 0
## Feature_17_ArimaVec_7 0
## Feature_17_ArimaVec_8 0
## Feature_17_ArimaVec_9 0
## Feature_18_ArimaVec_1 0
## Feature_18_ArimaVec_2 0
## Feature_18_ArimaVec_3 0
## Feature_18_ArimaVec_4 0
## Feature_18_ArimaVec_5 0
## Feature_18_ArimaVec_6 0
## Feature_18_ArimaVec_7 0
## Feature_18_ArimaVec_8 0
## Feature_18_ArimaVec_9 0
## Feature_19_ArimaVec_1 0
## Feature_19_ArimaVec_2 0
## Feature_19_ArimaVec_3 0
## Feature_19_ArimaVec_4 0
## Feature_19_ArimaVec_5 0
## Feature_19_ArimaVec_6 0
## Feature_19_ArimaVec_7 0
## Feature_19_ArimaVec_8 0
## Feature_19_ArimaVec_9 0
## Feature_20_ArimaVec_1 0
## Feature_20_ArimaVec_2 0
## Feature_20_ArimaVec_3 0
## Feature_20_ArimaVec_4 0
## Feature_20_ArimaVec_5 0
## Feature_20_ArimaVec_6 0
## Feature_20_ArimaVec_7 0
## Feature_20_ArimaVec_8 0
## Feature_20_ArimaVec_9 0
## Feature_21_ArimaVec_1 0
## Feature_21_ArimaVec_2 0
## Feature_21_ArimaVec_3 0
## Feature_21_ArimaVec_4 0
## Feature_21_ArimaVec_5 0
## Feature_21_ArimaVec_6 0
## Feature_21_ArimaVec_7 0
## Feature_21_ArimaVec_8 0
## Feature_21_ArimaVec_9 0
## Feature_22_ArimaVec_1 0
## Feature_22_ArimaVec_2 0
## Feature_22_ArimaVec_3 0
## Feature_22_ArimaVec_4 0
## Feature_22_ArimaVec_5 0
## Feature_22_ArimaVec_6 0
## Feature_22_ArimaVec_7 0
## Feature_22_ArimaVec_8 0
## Feature_22_ArimaVec_9 0
## Feature_23_ArimaVec_1 0
## Feature_23_ArimaVec_2 0
## Feature_23_ArimaVec_3 0
## Feature_23_ArimaVec_4 0
## Feature_23_ArimaVec_5 0
## Feature_23_ArimaVec_6 0
## Feature_23_ArimaVec_7 0
## Feature_23_ArimaVec_8 0
## Feature_23_ArimaVec_9 0
## Feature_24_ArimaVec_1 0
## Feature_24_ArimaVec_2 0
## Feature_24_ArimaVec_3 0
## Feature_24_ArimaVec_4 0
## Feature_24_ArimaVec_5 0
## Feature_24_ArimaVec_6 0
## Feature_24_ArimaVec_7 0
## Feature_24_ArimaVec_8 0
## Feature_24_ArimaVec_9 0
## Feature_25_ArimaVec_1 0
## Feature_25_ArimaVec_2 0
## Feature_25_ArimaVec_3 0
## Feature_25_ArimaVec_4 0
## Feature_25_ArimaVec_5 0
## Feature_25_ArimaVec_6 0
## Feature_25_ArimaVec_7 0
## Feature_25_ArimaVec_8 0
## Feature_25_ArimaVec_9 0
## Feature_26_ArimaVec_1 0
## Feature_26_ArimaVec_2 0
## Feature_26_ArimaVec_3 0
## Feature_26_ArimaVec_4 0
## Feature_26_ArimaVec_5 0
## Feature_26_ArimaVec_6 0
## Feature_26_ArimaVec_7 0
## Feature_26_ArimaVec_8 0
## Feature_26_ArimaVec_9 0
## Feature_27_ArimaVec_1 0
## Feature_27_ArimaVec_2 0
## Feature_27_ArimaVec_3 0
## Feature_27_ArimaVec_4 0
## Feature_27_ArimaVec_5 0
## Feature_27_ArimaVec_6 0
## Feature_27_ArimaVec_7 0
## Feature_27_ArimaVec_8 0
## Feature_27_ArimaVec_9 0
## Feature_28_ArimaVec_1 0
## Feature_28_ArimaVec_2 0
## Feature_28_ArimaVec_3 0
## Feature_28_ArimaVec_4 0
## Feature_28_ArimaVec_5 0
## Feature_28_ArimaVec_6 0
## Feature_28_ArimaVec_7 0
## Feature_28_ArimaVec_8 0
## Feature_28_ArimaVec_9 0
## Feature_29_ArimaVec_1 0
## Feature_29_ArimaVec_2 0
## Feature_29_ArimaVec_3 0
## Feature_29_ArimaVec_4 0
## Feature_29_ArimaVec_5 0
## Feature_29_ArimaVec_6 0
## Feature_29_ArimaVec_7 0
## Feature_29_ArimaVec_8 0
## Feature_29_ArimaVec_9 0
## Feature_30_ArimaVec_1 0
## Feature_30_ArimaVec_2 0
## Feature_30_ArimaVec_3 0
## Feature_30_ArimaVec_4 0
## Feature_30_ArimaVec_5 0
## Feature_30_ArimaVec_6 0
## Feature_30_ArimaVec_7 0
## Feature_30_ArimaVec_8 0
## Feature_30_ArimaVec_9 0
## Feature_31_ArimaVec_1 0
## Feature_31_ArimaVec_2 0
## Feature_31_ArimaVec_3 0
## Feature_31_ArimaVec_4 0
## Feature_31_ArimaVec_5 0
## Feature_31_ArimaVec_6 0
## Feature_31_ArimaVec_7 0
## Feature_31_ArimaVec_8 0
## Feature_31_ArimaVec_9 0
## Feature_32_ArimaVec_1 0
## Feature_32_ArimaVec_2 0
## Feature_32_ArimaVec_3 0
## Feature_32_ArimaVec_4 0
## Feature_32_ArimaVec_5 0
## Feature_32_ArimaVec_6 0
## Feature_32_ArimaVec_7 0
## Feature_32_ArimaVec_8 0
## Feature_32_ArimaVec_9 0
## Feature_33_ArimaVec_1 0
## Feature_33_ArimaVec_2 0
## Feature_33_ArimaVec_3 0
## Feature_33_ArimaVec_4 0
## Feature_33_ArimaVec_5 0
## Feature_33_ArimaVec_6 0
## Feature_33_ArimaVec_7 0
## Feature_33_ArimaVec_8 0
## Feature_33_ArimaVec_9 0
## Feature_34_ArimaVec_1 0
## Feature_34_ArimaVec_2 0
## Feature_34_ArimaVec_3 0
## Feature_34_ArimaVec_4 0
## Feature_34_ArimaVec_5 0
## Feature_34_ArimaVec_6 0
## Feature_34_ArimaVec_7 0
## Feature_34_ArimaVec_8 0
## Feature_34_ArimaVec_9 0
## Feature_35_ArimaVec_1 0
## Feature_35_ArimaVec_2 0
## Feature_35_ArimaVec_3 0
## Feature_35_ArimaVec_4 0
## Feature_35_ArimaVec_5 0
## Feature_35_ArimaVec_6 0
## Feature_35_ArimaVec_7 0
## Feature_35_ArimaVec_8 0
## Feature_35_ArimaVec_9 0
## Feature_36_ArimaVec_1 0
## Feature_36_ArimaVec_2 0
## Feature_36_ArimaVec_3 0
## Feature_36_ArimaVec_4 0
## Feature_36_ArimaVec_5 0
## Feature_36_ArimaVec_6 0
## Feature_36_ArimaVec_7 0
## Feature_36_ArimaVec_8 0
## Feature_36_ArimaVec_9 0
## Feature_37_ArimaVec_1 0
## Feature_37_ArimaVec_2 0
## Feature_37_ArimaVec_3 0
## Feature_37_ArimaVec_4 0
## Feature_37_ArimaVec_5 0
## Feature_37_ArimaVec_6 0
## Feature_37_ArimaVec_7 0
## Feature_37_ArimaVec_8 0
## Feature_37_ArimaVec_9 0
## Feature_38_ArimaVec_1 0
## Feature_38_ArimaVec_2 0
## Feature_38_ArimaVec_3 0
## Feature_38_ArimaVec_4 0
## Feature_38_ArimaVec_5 0
## Feature_38_ArimaVec_6 0
## Feature_38_ArimaVec_7 0
## Feature_38_ArimaVec_8 0
## Feature_38_ArimaVec_9 0
## Feature_39_ArimaVec_1 0
## Feature_39_ArimaVec_2 0
## Feature_39_ArimaVec_3 0
## Feature_39_ArimaVec_4 0
## Feature_39_ArimaVec_5 0
## Feature_39_ArimaVec_6 0
## Feature_39_ArimaVec_7 0
## Feature_39_ArimaVec_8 0
## Feature_39_ArimaVec_9 0
## Feature_40_ArimaVec_1 0
## Feature_40_ArimaVec_2 0
## Feature_40_ArimaVec_3 0
## Feature_40_ArimaVec_4 0
## Feature_40_ArimaVec_5 0
## Feature_40_ArimaVec_6 0
## Feature_40_ArimaVec_7 0
## Feature_40_ArimaVec_8 0
## Feature_40_ArimaVec_9 0
## Feature_41_ArimaVec_1 0
## Feature_41_ArimaVec_2 0
## Feature_41_ArimaVec_3 0
## Feature_41_ArimaVec_4 0
## Feature_41_ArimaVec_5 0
## Feature_41_ArimaVec_6 0
## Feature_41_ArimaVec_7 0
## Feature_41_ArimaVec_8 0
## Feature_41_ArimaVec_9 0
## Feature_42_ArimaVec_1 0
## Feature_42_ArimaVec_2 0
## Feature_42_ArimaVec_3 0
## Feature_42_ArimaVec_4 0
## Feature_42_ArimaVec_5 0
## Feature_42_ArimaVec_6 0
## Feature_42_ArimaVec_7 0
## Feature_42_ArimaVec_8 0
## Feature_42_ArimaVec_9 0
## IncomeGroup 0
## PopSizeGroup 0
## ED 0
## Edu 0
## HI 0
## QOL 0
## PE 0
## Relig 0coefList_kime <- coef(cvLASSO_kime, s=1) # 'lambda.min')
coefList_kime <- data.frame(coefList_kime@Dimnames[[1]][coefList_kime@i+1], coefList_kime@x)
names(coefList_kime) <- c('Feature','EffectSize')
arrange(coefList_kime, -abs(EffectSize))[1:9, ]## Feature EffectSize
## 1 (Intercept) 26.069326257
## 2 Feature_12_ArimaVec_8 -8.662856429
## 3 Feature_11_ArimaVec_4 8.585283751
## 4 Feature_12_ArimaVec_4 -5.023601843
## 5 Feature_30_ArimaVec_4 2.242157842
## 6 Feature_26_ArimaVec_6 1.760267217
## 7 Feature_39_ArimaVec_5 -1.256101949
## 8 Feature_34_ArimaVec_5 -1.148865337
## 9 Feature_37_ArimaVec_2 0.001322367# Feature EffectSize
#1 (Intercept) 26.069326257
#2 Feature_12_ArimaVec_8 -8.662856430
#3 Feature_11_ArimaVec_4 8.585283751
#4 Feature_12_ArimaVec_4 -5.023601842
#5 Feature_30_ArimaVec_4 2.242157842
#6 Feature_26_ArimaVec_6 1.760267216
#7 Feature_39_ArimaVec_5 -1.256101950
#8 Feature_34_ArimaVec_5 -1.148865337
#9 Feature_37_ArimaVec_2 0.001322367
# ARIMA-spacetime: 4=non-seasonal MA, 5=seasonal AR, 8=non-seasonal Diff
# ARIMA-spacekimeNil: 2=forecast_avg, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA, 8=non-seasonal Diff
#9 ARIMA-derived vector includes:
# (1=ts_avg, 2=forecast_avg, 3=non-seasonal AR, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA,
# 7=period, 8=non-seasonal Diff, 9=seasonal differences)
coef(cvLASSO_kime, s = 1/5) %>% ### "lambda.min") %>%
broom::tidy() %>%
filter(row != "(Intercept)") %>%
top_n(100, wt = abs(value)) %>%
ggplot(aes(value, reorder(row, value), color = value > 0)) +
geom_point(show.legend = FALSE, aes(size = abs(value))) +
ggtitle("(Spacekime) Top 9 salient features (LASSO penalty)") +
xlab("Effect-size") +
ylab(NULL)
# pack a 31*3 DF with (predLASSO_kime, IFT_NilPhase_FT_aggregate_arima_vector_Y, Y)
validation_kime <- cbind(predLASSO_kime[, 1],
IFT_NilPhase_FT_aggregate_arima_vector[ , 387], Y)
colnames(validation_kime) <- c("predLASSO_kime", "IFT_NilPhase_FT_Y", "Orig_Y")
head(validation_kime)## predLASSO_kime IFT_NilPhase_FT_Y Orig_Y
## Austria 18.60234 87.771967 18
## Belgium 20.87543 19.640349 19
## Bulgaria 21.61560 24.453327 38
## Croatia 23.50550 24.267994 28
## Cyprus 28.40317 8.137025 50
## Czech Republic 23.87474 11.737091 25# Prediction correlations:
cor(validation_kime[ , 1], validation_kime[, 2]) # Y=predLASSO_kime OA rank vs. kime_LASSO_pred: 0.99## [1] -0.3346322cor(validation_kime[ , 1], validation_kime[, 3]) # Y=predLASSO_kime OA rank vs. Orig_Y: 0.64## [1] 0.6055817# Plot observed Y (Overall Country ranking) vs. LASSO (9-parameters) predicted Y^
linFit1_kime <- lm(predLASSO_kime ~ validation_kime[ , 3])
plot(predLASSO_kime ~ validation_kime[ , 3],
col="blue", xaxt='n', yaxt='n', pch = 16, cex=3,
xlab="Observed Country Overall Ranking", ylab="IFT_NilPhase predLASSO_kime",
main = sprintf("Observed (x) vs. IFT_NilPhase Predicted (y) Overall Country Ranking, cor=%.02f",
cor(validation_kime[ , 1], validation_kime[, 3])))
abline(linFit1_kime, lwd=3, col="red")
# abline(linFit1, lwd=3, col="green")
##############################################
# 3. Swap Feature Phases and then synthesize the data (reconstruction)
# temp_Data <- aggregate_arima_vector_country_ranking_df
swappedPhase_FT_aggregate_arima_vector <- FT_aggregate_arima_vector_country_ranking_df$phases
dim(swappedPhase_FT_aggregate_arima_vector) # ; head(swappedPhase_FT_aggregate_arima_vector)## [1] 31 387# [1] 31 387
IFT_SwappedPhase_FT_aggregate_arima_vector <- array(complex(),
c(dim(temp_Data)[1], dim(temp_Data)[2]))
set.seed(12345) # sample randomly Phase-columns for each of the 131 covariates (X)
swappedPhase_FT_aggregate_arima_vector1 <- as.data.frame(cbind(
swappedPhase_FT_aggregate_arima_vector[ ,
sample(ncol(swappedPhase_FT_aggregate_arima_vector[ , 1:378]))], # mix ARIMA signature phases
swappedPhase_FT_aggregate_arima_vector[ ,
sample(ncol(swappedPhase_FT_aggregate_arima_vector[ , 379:386]))],# mix the meta-data phases
swappedPhase_FT_aggregate_arima_vector[ , 387])) # add correct Outcome phase
swappedPhase_FT_aggregate_arima_vector <- swappedPhase_FT_aggregate_arima_vector1
colnames(swappedPhase_FT_aggregate_arima_vector) <- colnames(temp_Data)
colnames(swappedPhase_FT_aggregate_arima_vector); dim(swappedPhase_FT_aggregate_arima_vector)## [1] "Feature_1_ArimaVec_1" "Feature_1_ArimaVec_2" "Feature_1_ArimaVec_3"
## [4] "Feature_1_ArimaVec_4" "Feature_1_ArimaVec_5" "Feature_1_ArimaVec_6"
## [7] "Feature_1_ArimaVec_7" "Feature_1_ArimaVec_8" "Feature_1_ArimaVec_9"
## [10] "Feature_2_ArimaVec_1" "Feature_2_ArimaVec_2" "Feature_2_ArimaVec_3"
## [13] "Feature_2_ArimaVec_4" "Feature_2_ArimaVec_5" "Feature_2_ArimaVec_6"
## [16] "Feature_2_ArimaVec_7" "Feature_2_ArimaVec_8" "Feature_2_ArimaVec_9"
## [19] "Feature_3_ArimaVec_1" "Feature_3_ArimaVec_2" "Feature_3_ArimaVec_3"
## [22] "Feature_3_ArimaVec_4" "Feature_3_ArimaVec_5" "Feature_3_ArimaVec_6"
## [25] "Feature_3_ArimaVec_7" "Feature_3_ArimaVec_8" "Feature_3_ArimaVec_9"
## [28] "Feature_4_ArimaVec_1" "Feature_4_ArimaVec_2" "Feature_4_ArimaVec_3"
## [31] "Feature_4_ArimaVec_4" "Feature_4_ArimaVec_5" "Feature_4_ArimaVec_6"
## [34] "Feature_4_ArimaVec_7" "Feature_4_ArimaVec_8" "Feature_4_ArimaVec_9"
## [37] "Feature_5_ArimaVec_1" "Feature_5_ArimaVec_2" "Feature_5_ArimaVec_3"
## [40] "Feature_5_ArimaVec_4" "Feature_5_ArimaVec_5" "Feature_5_ArimaVec_6"
## [43] "Feature_5_ArimaVec_7" "Feature_5_ArimaVec_8" "Feature_5_ArimaVec_9"
## [46] "Feature_6_ArimaVec_1" "Feature_6_ArimaVec_2" "Feature_6_ArimaVec_3"
## [49] "Feature_6_ArimaVec_4" "Feature_6_ArimaVec_5" "Feature_6_ArimaVec_6"
## [52] "Feature_6_ArimaVec_7" "Feature_6_ArimaVec_8" "Feature_6_ArimaVec_9"
## [55] "Feature_7_ArimaVec_1" "Feature_7_ArimaVec_2" "Feature_7_ArimaVec_3"
## [58] "Feature_7_ArimaVec_4" "Feature_7_ArimaVec_5" "Feature_7_ArimaVec_6"
## [61] "Feature_7_ArimaVec_7" "Feature_7_ArimaVec_8" "Feature_7_ArimaVec_9"
## [64] "Feature_8_ArimaVec_1" "Feature_8_ArimaVec_2" "Feature_8_ArimaVec_3"
## [67] "Feature_8_ArimaVec_4" "Feature_8_ArimaVec_5" "Feature_8_ArimaVec_6"
## [70] "Feature_8_ArimaVec_7" "Feature_8_ArimaVec_8" "Feature_8_ArimaVec_9"
## [73] "Feature_9_ArimaVec_1" "Feature_9_ArimaVec_2" "Feature_9_ArimaVec_3"
## [76] "Feature_9_ArimaVec_4" "Feature_9_ArimaVec_5" "Feature_9_ArimaVec_6"
## [79] "Feature_9_ArimaVec_7" "Feature_9_ArimaVec_8" "Feature_9_ArimaVec_9"
## [82] "Feature_10_ArimaVec_1" "Feature_10_ArimaVec_2" "Feature_10_ArimaVec_3"
## [85] "Feature_10_ArimaVec_4" "Feature_10_ArimaVec_5" "Feature_10_ArimaVec_6"
## [88] "Feature_10_ArimaVec_7" "Feature_10_ArimaVec_8" "Feature_10_ArimaVec_9"
## [91] "Feature_11_ArimaVec_1" "Feature_11_ArimaVec_2" "Feature_11_ArimaVec_3"
## [94] "Feature_11_ArimaVec_4" "Feature_11_ArimaVec_5" "Feature_11_ArimaVec_6"
## [97] "Feature_11_ArimaVec_7" "Feature_11_ArimaVec_8" "Feature_11_ArimaVec_9"
## [100] "Feature_12_ArimaVec_1" "Feature_12_ArimaVec_2" "Feature_12_ArimaVec_3"
## [103] "Feature_12_ArimaVec_4" "Feature_12_ArimaVec_5" "Feature_12_ArimaVec_6"
## [106] "Feature_12_ArimaVec_7" "Feature_12_ArimaVec_8" "Feature_12_ArimaVec_9"
## [109] "Feature_13_ArimaVec_1" "Feature_13_ArimaVec_2" "Feature_13_ArimaVec_3"
## [112] "Feature_13_ArimaVec_4" "Feature_13_ArimaVec_5" "Feature_13_ArimaVec_6"
## [115] "Feature_13_ArimaVec_7" "Feature_13_ArimaVec_8" "Feature_13_ArimaVec_9"
## [118] "Feature_14_ArimaVec_1" "Feature_14_ArimaVec_2" "Feature_14_ArimaVec_3"
## [121] "Feature_14_ArimaVec_4" "Feature_14_ArimaVec_5" "Feature_14_ArimaVec_6"
## [124] "Feature_14_ArimaVec_7" "Feature_14_ArimaVec_8" "Feature_14_ArimaVec_9"
## [127] "Feature_15_ArimaVec_1" "Feature_15_ArimaVec_2" "Feature_15_ArimaVec_3"
## [130] "Feature_15_ArimaVec_4" "Feature_15_ArimaVec_5" "Feature_15_ArimaVec_6"
## [133] "Feature_15_ArimaVec_7" "Feature_15_ArimaVec_8" "Feature_15_ArimaVec_9"
## [136] "Feature_16_ArimaVec_1" "Feature_16_ArimaVec_2" "Feature_16_ArimaVec_3"
## [139] "Feature_16_ArimaVec_4" "Feature_16_ArimaVec_5" "Feature_16_ArimaVec_6"
## [142] "Feature_16_ArimaVec_7" "Feature_16_ArimaVec_8" "Feature_16_ArimaVec_9"
## [145] "Feature_17_ArimaVec_1" "Feature_17_ArimaVec_2" "Feature_17_ArimaVec_3"
## [148] "Feature_17_ArimaVec_4" "Feature_17_ArimaVec_5" "Feature_17_ArimaVec_6"
## [151] "Feature_17_ArimaVec_7" "Feature_17_ArimaVec_8" "Feature_17_ArimaVec_9"
## [154] "Feature_18_ArimaVec_1" "Feature_18_ArimaVec_2" "Feature_18_ArimaVec_3"
## [157] "Feature_18_ArimaVec_4" "Feature_18_ArimaVec_5" "Feature_18_ArimaVec_6"
## [160] "Feature_18_ArimaVec_7" "Feature_18_ArimaVec_8" "Feature_18_ArimaVec_9"
## [163] "Feature_19_ArimaVec_1" "Feature_19_ArimaVec_2" "Feature_19_ArimaVec_3"
## [166] "Feature_19_ArimaVec_4" "Feature_19_ArimaVec_5" "Feature_19_ArimaVec_6"
## [169] "Feature_19_ArimaVec_7" "Feature_19_ArimaVec_8" "Feature_19_ArimaVec_9"
## [172] "Feature_20_ArimaVec_1" "Feature_20_ArimaVec_2" "Feature_20_ArimaVec_3"
## [175] "Feature_20_ArimaVec_4" "Feature_20_ArimaVec_5" "Feature_20_ArimaVec_6"
## [178] "Feature_20_ArimaVec_7" "Feature_20_ArimaVec_8" "Feature_20_ArimaVec_9"
## [181] "Feature_21_ArimaVec_1" "Feature_21_ArimaVec_2" "Feature_21_ArimaVec_3"
## [184] "Feature_21_ArimaVec_4" "Feature_21_ArimaVec_5" "Feature_21_ArimaVec_6"
## [187] "Feature_21_ArimaVec_7" "Feature_21_ArimaVec_8" "Feature_21_ArimaVec_9"
## [190] "Feature_22_ArimaVec_1" "Feature_22_ArimaVec_2" "Feature_22_ArimaVec_3"
## [193] "Feature_22_ArimaVec_4" "Feature_22_ArimaVec_5" "Feature_22_ArimaVec_6"
## [196] "Feature_22_ArimaVec_7" "Feature_22_ArimaVec_8" "Feature_22_ArimaVec_9"
## [199] "Feature_23_ArimaVec_1" "Feature_23_ArimaVec_2" "Feature_23_ArimaVec_3"
## [202] "Feature_23_ArimaVec_4" "Feature_23_ArimaVec_5" "Feature_23_ArimaVec_6"
## [205] "Feature_23_ArimaVec_7" "Feature_23_ArimaVec_8" "Feature_23_ArimaVec_9"
## [208] "Feature_24_ArimaVec_1" "Feature_24_ArimaVec_2" "Feature_24_ArimaVec_3"
## [211] "Feature_24_ArimaVec_4" "Feature_24_ArimaVec_5" "Feature_24_ArimaVec_6"
## [214] "Feature_24_ArimaVec_7" "Feature_24_ArimaVec_8" "Feature_24_ArimaVec_9"
## [217] "Feature_25_ArimaVec_1" "Feature_25_ArimaVec_2" "Feature_25_ArimaVec_3"
## [220] "Feature_25_ArimaVec_4" "Feature_25_ArimaVec_5" "Feature_25_ArimaVec_6"
## [223] "Feature_25_ArimaVec_7" "Feature_25_ArimaVec_8" "Feature_25_ArimaVec_9"
## [226] "Feature_26_ArimaVec_1" "Feature_26_ArimaVec_2" "Feature_26_ArimaVec_3"
## [229] "Feature_26_ArimaVec_4" "Feature_26_ArimaVec_5" "Feature_26_ArimaVec_6"
## [232] "Feature_26_ArimaVec_7" "Feature_26_ArimaVec_8" "Feature_26_ArimaVec_9"
## [235] "Feature_27_ArimaVec_1" "Feature_27_ArimaVec_2" "Feature_27_ArimaVec_3"
## [238] "Feature_27_ArimaVec_4" "Feature_27_ArimaVec_5" "Feature_27_ArimaVec_6"
## [241] "Feature_27_ArimaVec_7" "Feature_27_ArimaVec_8" "Feature_27_ArimaVec_9"
## [244] "Feature_28_ArimaVec_1" "Feature_28_ArimaVec_2" "Feature_28_ArimaVec_3"
## [247] "Feature_28_ArimaVec_4" "Feature_28_ArimaVec_5" "Feature_28_ArimaVec_6"
## [250] "Feature_28_ArimaVec_7" "Feature_28_ArimaVec_8" "Feature_28_ArimaVec_9"
## [253] "Feature_29_ArimaVec_1" "Feature_29_ArimaVec_2" "Feature_29_ArimaVec_3"
## [256] "Feature_29_ArimaVec_4" "Feature_29_ArimaVec_5" "Feature_29_ArimaVec_6"
## [259] "Feature_29_ArimaVec_7" "Feature_29_ArimaVec_8" "Feature_29_ArimaVec_9"
## [262] "Feature_30_ArimaVec_1" "Feature_30_ArimaVec_2" "Feature_30_ArimaVec_3"
## [265] "Feature_30_ArimaVec_4" "Feature_30_ArimaVec_5" "Feature_30_ArimaVec_6"
## [268] "Feature_30_ArimaVec_7" "Feature_30_ArimaVec_8" "Feature_30_ArimaVec_9"
## [271] "Feature_31_ArimaVec_1" "Feature_31_ArimaVec_2" "Feature_31_ArimaVec_3"
## [274] "Feature_31_ArimaVec_4" "Feature_31_ArimaVec_5" "Feature_31_ArimaVec_6"
## [277] "Feature_31_ArimaVec_7" "Feature_31_ArimaVec_8" "Feature_31_ArimaVec_9"
## [280] "Feature_32_ArimaVec_1" "Feature_32_ArimaVec_2" "Feature_32_ArimaVec_3"
## [283] "Feature_32_ArimaVec_4" "Feature_32_ArimaVec_5" "Feature_32_ArimaVec_6"
## [286] "Feature_32_ArimaVec_7" "Feature_32_ArimaVec_8" "Feature_32_ArimaVec_9"
## [289] "Feature_33_ArimaVec_1" "Feature_33_ArimaVec_2" "Feature_33_ArimaVec_3"
## [292] "Feature_33_ArimaVec_4" "Feature_33_ArimaVec_5" "Feature_33_ArimaVec_6"
## [295] "Feature_33_ArimaVec_7" "Feature_33_ArimaVec_8" "Feature_33_ArimaVec_9"
## [298] "Feature_34_ArimaVec_1" "Feature_34_ArimaVec_2" "Feature_34_ArimaVec_3"
## [301] "Feature_34_ArimaVec_4" "Feature_34_ArimaVec_5" "Feature_34_ArimaVec_6"
## [304] "Feature_34_ArimaVec_7" "Feature_34_ArimaVec_8" "Feature_34_ArimaVec_9"
## [307] "Feature_35_ArimaVec_1" "Feature_35_ArimaVec_2" "Feature_35_ArimaVec_3"
## [310] "Feature_35_ArimaVec_4" "Feature_35_ArimaVec_5" "Feature_35_ArimaVec_6"
## [313] "Feature_35_ArimaVec_7" "Feature_35_ArimaVec_8" "Feature_35_ArimaVec_9"
## [316] "Feature_36_ArimaVec_1" "Feature_36_ArimaVec_2" "Feature_36_ArimaVec_3"
## [319] "Feature_36_ArimaVec_4" "Feature_36_ArimaVec_5" "Feature_36_ArimaVec_6"
## [322] "Feature_36_ArimaVec_7" "Feature_36_ArimaVec_8" "Feature_36_ArimaVec_9"
## [325] "Feature_37_ArimaVec_1" "Feature_37_ArimaVec_2" "Feature_37_ArimaVec_3"
## [328] "Feature_37_ArimaVec_4" "Feature_37_ArimaVec_5" "Feature_37_ArimaVec_6"
## [331] "Feature_37_ArimaVec_7" "Feature_37_ArimaVec_8" "Feature_37_ArimaVec_9"
## [334] "Feature_38_ArimaVec_1" "Feature_38_ArimaVec_2" "Feature_38_ArimaVec_3"
## [337] "Feature_38_ArimaVec_4" "Feature_38_ArimaVec_5" "Feature_38_ArimaVec_6"
## [340] "Feature_38_ArimaVec_7" "Feature_38_ArimaVec_8" "Feature_38_ArimaVec_9"
## [343] "Feature_39_ArimaVec_1" "Feature_39_ArimaVec_2" "Feature_39_ArimaVec_3"
## [346] "Feature_39_ArimaVec_4" "Feature_39_ArimaVec_5" "Feature_39_ArimaVec_6"
## [349] "Feature_39_ArimaVec_7" "Feature_39_ArimaVec_8" "Feature_39_ArimaVec_9"
## [352] "Feature_40_ArimaVec_1" "Feature_40_ArimaVec_2" "Feature_40_ArimaVec_3"
## [355] "Feature_40_ArimaVec_4" "Feature_40_ArimaVec_5" "Feature_40_ArimaVec_6"
## [358] "Feature_40_ArimaVec_7" "Feature_40_ArimaVec_8" "Feature_40_ArimaVec_9"
## [361] "Feature_41_ArimaVec_1" "Feature_41_ArimaVec_2" "Feature_41_ArimaVec_3"
## [364] "Feature_41_ArimaVec_4" "Feature_41_ArimaVec_5" "Feature_41_ArimaVec_6"
## [367] "Feature_41_ArimaVec_7" "Feature_41_ArimaVec_8" "Feature_41_ArimaVec_9"
## [370] "Feature_42_ArimaVec_1" "Feature_42_ArimaVec_2" "Feature_42_ArimaVec_3"
## [373] "Feature_42_ArimaVec_4" "Feature_42_ArimaVec_5" "Feature_42_ArimaVec_6"
## [376] "Feature_42_ArimaVec_7" "Feature_42_ArimaVec_8" "Feature_42_ArimaVec_9"
## [379] "IncomeGroup" "PopSizeGroup" "ED"
## [382] "Edu" "HI" "QOL"
## [385] "PE" "Relig" "OA"## [1] 31 387# 31 387
# Invert back to spacetime the
# FT_aggregate_arima_vector$magnitudes[ , i] signal with swapped-X-phases (Y-phase is fixed)
IFT_SwappedPhase_FT_aggregate_arima_vector <-
Re(kSpaceTransform(FT_aggregate_arima_vector_country_ranking_df$magnitudes,
TRUE, swappedPhase_FT_aggregate_arima_vector))
colnames(IFT_SwappedPhase_FT_aggregate_arima_vector) <-
colnames(aggregate_arima_vector_country_ranking_df)
rownames(IFT_SwappedPhase_FT_aggregate_arima_vector) <-
rownames(aggregate_arima_vector_country_ranking_df)
dim(IFT_SwappedPhase_FT_aggregate_arima_vector)## [1] 31 387dim(FT_aggregate_arima_vector_country_ranking_df$magnitudes)## [1] 31 387colnames(IFT_SwappedPhase_FT_aggregate_arima_vector)## [1] "Feature_1_ArimaVec_1" "Feature_1_ArimaVec_2" "Feature_1_ArimaVec_3"
## [4] "Feature_1_ArimaVec_4" "Feature_1_ArimaVec_5" "Feature_1_ArimaVec_6"
## [7] "Feature_1_ArimaVec_7" "Feature_1_ArimaVec_8" "Feature_1_ArimaVec_9"
## [10] "Feature_2_ArimaVec_1" "Feature_2_ArimaVec_2" "Feature_2_ArimaVec_3"
## [13] "Feature_2_ArimaVec_4" "Feature_2_ArimaVec_5" "Feature_2_ArimaVec_6"
## [16] "Feature_2_ArimaVec_7" "Feature_2_ArimaVec_8" "Feature_2_ArimaVec_9"
## [19] "Feature_3_ArimaVec_1" "Feature_3_ArimaVec_2" "Feature_3_ArimaVec_3"
## [22] "Feature_3_ArimaVec_4" "Feature_3_ArimaVec_5" "Feature_3_ArimaVec_6"
## [25] "Feature_3_ArimaVec_7" "Feature_3_ArimaVec_8" "Feature_3_ArimaVec_9"
## [28] "Feature_4_ArimaVec_1" "Feature_4_ArimaVec_2" "Feature_4_ArimaVec_3"
## [31] "Feature_4_ArimaVec_4" "Feature_4_ArimaVec_5" "Feature_4_ArimaVec_6"
## [34] "Feature_4_ArimaVec_7" "Feature_4_ArimaVec_8" "Feature_4_ArimaVec_9"
## [37] "Feature_5_ArimaVec_1" "Feature_5_ArimaVec_2" "Feature_5_ArimaVec_3"
## [40] "Feature_5_ArimaVec_4" "Feature_5_ArimaVec_5" "Feature_5_ArimaVec_6"
## [43] "Feature_5_ArimaVec_7" "Feature_5_ArimaVec_8" "Feature_5_ArimaVec_9"
## [46] "Feature_6_ArimaVec_1" "Feature_6_ArimaVec_2" "Feature_6_ArimaVec_3"
## [49] "Feature_6_ArimaVec_4" "Feature_6_ArimaVec_5" "Feature_6_ArimaVec_6"
## [52] "Feature_6_ArimaVec_7" "Feature_6_ArimaVec_8" "Feature_6_ArimaVec_9"
## [55] "Feature_7_ArimaVec_1" "Feature_7_ArimaVec_2" "Feature_7_ArimaVec_3"
## [58] "Feature_7_ArimaVec_4" "Feature_7_ArimaVec_5" "Feature_7_ArimaVec_6"
## [61] "Feature_7_ArimaVec_7" "Feature_7_ArimaVec_8" "Feature_7_ArimaVec_9"
## [64] "Feature_8_ArimaVec_1" "Feature_8_ArimaVec_2" "Feature_8_ArimaVec_3"
## [67] "Feature_8_ArimaVec_4" "Feature_8_ArimaVec_5" "Feature_8_ArimaVec_6"
## [70] "Feature_8_ArimaVec_7" "Feature_8_ArimaVec_8" "Feature_8_ArimaVec_9"
## [73] "Feature_9_ArimaVec_1" "Feature_9_ArimaVec_2" "Feature_9_ArimaVec_3"
## [76] "Feature_9_ArimaVec_4" "Feature_9_ArimaVec_5" "Feature_9_ArimaVec_6"
## [79] "Feature_9_ArimaVec_7" "Feature_9_ArimaVec_8" "Feature_9_ArimaVec_9"
## [82] "Feature_10_ArimaVec_1" "Feature_10_ArimaVec_2" "Feature_10_ArimaVec_3"
## [85] "Feature_10_ArimaVec_4" "Feature_10_ArimaVec_5" "Feature_10_ArimaVec_6"
## [88] "Feature_10_ArimaVec_7" "Feature_10_ArimaVec_8" "Feature_10_ArimaVec_9"
## [91] "Feature_11_ArimaVec_1" "Feature_11_ArimaVec_2" "Feature_11_ArimaVec_3"
## [94] "Feature_11_ArimaVec_4" "Feature_11_ArimaVec_5" "Feature_11_ArimaVec_6"
## [97] "Feature_11_ArimaVec_7" "Feature_11_ArimaVec_8" "Feature_11_ArimaVec_9"
## [100] "Feature_12_ArimaVec_1" "Feature_12_ArimaVec_2" "Feature_12_ArimaVec_3"
## [103] "Feature_12_ArimaVec_4" "Feature_12_ArimaVec_5" "Feature_12_ArimaVec_6"
## [106] "Feature_12_ArimaVec_7" "Feature_12_ArimaVec_8" "Feature_12_ArimaVec_9"
## [109] "Feature_13_ArimaVec_1" "Feature_13_ArimaVec_2" "Feature_13_ArimaVec_3"
## [112] "Feature_13_ArimaVec_4" "Feature_13_ArimaVec_5" "Feature_13_ArimaVec_6"
## [115] "Feature_13_ArimaVec_7" "Feature_13_ArimaVec_8" "Feature_13_ArimaVec_9"
## [118] "Feature_14_ArimaVec_1" "Feature_14_ArimaVec_2" "Feature_14_ArimaVec_3"
## [121] "Feature_14_ArimaVec_4" "Feature_14_ArimaVec_5" "Feature_14_ArimaVec_6"
## [124] "Feature_14_ArimaVec_7" "Feature_14_ArimaVec_8" "Feature_14_ArimaVec_9"
## [127] "Feature_15_ArimaVec_1" "Feature_15_ArimaVec_2" "Feature_15_ArimaVec_3"
## [130] "Feature_15_ArimaVec_4" "Feature_15_ArimaVec_5" "Feature_15_ArimaVec_6"
## [133] "Feature_15_ArimaVec_7" "Feature_15_ArimaVec_8" "Feature_15_ArimaVec_9"
## [136] "Feature_16_ArimaVec_1" "Feature_16_ArimaVec_2" "Feature_16_ArimaVec_3"
## [139] "Feature_16_ArimaVec_4" "Feature_16_ArimaVec_5" "Feature_16_ArimaVec_6"
## [142] "Feature_16_ArimaVec_7" "Feature_16_ArimaVec_8" "Feature_16_ArimaVec_9"
## [145] "Feature_17_ArimaVec_1" "Feature_17_ArimaVec_2" "Feature_17_ArimaVec_3"
## [148] "Feature_17_ArimaVec_4" "Feature_17_ArimaVec_5" "Feature_17_ArimaVec_6"
## [151] "Feature_17_ArimaVec_7" "Feature_17_ArimaVec_8" "Feature_17_ArimaVec_9"
## [154] "Feature_18_ArimaVec_1" "Feature_18_ArimaVec_2" "Feature_18_ArimaVec_3"
## [157] "Feature_18_ArimaVec_4" "Feature_18_ArimaVec_5" "Feature_18_ArimaVec_6"
## [160] "Feature_18_ArimaVec_7" "Feature_18_ArimaVec_8" "Feature_18_ArimaVec_9"
## [163] "Feature_19_ArimaVec_1" "Feature_19_ArimaVec_2" "Feature_19_ArimaVec_3"
## [166] "Feature_19_ArimaVec_4" "Feature_19_ArimaVec_5" "Feature_19_ArimaVec_6"
## [169] "Feature_19_ArimaVec_7" "Feature_19_ArimaVec_8" "Feature_19_ArimaVec_9"
## [172] "Feature_20_ArimaVec_1" "Feature_20_ArimaVec_2" "Feature_20_ArimaVec_3"
## [175] "Feature_20_ArimaVec_4" "Feature_20_ArimaVec_5" "Feature_20_ArimaVec_6"
## [178] "Feature_20_ArimaVec_7" "Feature_20_ArimaVec_8" "Feature_20_ArimaVec_9"
## [181] "Feature_21_ArimaVec_1" "Feature_21_ArimaVec_2" "Feature_21_ArimaVec_3"
## [184] "Feature_21_ArimaVec_4" "Feature_21_ArimaVec_5" "Feature_21_ArimaVec_6"
## [187] "Feature_21_ArimaVec_7" "Feature_21_ArimaVec_8" "Feature_21_ArimaVec_9"
## [190] "Feature_22_ArimaVec_1" "Feature_22_ArimaVec_2" "Feature_22_ArimaVec_3"
## [193] "Feature_22_ArimaVec_4" "Feature_22_ArimaVec_5" "Feature_22_ArimaVec_6"
## [196] "Feature_22_ArimaVec_7" "Feature_22_ArimaVec_8" "Feature_22_ArimaVec_9"
## [199] "Feature_23_ArimaVec_1" "Feature_23_ArimaVec_2" "Feature_23_ArimaVec_3"
## [202] "Feature_23_ArimaVec_4" "Feature_23_ArimaVec_5" "Feature_23_ArimaVec_6"
## [205] "Feature_23_ArimaVec_7" "Feature_23_ArimaVec_8" "Feature_23_ArimaVec_9"
## [208] "Feature_24_ArimaVec_1" "Feature_24_ArimaVec_2" "Feature_24_ArimaVec_3"
## [211] "Feature_24_ArimaVec_4" "Feature_24_ArimaVec_5" "Feature_24_ArimaVec_6"
## [214] "Feature_24_ArimaVec_7" "Feature_24_ArimaVec_8" "Feature_24_ArimaVec_9"
## [217] "Feature_25_ArimaVec_1" "Feature_25_ArimaVec_2" "Feature_25_ArimaVec_3"
## [220] "Feature_25_ArimaVec_4" "Feature_25_ArimaVec_5" "Feature_25_ArimaVec_6"
## [223] "Feature_25_ArimaVec_7" "Feature_25_ArimaVec_8" "Feature_25_ArimaVec_9"
## [226] "Feature_26_ArimaVec_1" "Feature_26_ArimaVec_2" "Feature_26_ArimaVec_3"
## [229] "Feature_26_ArimaVec_4" "Feature_26_ArimaVec_5" "Feature_26_ArimaVec_6"
## [232] "Feature_26_ArimaVec_7" "Feature_26_ArimaVec_8" "Feature_26_ArimaVec_9"
## [235] "Feature_27_ArimaVec_1" "Feature_27_ArimaVec_2" "Feature_27_ArimaVec_3"
## [238] "Feature_27_ArimaVec_4" "Feature_27_ArimaVec_5" "Feature_27_ArimaVec_6"
## [241] "Feature_27_ArimaVec_7" "Feature_27_ArimaVec_8" "Feature_27_ArimaVec_9"
## [244] "Feature_28_ArimaVec_1" "Feature_28_ArimaVec_2" "Feature_28_ArimaVec_3"
## [247] "Feature_28_ArimaVec_4" "Feature_28_ArimaVec_5" "Feature_28_ArimaVec_6"
## [250] "Feature_28_ArimaVec_7" "Feature_28_ArimaVec_8" "Feature_28_ArimaVec_9"
## [253] "Feature_29_ArimaVec_1" "Feature_29_ArimaVec_2" "Feature_29_ArimaVec_3"
## [256] "Feature_29_ArimaVec_4" "Feature_29_ArimaVec_5" "Feature_29_ArimaVec_6"
## [259] "Feature_29_ArimaVec_7" "Feature_29_ArimaVec_8" "Feature_29_ArimaVec_9"
## [262] "Feature_30_ArimaVec_1" "Feature_30_ArimaVec_2" "Feature_30_ArimaVec_3"
## [265] "Feature_30_ArimaVec_4" "Feature_30_ArimaVec_5" "Feature_30_ArimaVec_6"
## [268] "Feature_30_ArimaVec_7" "Feature_30_ArimaVec_8" "Feature_30_ArimaVec_9"
## [271] "Feature_31_ArimaVec_1" "Feature_31_ArimaVec_2" "Feature_31_ArimaVec_3"
## [274] "Feature_31_ArimaVec_4" "Feature_31_ArimaVec_5" "Feature_31_ArimaVec_6"
## [277] "Feature_31_ArimaVec_7" "Feature_31_ArimaVec_8" "Feature_31_ArimaVec_9"
## [280] "Feature_32_ArimaVec_1" "Feature_32_ArimaVec_2" "Feature_32_ArimaVec_3"
## [283] "Feature_32_ArimaVec_4" "Feature_32_ArimaVec_5" "Feature_32_ArimaVec_6"
## [286] "Feature_32_ArimaVec_7" "Feature_32_ArimaVec_8" "Feature_32_ArimaVec_9"
## [289] "Feature_33_ArimaVec_1" "Feature_33_ArimaVec_2" "Feature_33_ArimaVec_3"
## [292] "Feature_33_ArimaVec_4" "Feature_33_ArimaVec_5" "Feature_33_ArimaVec_6"
## [295] "Feature_33_ArimaVec_7" "Feature_33_ArimaVec_8" "Feature_33_ArimaVec_9"
## [298] "Feature_34_ArimaVec_1" "Feature_34_ArimaVec_2" "Feature_34_ArimaVec_3"
## [301] "Feature_34_ArimaVec_4" "Feature_34_ArimaVec_5" "Feature_34_ArimaVec_6"
## [304] "Feature_34_ArimaVec_7" "Feature_34_ArimaVec_8" "Feature_34_ArimaVec_9"
## [307] "Feature_35_ArimaVec_1" "Feature_35_ArimaVec_2" "Feature_35_ArimaVec_3"
## [310] "Feature_35_ArimaVec_4" "Feature_35_ArimaVec_5" "Feature_35_ArimaVec_6"
## [313] "Feature_35_ArimaVec_7" "Feature_35_ArimaVec_8" "Feature_35_ArimaVec_9"
## [316] "Feature_36_ArimaVec_1" "Feature_36_ArimaVec_2" "Feature_36_ArimaVec_3"
## [319] "Feature_36_ArimaVec_4" "Feature_36_ArimaVec_5" "Feature_36_ArimaVec_6"
## [322] "Feature_36_ArimaVec_7" "Feature_36_ArimaVec_8" "Feature_36_ArimaVec_9"
## [325] "Feature_37_ArimaVec_1" "Feature_37_ArimaVec_2" "Feature_37_ArimaVec_3"
## [328] "Feature_37_ArimaVec_4" "Feature_37_ArimaVec_5" "Feature_37_ArimaVec_6"
## [331] "Feature_37_ArimaVec_7" "Feature_37_ArimaVec_8" "Feature_37_ArimaVec_9"
## [334] "Feature_38_ArimaVec_1" "Feature_38_ArimaVec_2" "Feature_38_ArimaVec_3"
## [337] "Feature_38_ArimaVec_4" "Feature_38_ArimaVec_5" "Feature_38_ArimaVec_6"
## [340] "Feature_38_ArimaVec_7" "Feature_38_ArimaVec_8" "Feature_38_ArimaVec_9"
## [343] "Feature_39_ArimaVec_1" "Feature_39_ArimaVec_2" "Feature_39_ArimaVec_3"
## [346] "Feature_39_ArimaVec_4" "Feature_39_ArimaVec_5" "Feature_39_ArimaVec_6"
## [349] "Feature_39_ArimaVec_7" "Feature_39_ArimaVec_8" "Feature_39_ArimaVec_9"
## [352] "Feature_40_ArimaVec_1" "Feature_40_ArimaVec_2" "Feature_40_ArimaVec_3"
## [355] "Feature_40_ArimaVec_4" "Feature_40_ArimaVec_5" "Feature_40_ArimaVec_6"
## [358] "Feature_40_ArimaVec_7" "Feature_40_ArimaVec_8" "Feature_40_ArimaVec_9"
## [361] "Feature_41_ArimaVec_1" "Feature_41_ArimaVec_2" "Feature_41_ArimaVec_3"
## [364] "Feature_41_ArimaVec_4" "Feature_41_ArimaVec_5" "Feature_41_ArimaVec_6"
## [367] "Feature_41_ArimaVec_7" "Feature_41_ArimaVec_8" "Feature_41_ArimaVec_9"
## [370] "Feature_42_ArimaVec_1" "Feature_42_ArimaVec_2" "Feature_42_ArimaVec_3"
## [373] "Feature_42_ArimaVec_4" "Feature_42_ArimaVec_5" "Feature_42_ArimaVec_6"
## [376] "Feature_42_ArimaVec_7" "Feature_42_ArimaVec_8" "Feature_42_ArimaVec_9"
## [379] "IncomeGroup" "PopSizeGroup" "ED"
## [382] "Edu" "HI" "QOL"
## [385] "PE" "Relig" "OA"# IFT_SwappedPhase_FT_aggregate_arima_vector[1:5, 1:4]; temp_Data[1:5, 1:4]
# 2. Perform LASSO modeling on IFT_SwappedPhase_FT_aggregate_arima_vector;
# report param estimates and quality metrics AIC/BIC
set.seed(12345)
cvLASSO_kime_swapped =
cv.glmnet(data.matrix(IFT_SwappedPhase_FT_aggregate_arima_vector[ , -387]),
# IFT_SwappedPhase_FT_aggregate_arima_vector[ , 387], alpha = 1, parallel=TRUE)
Y, alpha = 1, parallel=TRUE)
plot(cvLASSO_kime_swapped)
mtext("(Spacekime, Swapped-Phases) CV LASSO: Number of Nonzero (Active) Coefficients", side=3, line=2.5)
##################################Use only ARIMA effects, no SOCR meta-data#####
set.seed(12345)
cvLASSO_kime_swapped_lim = cv.glmnet(data.matrix(
IFT_SwappedPhase_FT_aggregate_arima_vector[ , 1:(42*9)]), Y, alpha = 1, parallel=TRUE)
plot(cvLASSO_kime_swapped_lim)
mtext("CV LASSO Swapped-Phase (using only Timeseries data): Number of Nonzero (Active) Coefficients", side=3, line=2.5)
# Identify top predictors and forecast the Y=Overall (OA) Country ranking outcome
predLASSO_kime_swapped_lim <- predict(cvLASSO_kime_swapped_lim,
s = cvLASSO_kime_swapped_lim$lambda.min,
newx = data.matrix(IFT_SwappedPhase_FT_aggregate_arima_vector[ , 1:(42*9)]))
coefList_kime_swapped_lim <- coef(cvLASSO_kime_swapped_lim, s='lambda.min')
coefList_kime_swapped_lim <- data.frame(coefList_kime_swapped_lim@Dimnames[[1]][coefList_kime_swapped_lim@i+1],coefList_kime_swapped_lim@x)
names(coefList_kime_swapped_lim) <- c('Feature','EffectSize')
arrange(coefList_kime_swapped_lim, -abs(EffectSize))[2:10, ]## Feature EffectSize
## 2 Feature_24_ArimaVec_5 -1.78958
## NA <NA> NA
## NA.1 <NA> NA
## NA.2 <NA> NA
## NA.3 <NA> NA
## NA.4 <NA> NA
## NA.5 <NA> NA
## NA.6 <NA> NA
## NA.7 <NA> NAcor(Y, predLASSO_kime_swapped_lim[, 1]) # 0.86## [1] 0.5808904################################################################################
# Identify top predictors and forecast the Y=Overall (OA) Country ranking outcome
predLASSO_kime_swapped <- predict(cvLASSO_kime_swapped, s = cvLASSO_kime_swapped$lambda.min,
newx = data.matrix(IFT_SwappedPhase_FT_aggregate_arima_vector[ , -387]))
# testMSE_LASSO_kime_swapped <-
# mean((predLASSO_kime_swapped - IFT_SwappedPhase_FT_aggregate_arima_vector[ , 387])^2)
# testMSE_LASSO_kime_swapped
predLASSO_kime_swapped = predict(cvLASSO_kime_swapped, s = 3,
newx = data.matrix(IFT_SwappedPhase_FT_aggregate_arima_vector[ , -387]))
predLASSO_kime_swapped## s1
## Austria 23.27402
## Belgium 25.09877
## Bulgaria 26.19491
## Croatia 24.60106
## Cyprus 32.26734
## Czech Republic 23.48426
## Denmark 22.50837
## Estonia 27.90674
## Finland 12.41476
## France 17.51471
## Germany (until 1990 former territory of the FRG) 16.67560
## Greece 23.71843
## Hungary 28.57275
## Iceland 30.90331
## Ireland 23.02254
## Italy 25.30803
## Latvia 27.00298
## Lithuania 30.21699
## Luxembourg 16.96024
## Malta 35.22264
## Netherlands 12.50073
## Norway 14.19769
## Poland 24.93168
## Portugal 22.84419
## Romania 25.42131
## Slovakia 29.57433
## Slovenia 20.27913
## Spain 21.10127
## Sweden 20.83850
## Switzerland 18.43727
## United Kingdom 14.00545# Plot Regression Coefficients: create variable names for plotting
betaHatLASSO_kime_swapped = as.double(coef(cvLASSO_kime_swapped,
s=cvLASSO_kime_swapped$lambda.min))
#cvLASSO_kime_swapped$lambda.1se
coefplot(betaHatLASSO_kime_swapped[377:386], sd = rep(0, 10), pch=0, cex.pts = 3, col="red",
main = "(Spacekime, Swapped-Phases) LASSO-Regularized Regression Coefficient Estimates",
varnames = varNames[377:386])
varImp(cvLASSO_kime_swapped, lambda = cvLASSO_kime_swapped$lambda.min)## Overall
## Feature_1_ArimaVec_1 0.000000
## Feature_1_ArimaVec_2 0.000000
## Feature_1_ArimaVec_3 0.000000
## Feature_1_ArimaVec_4 0.000000
## Feature_1_ArimaVec_5 0.000000
## Feature_1_ArimaVec_6 0.000000
## Feature_1_ArimaVec_7 0.000000
## Feature_1_ArimaVec_8 0.000000
## Feature_1_ArimaVec_9 0.000000
## Feature_2_ArimaVec_1 0.000000
## Feature_2_ArimaVec_2 0.000000
## Feature_2_ArimaVec_3 0.000000
## Feature_2_ArimaVec_4 0.000000
## Feature_2_ArimaVec_5 0.000000
## Feature_2_ArimaVec_6 0.000000
## Feature_2_ArimaVec_7 0.000000
## Feature_2_ArimaVec_8 0.000000
## Feature_2_ArimaVec_9 0.000000
## Feature_3_ArimaVec_1 0.000000
## Feature_3_ArimaVec_2 0.000000
## Feature_3_ArimaVec_3 0.000000
## Feature_3_ArimaVec_4 0.000000
## Feature_3_ArimaVec_5 0.000000
## Feature_3_ArimaVec_6 0.000000
## Feature_3_ArimaVec_7 0.000000
## Feature_3_ArimaVec_8 0.000000
## Feature_3_ArimaVec_9 0.000000
## Feature_4_ArimaVec_1 0.000000
## Feature_4_ArimaVec_2 0.000000
## Feature_4_ArimaVec_3 0.000000
## Feature_4_ArimaVec_4 0.000000
## Feature_4_ArimaVec_5 0.000000
## Feature_4_ArimaVec_6 0.000000
## Feature_4_ArimaVec_7 0.000000
## Feature_4_ArimaVec_8 0.000000
## Feature_4_ArimaVec_9 0.000000
## Feature_5_ArimaVec_1 0.000000
## Feature_5_ArimaVec_2 0.000000
## Feature_5_ArimaVec_3 0.000000
## Feature_5_ArimaVec_4 0.000000
## Feature_5_ArimaVec_5 0.000000
## Feature_5_ArimaVec_6 0.000000
## Feature_5_ArimaVec_7 0.000000
## Feature_5_ArimaVec_8 0.000000
## Feature_5_ArimaVec_9 0.000000
## Feature_6_ArimaVec_1 0.000000
## Feature_6_ArimaVec_2 0.000000
## Feature_6_ArimaVec_3 0.000000
## Feature_6_ArimaVec_4 0.000000
## Feature_6_ArimaVec_5 0.000000
## Feature_6_ArimaVec_6 0.000000
## Feature_6_ArimaVec_7 0.000000
## Feature_6_ArimaVec_8 0.000000
## Feature_6_ArimaVec_9 0.000000
## Feature_7_ArimaVec_1 0.000000
## Feature_7_ArimaVec_2 0.000000
## Feature_7_ArimaVec_3 0.000000
## Feature_7_ArimaVec_4 0.000000
## Feature_7_ArimaVec_5 0.000000
## Feature_7_ArimaVec_6 0.000000
## Feature_7_ArimaVec_7 0.000000
## Feature_7_ArimaVec_8 0.000000
## Feature_7_ArimaVec_9 0.000000
## Feature_8_ArimaVec_1 0.000000
## Feature_8_ArimaVec_2 0.000000
## Feature_8_ArimaVec_3 0.000000
## Feature_8_ArimaVec_4 0.000000
## Feature_8_ArimaVec_5 0.000000
## Feature_8_ArimaVec_6 0.000000
## Feature_8_ArimaVec_7 0.000000
## Feature_8_ArimaVec_8 0.000000
## Feature_8_ArimaVec_9 0.000000
## Feature_9_ArimaVec_1 0.000000
## Feature_9_ArimaVec_2 0.000000
## Feature_9_ArimaVec_3 0.000000
## Feature_9_ArimaVec_4 0.000000
## Feature_9_ArimaVec_5 0.000000
## Feature_9_ArimaVec_6 0.000000
## Feature_9_ArimaVec_7 0.000000
## Feature_9_ArimaVec_8 0.000000
## Feature_9_ArimaVec_9 0.000000
## Feature_10_ArimaVec_1 0.000000
## Feature_10_ArimaVec_2 0.000000
## Feature_10_ArimaVec_3 0.000000
## Feature_10_ArimaVec_4 0.000000
## Feature_10_ArimaVec_5 0.000000
## Feature_10_ArimaVec_6 0.000000
## Feature_10_ArimaVec_7 0.000000
## Feature_10_ArimaVec_8 0.000000
## Feature_10_ArimaVec_9 0.000000
## Feature_11_ArimaVec_1 0.000000
## Feature_11_ArimaVec_2 0.000000
## Feature_11_ArimaVec_3 0.000000
## Feature_11_ArimaVec_4 0.000000
## Feature_11_ArimaVec_5 0.000000
## Feature_11_ArimaVec_6 0.000000
## Feature_11_ArimaVec_7 0.000000
## Feature_11_ArimaVec_8 0.000000
## Feature_11_ArimaVec_9 0.000000
## Feature_12_ArimaVec_1 0.000000
## Feature_12_ArimaVec_2 0.000000
## Feature_12_ArimaVec_3 0.000000
## Feature_12_ArimaVec_4 0.000000
## Feature_12_ArimaVec_5 0.000000
## Feature_12_ArimaVec_6 0.000000
## Feature_12_ArimaVec_7 0.000000
## Feature_12_ArimaVec_8 0.000000
## Feature_12_ArimaVec_9 0.000000
## Feature_13_ArimaVec_1 0.000000
## Feature_13_ArimaVec_2 0.000000
## Feature_13_ArimaVec_3 0.000000
## Feature_13_ArimaVec_4 0.000000
## Feature_13_ArimaVec_5 0.000000
## Feature_13_ArimaVec_6 0.000000
## Feature_13_ArimaVec_7 0.000000
## Feature_13_ArimaVec_8 0.000000
## Feature_13_ArimaVec_9 0.000000
## Feature_14_ArimaVec_1 0.000000
## Feature_14_ArimaVec_2 0.000000
## Feature_14_ArimaVec_3 0.000000
## Feature_14_ArimaVec_4 0.000000
## Feature_14_ArimaVec_5 0.000000
## Feature_14_ArimaVec_6 0.000000
## Feature_14_ArimaVec_7 0.000000
## Feature_14_ArimaVec_8 0.000000
## Feature_14_ArimaVec_9 0.000000
## Feature_15_ArimaVec_1 0.000000
## Feature_15_ArimaVec_2 0.000000
## Feature_15_ArimaVec_3 0.000000
## Feature_15_ArimaVec_4 0.000000
## Feature_15_ArimaVec_5 0.000000
## Feature_15_ArimaVec_6 0.000000
## Feature_15_ArimaVec_7 0.000000
## Feature_15_ArimaVec_8 0.000000
## Feature_15_ArimaVec_9 0.000000
## Feature_16_ArimaVec_1 0.000000
## Feature_16_ArimaVec_2 0.000000
## Feature_16_ArimaVec_3 0.000000
## Feature_16_ArimaVec_4 0.000000
## Feature_16_ArimaVec_5 0.000000
## Feature_16_ArimaVec_6 0.000000
## Feature_16_ArimaVec_7 0.000000
## Feature_16_ArimaVec_8 0.000000
## Feature_16_ArimaVec_9 0.000000
## Feature_17_ArimaVec_1 0.000000
## Feature_17_ArimaVec_2 0.000000
## Feature_17_ArimaVec_3 0.000000
## Feature_17_ArimaVec_4 0.000000
## Feature_17_ArimaVec_5 0.000000
## Feature_17_ArimaVec_6 0.000000
## Feature_17_ArimaVec_7 0.000000
## Feature_17_ArimaVec_8 0.000000
## Feature_17_ArimaVec_9 0.000000
## Feature_18_ArimaVec_1 0.000000
## Feature_18_ArimaVec_2 0.000000
## Feature_18_ArimaVec_3 0.000000
## Feature_18_ArimaVec_4 0.000000
## Feature_18_ArimaVec_5 0.000000
## Feature_18_ArimaVec_6 0.000000
## Feature_18_ArimaVec_7 0.000000
## Feature_18_ArimaVec_8 0.000000
## Feature_18_ArimaVec_9 0.000000
## Feature_19_ArimaVec_1 0.000000
## Feature_19_ArimaVec_2 0.000000
## Feature_19_ArimaVec_3 0.000000
## Feature_19_ArimaVec_4 0.000000
## Feature_19_ArimaVec_5 0.000000
## Feature_19_ArimaVec_6 0.000000
## Feature_19_ArimaVec_7 0.000000
## Feature_19_ArimaVec_8 0.000000
## Feature_19_ArimaVec_9 0.000000
## Feature_20_ArimaVec_1 0.000000
## Feature_20_ArimaVec_2 0.000000
## Feature_20_ArimaVec_3 0.000000
## Feature_20_ArimaVec_4 0.000000
## Feature_20_ArimaVec_5 0.000000
## Feature_20_ArimaVec_6 0.000000
## Feature_20_ArimaVec_7 0.000000
## Feature_20_ArimaVec_8 0.000000
## Feature_20_ArimaVec_9 0.000000
## Feature_21_ArimaVec_1 0.000000
## Feature_21_ArimaVec_2 0.000000
## Feature_21_ArimaVec_3 0.000000
## Feature_21_ArimaVec_4 0.000000
## Feature_21_ArimaVec_5 0.000000
## Feature_21_ArimaVec_6 0.000000
## Feature_21_ArimaVec_7 0.000000
## Feature_21_ArimaVec_8 0.000000
## Feature_21_ArimaVec_9 0.000000
## Feature_22_ArimaVec_1 0.000000
## Feature_22_ArimaVec_2 0.000000
## Feature_22_ArimaVec_3 0.000000
## Feature_22_ArimaVec_4 0.000000
## Feature_22_ArimaVec_5 0.000000
## Feature_22_ArimaVec_6 0.000000
## Feature_22_ArimaVec_7 0.000000
## Feature_22_ArimaVec_8 0.000000
## Feature_22_ArimaVec_9 0.000000
## Feature_23_ArimaVec_1 0.000000
## Feature_23_ArimaVec_2 0.000000
## Feature_23_ArimaVec_3 0.000000
## Feature_23_ArimaVec_4 0.000000
## Feature_23_ArimaVec_5 0.000000
## Feature_23_ArimaVec_6 0.000000
## Feature_23_ArimaVec_7 0.000000
## Feature_23_ArimaVec_8 0.000000
## Feature_23_ArimaVec_9 0.000000
## Feature_24_ArimaVec_1 0.000000
## Feature_24_ArimaVec_2 0.000000
## Feature_24_ArimaVec_3 0.000000
## Feature_24_ArimaVec_4 0.000000
## Feature_24_ArimaVec_5 1.372902
## Feature_24_ArimaVec_6 0.000000
## Feature_24_ArimaVec_7 0.000000
## Feature_24_ArimaVec_8 0.000000
## Feature_24_ArimaVec_9 0.000000
## Feature_25_ArimaVec_1 0.000000
## Feature_25_ArimaVec_2 0.000000
## Feature_25_ArimaVec_3 0.000000
## Feature_25_ArimaVec_4 0.000000
## Feature_25_ArimaVec_5 0.000000
## Feature_25_ArimaVec_6 0.000000
## Feature_25_ArimaVec_7 0.000000
## Feature_25_ArimaVec_8 0.000000
## Feature_25_ArimaVec_9 0.000000
## Feature_26_ArimaVec_1 0.000000
## Feature_26_ArimaVec_2 0.000000
## Feature_26_ArimaVec_3 0.000000
## Feature_26_ArimaVec_4 0.000000
## Feature_26_ArimaVec_5 0.000000
## Feature_26_ArimaVec_6 0.000000
## Feature_26_ArimaVec_7 0.000000
## Feature_26_ArimaVec_8 0.000000
## Feature_26_ArimaVec_9 0.000000
## Feature_27_ArimaVec_1 0.000000
## Feature_27_ArimaVec_2 0.000000
## Feature_27_ArimaVec_3 0.000000
## Feature_27_ArimaVec_4 0.000000
## Feature_27_ArimaVec_5 0.000000
## Feature_27_ArimaVec_6 0.000000
## Feature_27_ArimaVec_7 0.000000
## Feature_27_ArimaVec_8 0.000000
## Feature_27_ArimaVec_9 0.000000
## Feature_28_ArimaVec_1 0.000000
## Feature_28_ArimaVec_2 0.000000
## Feature_28_ArimaVec_3 0.000000
## Feature_28_ArimaVec_4 0.000000
## Feature_28_ArimaVec_5 0.000000
## Feature_28_ArimaVec_6 0.000000
## Feature_28_ArimaVec_7 0.000000
## Feature_28_ArimaVec_8 0.000000
## Feature_28_ArimaVec_9 0.000000
## Feature_29_ArimaVec_1 0.000000
## Feature_29_ArimaVec_2 0.000000
## Feature_29_ArimaVec_3 0.000000
## Feature_29_ArimaVec_4 0.000000
## Feature_29_ArimaVec_5 0.000000
## Feature_29_ArimaVec_6 0.000000
## Feature_29_ArimaVec_7 0.000000
## Feature_29_ArimaVec_8 0.000000
## Feature_29_ArimaVec_9 0.000000
## Feature_30_ArimaVec_1 0.000000
## Feature_30_ArimaVec_2 0.000000
## Feature_30_ArimaVec_3 0.000000
## Feature_30_ArimaVec_4 0.000000
## Feature_30_ArimaVec_5 0.000000
## Feature_30_ArimaVec_6 0.000000
## Feature_30_ArimaVec_7 0.000000
## Feature_30_ArimaVec_8 0.000000
## Feature_30_ArimaVec_9 0.000000
## Feature_31_ArimaVec_1 0.000000
## Feature_31_ArimaVec_2 0.000000
## Feature_31_ArimaVec_3 0.000000
## Feature_31_ArimaVec_4 0.000000
## Feature_31_ArimaVec_5 0.000000
## Feature_31_ArimaVec_6 0.000000
## Feature_31_ArimaVec_7 0.000000
## Feature_31_ArimaVec_8 0.000000
## Feature_31_ArimaVec_9 0.000000
## Feature_32_ArimaVec_1 0.000000
## Feature_32_ArimaVec_2 0.000000
## Feature_32_ArimaVec_3 0.000000
## Feature_32_ArimaVec_4 0.000000
## Feature_32_ArimaVec_5 0.000000
## Feature_32_ArimaVec_6 0.000000
## Feature_32_ArimaVec_7 0.000000
## Feature_32_ArimaVec_8 0.000000
## Feature_32_ArimaVec_9 0.000000
## Feature_33_ArimaVec_1 0.000000
## Feature_33_ArimaVec_2 0.000000
## Feature_33_ArimaVec_3 0.000000
## Feature_33_ArimaVec_4 0.000000
## Feature_33_ArimaVec_5 0.000000
## Feature_33_ArimaVec_6 0.000000
## Feature_33_ArimaVec_7 0.000000
## Feature_33_ArimaVec_8 0.000000
## Feature_33_ArimaVec_9 0.000000
## Feature_34_ArimaVec_1 0.000000
## Feature_34_ArimaVec_2 0.000000
## Feature_34_ArimaVec_3 0.000000
## Feature_34_ArimaVec_4 0.000000
## Feature_34_ArimaVec_5 0.000000
## Feature_34_ArimaVec_6 0.000000
## Feature_34_ArimaVec_7 0.000000
## Feature_34_ArimaVec_8 0.000000
## Feature_34_ArimaVec_9 0.000000
## Feature_35_ArimaVec_1 0.000000
## Feature_35_ArimaVec_2 0.000000
## Feature_35_ArimaVec_3 0.000000
## Feature_35_ArimaVec_4 0.000000
## Feature_35_ArimaVec_5 0.000000
## Feature_35_ArimaVec_6 0.000000
## Feature_35_ArimaVec_7 0.000000
## Feature_35_ArimaVec_8 0.000000
## Feature_35_ArimaVec_9 0.000000
## Feature_36_ArimaVec_1 0.000000
## Feature_36_ArimaVec_2 0.000000
## Feature_36_ArimaVec_3 0.000000
## Feature_36_ArimaVec_4 0.000000
## Feature_36_ArimaVec_5 0.000000
## Feature_36_ArimaVec_6 0.000000
## Feature_36_ArimaVec_7 0.000000
## Feature_36_ArimaVec_8 0.000000
## Feature_36_ArimaVec_9 0.000000
## Feature_37_ArimaVec_1 0.000000
## Feature_37_ArimaVec_2 0.000000
## Feature_37_ArimaVec_3 0.000000
## Feature_37_ArimaVec_4 0.000000
## Feature_37_ArimaVec_5 0.000000
## Feature_37_ArimaVec_6 0.000000
## Feature_37_ArimaVec_7 0.000000
## Feature_37_ArimaVec_8 0.000000
## Feature_37_ArimaVec_9 0.000000
## Feature_38_ArimaVec_1 0.000000
## Feature_38_ArimaVec_2 0.000000
## Feature_38_ArimaVec_3 0.000000
## Feature_38_ArimaVec_4 0.000000
## Feature_38_ArimaVec_5 0.000000
## Feature_38_ArimaVec_6 0.000000
## Feature_38_ArimaVec_7 0.000000
## Feature_38_ArimaVec_8 0.000000
## Feature_38_ArimaVec_9 0.000000
## Feature_39_ArimaVec_1 0.000000
## Feature_39_ArimaVec_2 0.000000
## Feature_39_ArimaVec_3 0.000000
## Feature_39_ArimaVec_4 0.000000
## Feature_39_ArimaVec_5 0.000000
## Feature_39_ArimaVec_6 0.000000
## Feature_39_ArimaVec_7 0.000000
## Feature_39_ArimaVec_8 0.000000
## Feature_39_ArimaVec_9 0.000000
## Feature_40_ArimaVec_1 0.000000
## Feature_40_ArimaVec_2 0.000000
## Feature_40_ArimaVec_3 0.000000
## Feature_40_ArimaVec_4 0.000000
## Feature_40_ArimaVec_5 0.000000
## Feature_40_ArimaVec_6 0.000000
## Feature_40_ArimaVec_7 0.000000
## Feature_40_ArimaVec_8 0.000000
## Feature_40_ArimaVec_9 0.000000
## Feature_41_ArimaVec_1 0.000000
## Feature_41_ArimaVec_2 0.000000
## Feature_41_ArimaVec_3 0.000000
## Feature_41_ArimaVec_4 0.000000
## Feature_41_ArimaVec_5 0.000000
## Feature_41_ArimaVec_6 0.000000
## Feature_41_ArimaVec_7 0.000000
## Feature_41_ArimaVec_8 0.000000
## Feature_41_ArimaVec_9 0.000000
## Feature_42_ArimaVec_1 0.000000
## Feature_42_ArimaVec_2 0.000000
## Feature_42_ArimaVec_3 0.000000
## Feature_42_ArimaVec_4 0.000000
## Feature_42_ArimaVec_5 0.000000
## Feature_42_ArimaVec_6 0.000000
## Feature_42_ArimaVec_7 0.000000
## Feature_42_ArimaVec_8 0.000000
## Feature_42_ArimaVec_9 0.000000
## IncomeGroup 0.000000
## PopSizeGroup 0.000000
## ED 0.000000
## Edu 0.000000
## HI 0.000000
## QOL 0.000000
## PE 0.000000
## Relig 0.000000coefList_kime_swapped <- coef(cvLASSO_kime_swapped, s=3) # 'lambda.min')
coefList_kime_swapped <- data.frame(coefList_kime_swapped@Dimnames[[1]][coefList_kime_swapped@i+1], coefList_kime_swapped@x)
names(coefList_kime_swapped) <- c('Feature','EffectSize')
arrange(coefList_kime_swapped, -abs(EffectSize))[2:10, ]## Feature EffectSize
## 2 Feature_24_ArimaVec_5 -4.94721216
## 3 Feature_3_ArimaVec_8 3.87698995
## 4 IncomeGroup 0.95599615
## 5 Feature_7_ArimaVec_6 -0.94552368
## 6 Feature_41_ArimaVec_3 -0.74480344
## 7 Feature_42_ArimaVec_3 0.57686868
## 8 Feature_41_ArimaVec_6 0.50219996
## 9 ED 0.10999787
## 10 Feature_33_ArimaVec_8 0.05428669# Feature EffectSize
#2 Feature_32_ArimaVec_6 3.3820076
#3 Feature_1_ArimaVec_3 2.2133139
#4 Feature_21_ArimaVec_4 1.5376447
#5 Feature_22_ArimaVec_3 1.0546605
#6 Feature_14_ArimaVec_5 0.7428693
#7 ED 0.6525794
#8 Feature_24_ArimaVec_5 0.5987113
#9 Feature_12_ArimaVec_5 0.3177650
#10 Feature_37_ArimaVec_6 0.1598574
#
# ARIMA-spacetime: 4=non-seasonal MA, 5=seasonal AR, 8=non-seasonal Diff
# ARIMA-spacekime_nill: 3=non-seasonal AR, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA
# ARIMA-spacekime_swapped: 3=non-seasonal AR, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA
# 9 ARIMA-derived vector includes:
# (1=ts_avg, 2=forecast_avg, 3=non-seasonal AR, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA,
# 7=period, 8=non-seasonal Diff, 9=seasonal differences)
coef(cvLASSO_kime_swapped, s = 3) %>% # "lambda.min") %>%
broom::tidy() %>%
filter(row != "(Intercept)") %>%
top_n(100, wt = abs(value)) %>%
ggplot(aes(value, reorder(row, value), color = value > 0)) +
geom_point(show.legend = FALSE, aes(size = abs(value))) +
ggtitle("(Spacekime, Swapped-Phases) Top 9 salient features (LASSO penalty)") +
xlab("Effect-size") +
ylab(NULL)
# pack a 31*4 DF with (predLASSO_kime, IFT_NilPhase_FT_aggregate_arima_vector_Y,
# IFT_SwappedPhase_FT_aggregate_arima_vector_Y, Y)
validation_kime_swapped <- cbind(predLASSO_lim[, 1],
predLASSO_kime[ , 1], predLASSO_kime_swapped[ , 1], Y)
colnames(validation_kime_swapped) <- c("predLASSO (spacetime)", "predLASSO_IFT_NilPhase",
"predLASSO_IFT_SwappedPhase", "Orig_Y")
head(validation_kime_swapped); dim(validation_kime_swapped)## predLASSO (spacetime) predLASSO_IFT_NilPhase
## Austria 20.21660 18.60234
## Belgium 24.57457 20.87543
## Bulgaria 27.42736 21.61560
## Croatia 25.84568 23.50550
## Cyprus 27.80166 28.40317
## Czech Republic 24.17704 23.87474
## predLASSO_IFT_SwappedPhase Orig_Y
## Austria 23.27402 18
## Belgium 25.09877 19
## Bulgaria 26.19491 38
## Croatia 24.60106 28
## Cyprus 32.26734 50
## Czech Republic 23.48426 25## [1] 31 4# Prediction correlations:
cor(validation_kime_swapped[ , 3], validation_kime_swapped[, 4]) ## [1] 0.86935# predLASSO_IFT_SwappedPhase OA rank vs. predLASSO_spacekime: 0.7
cor(validation_kime_swapped[ , 1], validation_kime_swapped[, 3]) ## [1] 0.8660305# predLASSO (spacetime) vs. predLASSO_IFT_SwappedPhase OA rank: 0.83
# Plot observed Y (Overall Country ranking) vs. LASSO (9-parameters) predicted Y^
linFit1_kime_swapped <- lm(validation_kime_swapped[ , 4] ~ predLASSO)
plot(validation_kime_swapped[ , 4] ~ predLASSO,
col="blue", xaxt='n', yaxt='n', pch = 16, cex=3,
xlab="predLASSO_spacekime Country Overall Ranking", ylab="predLASSO_IFT_SwappedPhase_FT_Y",
main = sprintf("Spacetime Predicted (x) vs. Kime IFT_SwappedPhase_FT_Y (y) Overall Country Ranking, cor=%.02f",
cor(validation_kime_swapped[ , 3], validation_kime_swapped[, 4])))
abline(linFit1_kime_swapped, lwd=3, col="red")
#abline(linFit1_kime, lwd=3, col="green")
# Plot Spacetime LASSO forecasting
# Plot observed Y (Overall Country ranking) vs. LASSO (9-parameters) predicted Y^
linFit1_spacetime <- lm(validation_kime_swapped[ , 1] ~ validation_kime_swapped[ , 4])
plot(validation_kime_swapped[ , 1] ~ validation_kime_swapped[ , 4],
col="blue", xaxt='n', yaxt='n', pch = 16, cex=3,
xlab="Observed Country Overall Ranking", ylab="predLASSO_spacetime",
main = sprintf("Spacetime Predicted (y) vs. Observed (x) Overall Country Ranking, cor=%.02f",
cor(validation_kime_swapped[ , 1], validation_kime_swapped[, 4])))
abline(linFit1_spacetime, lwd=3, col="red")
# test with using swapped-phases LASSO estimates
linFit1_spacekime <- lm(validation_kime_swapped[ , 3] ~ validation_kime_swapped[ , 4])
plot(validation_kime_swapped[ , 3] ~ validation_kime_swapped[ , 4],
col="blue", xaxt='n', yaxt='n', pch = 16, cex=3,
xlab="Observed Country Overall Ranking", ylab="predLASSO_spacekime Swapped-Phases",
main = sprintf("Spacekime Predicted, Swapped-Phases (y) vs. Observed (x) Overall Country Ranking, cor=%.02f",
cor(validation_kime_swapped[ , 3], validation_kime_swapped[, 4])))
abline(linFit1_spacekime, lwd=3, col="red")
# add Top_30_Ranking_Indicator
validation_kime_swapped <- as.data.frame(cbind(validation_kime_swapped, ifelse (validation_kime_swapped[,4]<=30, 1, 0)))
colnames(validation_kime_swapped)[5] <- "Top30Rank"
head(validation_kime_swapped)## predLASSO (spacetime) predLASSO_IFT_NilPhase
## Austria 20.21660 18.60234
## Belgium 24.57457 20.87543
## Bulgaria 27.42736 21.61560
## Croatia 25.84568 23.50550
## Cyprus 27.80166 28.40317
## Czech Republic 24.17704 23.87474
## predLASSO_IFT_SwappedPhase Orig_Y Top30Rank
## Austria 23.27402 18 1
## Belgium 25.09877 19 1
## Bulgaria 26.19491 38 0
## Croatia 24.60106 28 1
## Cyprus 32.26734 50 0
## Czech Republic 23.48426 25 1library("ggrepel")
# Spacetime LASSO modeling
myPlotSpacetime <- ggplot(as.data.frame(validation_kime_swapped), aes(x=Orig_Y,
y=`predLASSO (spacetime)`, label=rownames(validation_kime_swapped))) +
geom_point() +
# Color by groups
# geom_text(aes(color=factor(rownames(validation_kime_swapped)))) +
geom_label_repel(aes(label = rownames(validation_kime_swapped),
fill = factor(Top30Rank)), color = 'black', size = 5,
point.padding = unit(0.3, "lines")) +
# theme(legend.position = "bottom") +
theme(legend.position = c(0.1, 0.9),
legend.text = element_text(colour="black", size=12, face="bold"),
legend.title = element_text(colour="black", size=14, face="bold")) +
scale_fill_discrete(name = "Country Overall Ranking",
labels = c("Below 30 Rank", "Top 30 Rank")) +
labs(title=sprintf("Spacetime LASSO Prediction (y) vs. Observed (x) Overall Country Ranking, cor=%.02f", cor(validation_kime_swapped[ , 1], validation_kime_swapped[, 4])),
x ="Observed Overall Country Ranking (1 is 'best')",
y = "Spacetime LASSO Rank Forecasting")
myPlotSpacetime
# NIL-PHASE KIME reconstruction
myPlotNilPhase <- ggplot(as.data.frame(validation_kime_swapped), aes(x=Orig_Y,
y=predLASSO_kime, label=rownames(validation_kime_swapped))) +
geom_point() +
# Color by groups
# geom_text(aes(color=factor(rownames(validation_kime_swapped)))) +
geom_label_repel(aes(label = rownames(validation_kime_swapped),
fill = factor(Top30Rank)), color = 'black', size = 5,
point.padding = unit(0.3, "lines")) +
# theme(legend.position = "bottom") +
theme(legend.position = c(0.1, 0.9),
legend.text = element_text(colour="black", size=12, face="bold"),
legend.title = element_text(colour="black", size=14, face="bold")) +
scale_fill_discrete(name = "Country Overall Ranking",
labels = c("Below 30 Rank", "Top 30 Rank")) +
labs(title=sprintf("Spacekime LASSO Predicted, Nil-Phases, (y) vs. Observed (x) Overall Country Ranking, cor=%.02f", cor(validation_kime_swapped[ , 2], validation_kime_swapped[, 4])),
x ="Observed Overall Country Ranking (1 is 'best')",
y = "Spacekime LASSO Predicted, using Nil-Phases")
myPlotNilPhase
# SWAPPED PHASE KIME reconstruction
myPlotSwappedPhase <- ggplot(as.data.frame(validation_kime_swapped), aes(x=Orig_Y,
y=predLASSO_kime_swapped, label=rownames(validation_kime_swapped))) +
geom_point() +
# Color by groups
# geom_text(aes(color=factor(rownames(validation_kime_swapped)))) +
geom_label_repel(aes(label = rownames(validation_kime_swapped),
fill = factor(Top30Rank)), color = 'black', size = 5,
point.padding = unit(0.3, "lines")) +
# theme(legend.position = "bottom") +
theme(legend.position = c(0.1, 0.9),
legend.text = element_text(colour="black", size=12, face="bold"),
legend.title = element_text(colour="black", size=14, face="bold")) +
scale_fill_discrete(name = "Country Overall Ranking",
labels = c("Below 30 Rank", "Top 30 Rank")) +
labs(title=sprintf("Spacekime LASSO Predicted, Swapped-Phases, (y) vs. Observed (x) Overall Country Ranking, cor=%.02f", cor(validation_kime_swapped[ , 3], validation_kime_swapped[, 4])),
x ="Observed Overall Country Ranking (1 is 'best')",
y = "Spacekime LASSO Predicted, using Swapped-Phases")
myPlotSwappedPhase
countryNames[11]<-"Germany"
aggregateResults <- (rbind(cbind(as.character(countryNames), "predLASSO_spacetime", as.numeric(predLASSO)),
cbind(as.character(countryNames), "predLASSO_lim", predLASSO_lim),
cbind(as.character(countryNames), "predLASSO_nil", predLASSO_kime),
cbind(as.character(countryNames), "predLASSO_swapped", predLASSO_kime_swapped),
cbind(as.character(countryNames), "observed", Y)
))
aggregateResults <- data.frame(aggregateResults[ , -3], as.numeric(aggregateResults[,3]))
colnames(aggregateResults) <- c("country", "estimate_method", "ranking")
ggplot(aggregateResults, aes(x=country, y=ranking, color=estimate_method)) +
geom_point(aes(shape=estimate_method, color=estimate_method, size=estimate_method)) + geom_point(size = 5) +
geom_line(data = aggregateResults[aggregateResults$estimate_method == "observed", ],
aes(group = estimate_method), size=2, linetype = "dashed") +
theme(axis.text.x = element_text(angle=90, hjust=1, vjust=.5)) +
# theme(legend.position = "bottom") +
# scale_shape_manual(values = as.factor(aggregateResults$estimate_method)) +
theme(text = element_text(size = 15), legend.position = c(0.3, 0.85),
axis.text=element_text(size=16),
legend.text = element_text(colour="black", size=12, face="bold"),
legend.title = element_text(colour="black", size=14, face="bold"))
# + scale_fill_discrete(
# name="Country Overall Ranking",
# breaks=c("predLASSO_spacetime", "predLASSO_lim", "predLASSO_nil", "predLASSO_swapped", "observed"),
# labels=c(sprintf("predLASSO_spacetime LASSO Predicted (386), cor=%.02f", cor(predLASSO, Y)),
# sprintf("predLASSO_lim LASSO Predicted (378), cor=%.02f", cor(predLASSO_lim, Y)),
# sprintf("predLASSO_nil (spacekime) LASSO Predicted, cor=%.02f", cor(predLASSO_kime, Y)),
# sprintf("predLASSO_swapped (spacekime) LASSO Predicted, cor=%.02f", cor(predLASSO_kime_swapped, Y)),
# "observed"))12.3.2 Core redesign
Generic Functions
# Plotting the coefficients
coef_plot <- function(betahat, varn, plotname) {
betahat<-betahat[-1]
P <- coefplot(betahat[which(betahat!=0)], sd = rep(0, length(betahat[which(betahat!=0)])),
pch=0, cex.pts = 3, col="red", main = plotname, varnames = varn[which(betahat!=0)])
return(P)
}
# Plotting the coefficients for those two methods
findfeatures <- function(lassobeta, ridgebeta=NULL) {
lassobeta<-lassobeta[-1]
feat1 <- which(lassobeta!=0)
features <- feat1
if (!is.null(ridgebeta)) {
ridgebeta<-ridgebeta[-1]
feat2 <- order(abs(ridgebeta),decreasing = TRUE)[1:10]
features <- union(feat1, feat2)
}
return(features)
}
varImp <- function(object, lambda = NULL, ...) {
## skipping a few lines
beta <- predict(object, s = lambda, type = "coef")
if(is.list(beta)) {
out <- do.call("cbind", lapply(beta, function(x) x[,1]))
out <- as.data.frame(out)
s <- rowSums(out)
out <- out[which(s)!=0,,drop=FALSE]
} else {
out<-data.frame(Overall = beta[,1])
out<-out[which(out!=0),,drop=FALSE]
}
out <- abs(out[rownames(out) != "(Intercept)",,drop = FALSE])
out
}12.3.2.1 Weak-signal Analytics
Using only the 378 ARIMA signatures for the prediction (out of the total of 386 features).
12.3.2.1.1 Space-Time Analytics
# 1. LASSO regression/feature extraction
library(glmnet)
library(arm)
library(knitr)
# subset test data
Y = aggregate_arima_vector_country_ranking_df$OA
X = aggregate_arima_vector_country_ranking_df[ , 1:378]
# remove columns containing NAs
X = X[ , colSums(is.na(X)) == 0]; dim(X) # [1] 31 378## [1] 31 378#### 10-fold cross validation: for the LASSO
library("glmnet")
library(doParallel)
registerDoParallel(6)
set.seed(4321)
cvLASSO_lim = cv.glmnet(data.matrix(X[ , 1:(42*9)]), Y, alpha = 1, parallel=TRUE)
plot(cvLASSO_lim)
mtext("CV LASSO (using only Timeseries data): Number of Nonzero (Active) Coefficients", side=3, line=2.5)
# Identify top predictors and forecast the Y=Overall (OA) Country ranking outcome
predLASSO_lim <- predict(cvLASSO_lim, s = 3, # cvLASSO_lim$lambda.min,
newx = data.matrix(X[ , 1:(42*9)]))
coefList_lim <- coef(cvLASSO_lim, s=3) # 'lambda.min')
coefList_lim <- data.frame(coefList_lim@Dimnames[[1]][coefList_lim@i+1],coefList_lim@x)
names(coefList_lim) <- c('Feature','EffectSize')
arrange(coefList_lim, -abs(EffectSize))[2:10, ]## Feature EffectSize
## 2 Feature_1_ArimaVec_8 -2.3864299
## 3 Feature_19_ArimaVec_8 2.0871310
## 4 Feature_16_ArimaVec_3 2.0465254
## 5 Feature_13_ArimaVec_8 -1.7348553
## 6 Feature_15_ArimaVec_4 -1.4588173
## 7 Feature_22_ArimaVec_4 -1.1068801
## 8 Feature_25_ArimaVec_5 0.9336800
## 9 Feature_35_ArimaVec_4 -0.9276244
## 10 Feature_25_ArimaVec_4 -0.8486434cor(Y, predLASSO_lim[, 1]) # 0.84## [1] 0.8428065################################################################################
varImp(cvLASSO_lim, lambda = cvLASSO_lim$lambda.min)## Overall
## Feature_12_ArimaVec_3 0.147339633
## Feature_15_ArimaVec_4 0.317167525
## Feature_16_ArimaVec_3 1.018568602
## Feature_25_ArimaVec_1 0.001164192#2 Feature_1_ArimaVec_8 -2.3864299
#3 Feature_19_ArimaVec_8 2.0871310
#4 Feature_16_ArimaVec_3 2.0465254
#5 Feature_13_ArimaVec_8 -1.7348553
#6 Feature_15_ArimaVec_4 -1.4588173
#7 Feature_22_ArimaVec_4 -1.1068801
#8 Feature_25_ArimaVec_5 0.9336800
#9 Feature_35_ArimaVec_4 -0.9276244
#10 Feature_25_ArimaVec_4 -0.8486434
#coefList_lim <- coef(cvLASSO_lim, s='lambda.min')
#coefList_lim <- data.frame(coefList_lim@Dimnames[[1]][coefList_lim@i+1], coefList_lim@x)
#names(coefList_lim) <- c('Feature','EffectSize')
#arrange(coefList_lim, -abs(EffectSize))[2:10, ]
#
# 9 ARIMA-derived vector includes:
# (1=ts_avg, 2=forecast_avg, 3=non-seasonal AR, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA,
# 7=period, 8=non-seasonal Diff, 9=seasonal differences)
# [1] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels"
# [2] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
# [3] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Tertiary education (levels 5-8)"
# [4] "Active population by sex, age and educational attainment level, Females, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
# [5] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, All ISCED 2011 levels"
# [6] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
# [7] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Tertiary education (levels 5-8)"
# [8] "Active population by sex, age and educational attainment level, Males, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
# [9] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, All ISCED 2011 levels"
#[10] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
#[11] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Tertiary education (levels 5-8)"
#[12] "Active population by sex, age and educational attainment level, Total, From 15 to 64 years, Upper secondary and post-secondary non-tertiary education (levels 3 and 4)"
#[13] "All ISCED 2011 levels "
# [14] "All ISCED 2011 levels, Females"
# [15] "All ISCED 2011 levels, Males"
# [16] "Capital transfers, payable"
# [17] "Capital transfers, receivable"
# [18] "Compensation of employees, payable"
# [19] "Current taxes on income, wealth, etc., receivable"
#[20] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, All ISCED 2011 levels "
# [21] "Employment by sex, age and educational attainment level, Females, From 15 to 64 years, Less than primary, primary and lower secondary education (levels 0-2)"
# [22] "Other current transfers, payable"
# [23] "Other current transfers, receivable"
# [24] "Property income, payable"
# [25] "Property income, receivable"
# [26] "Savings, gross"
# [27] "Subsidies, payable"
# [28] "Taxes on production and imports, receivable"
# [29] "Total general government expenditure"
# [30] "Total general government revenue"
# [31] "Unemployment , Females, From 15-64 years, Total"
# [32] "Unemployment , Males, From 15-64 years"
# [33] "Unemployment , Males, From 15-64 years, from 1 to 2 months"
# [34] "Unemployment , Males, From 15-64 years, from 3 to 5 months"
# [35] "Unemployment , Males, From 15-64 years, from 6 to 11 months"
# [36] "Unemployment , Total, From 15-64 years, From 1 to 2 months"
# [37] "Unemployment , Total, From 15-64 years, From 12 to 17 months"
# [38] "Unemployment , Total, From 15-64 years, From 3 to 5 months"
# [39] "Unemployment , Total, From 15-64 years, From 6 to 11 months"
# [40] "Unemployment , Total, From 15-64 years, Less than 1 month"
# [41] "Unemployment by sex, age, duration. DurationNA not started"
# [42] "VAT, receivable"
coef(cvLASSO_lim, s = 3) %>% # "lambda.min"
broom::tidy() %>%
filter(row != "(Intercept)") %>%
top_n(100, wt = abs(value)) %>%
ggplot(aes(value, reorder(row, value), color = value > 0)) +
geom_point(show.legend = FALSE, aes(size = abs(value))) +
ggtitle("Top 9 salient features (LASSO penalty)") +
xlab("Effect-size") +
ylab(NULL)
validation_lim <- data.frame(matrix(NA, nrow = dim(predLASSO_lim)[1], ncol=2), row.names=countryNames)
validation_lim [ , 1] <- Y; validation_lim[ , 2] <- predLASSO_lim[, 1]
colnames(validation_lim) <- c("Orig_Y", "LASSO")
dim(validation_lim); head(validation_lim)## [1] 31 2## Orig_Y LASSO
## Austria 18 20.21660
## Belgium 19 24.57457
## Bulgaria 38 27.42736
## Croatia 28 25.84568
## Cyprus 50 27.80166
## Czech Republic 25 24.17704# add Top_30_Ranking_Indicator
validation_lim <- as.data.frame(cbind(validation_lim, ifelse (validation_lim[, 1]<=30, 1, 0)))
colnames(validation_lim)[3] <- "Top30Rank"
head(validation_lim)## Orig_Y LASSO Top30Rank
## Austria 18 20.21660 1
## Belgium 19 24.57457 1
## Bulgaria 38 27.42736 0
## Croatia 28 25.84568 1
## Cyprus 50 27.80166 0
## Czech Republic 25 24.17704 1# Prediction correlations:
cor(validation_lim[ , 1], validation_lim[, 2]) # Y=observed OA rank vs. LASSO-pred 0.98 (lim) 0.84## [1] 0.8428065# Plot observed Y (Overall Country ranking) vs. LASSO (9-parameters) predicted Y^
linFit_lim <- lm(validation_lim[ , 1] ~ validation_lim[, 2])
plot(validation_lim[ , 1] ~ validation_lim[, 2],
col="blue", xaxt='n', yaxt='n', pch = 16, cex=3,
xlab="Observed Country Overall Ranking", ylab="LASSO (42*9 +8) param model",
main = sprintf("Observed (X) vs. LASSO-Predicted (Y) Overall Country Ranking, cor=%.02f",
cor(validation_lim[ , 1], validation_lim[, 2])))
abline(linFit_lim, lwd=3, col="red")
# Plot
myPlot <- ggplot(as.data.frame(validation_lim), aes(x=validation_lim[ , 1],
y=validation_lim[ , 2], label=rownames(validation_lim))) +
geom_smooth(method='lm') +
geom_point() +
# Color by groups
# geom_text(aes(color=factor(rownames(validation_lim)))) +
geom_label_repel(aes(label = rownames(validation_lim),
fill = factor(Top30Rank)), color = 'black', size = 5,
point.padding = unit(0.3, "lines")) +
# theme(legend.position = "bottom") +
theme(legend.position = c(0.1, 0.9),
legend.text = element_text(colour="black", size=12, face="bold"),
legend.title = element_text(colour="black", size=14, face="bold")) +
scale_fill_discrete(name = "Country Overall Ranking",
labels = c("Below 30 Rank", "Top 30 Rank")) +
labs(title=sprintf("Spacetime LASSO Predicted (y) vs. Observed (x) Overall Country Ranking, cor=%.02f", cor(validation_lim[ , 1], validation_lim[, 2])),
x ="Observed Overall Country Ranking (1 is 'best')",
y = "Spacetime LASSO Predicted")
myPlot
12.3.2.1.2 Space-Kime Analytics
Nil-Phase Synthesis and LASSO model estimation …
# Generic function to Transform Data ={all predictors (X) and outcome (Y)} to k-space (Fourier domain): kSpaceTransform(data, inverse = FALSE, reconPhases = NULL)
# ForwardFT (rawData, FALSE, NULL)
# InverseFT(magnitudes, TRUE, reconPhasesToUse) or InverseFT(FT_data, TRUE, NULL)
# DATA
# subset test data
aggregate_arima_vector_country_ranking_df <- as.data.frame(apply(
aggregate_arima_vector_country_ranking_df[ , colSums(is.na(aggregate_arima_vector_country_ranking_df)) == 0],
2, as.numeric))
Y = aggregate_arima_vector_country_ranking_df$OA
X = aggregate_arima_vector_country_ranking_df[ , 1:378]
# remove columns containing NAs
# X = X[ , colSums(is.na(X)) == 0]; dim(X) # [1] 31 386
length(Y); dim(X)## [1] 31## [1] 31 378FT_aggregate_arima_vector_country_ranking_df <-
kSpaceTransform(aggregate_arima_vector_country_ranking_df, inverse = FALSE, reconPhases = NULL)
## Kime-Phase Distributions
# Examine the Kime-direction Distributions of the Phases for all *Belgium* features (predictors + outcome). Define a generic function that plots the Phase distributions.
# plotPhaseDistributions(dataFT, dataColnames)
plotPhaseDistributions(FT_aggregate_arima_vector_country_ranking_df,
colnames(aggregate_arima_vector_country_ranking_df), size=4, cex=0.1)
IFT_FT_aggregate_arima_vector_country_ranking_df <-
kSpaceTransform(FT_aggregate_arima_vector_country_ranking_df$magnitudes,
TRUE, FT_aggregate_arima_vector_country_ranking_df$phases)
# Check IFT(FT) == I:
# ifelse(aggregate_arima_vector_country_ranking_df[5,4] -
# Re(IFT_FT_aggregate_arima_vector_country_ranking_df[5,4]) < 0.001, "Perfect Synthesis", "Problems!!!")
##############################################
# Nil-Phase Synthesis and LASSO model estimation
# 1. Nil-Phase data synthesis (reconstruction)
temp_Data <- aggregate_arima_vector_country_ranking_df
nilPhase_FT_aggregate_arima_vector <-
array(complex(real=0, imaginary=0), c(dim(temp_Data)[1], dim(temp_Data)[2]))
dim(nilPhase_FT_aggregate_arima_vector) # ; head(nilPhase_FT_aggregate_arima_vector)## [1] 31 387# [1] 31 387
IFT_NilPhase_FT_aggregate_arima_vector <- array(complex(), c(dim(temp_Data)[1], dim(temp_Data)[2]))
# Invert back to spacetime the
# FT_aggregate_arima_vector_country_ranking_df$magnitudes[ , i] signal with nil-phase
IFT_NilPhase_FT_aggregate_arima_vector <-
Re(kSpaceTransform(FT_aggregate_arima_vector_country_ranking_df$magnitudes,
TRUE, nilPhase_FT_aggregate_arima_vector))
colnames(IFT_NilPhase_FT_aggregate_arima_vector) <-
colnames(aggregate_arima_vector_country_ranking_df)
rownames(IFT_NilPhase_FT_aggregate_arima_vector) <-
rownames(aggregate_arima_vector_country_ranking_df)
dim(IFT_NilPhase_FT_aggregate_arima_vector)## [1] 31 387dim(FT_aggregate_arima_vector_country_ranking_df$magnitudes)## [1] 31 387colnames(IFT_NilPhase_FT_aggregate_arima_vector)## [1] "Feature_1_ArimaVec_1" "Feature_1_ArimaVec_2" "Feature_1_ArimaVec_3"
## [4] "Feature_1_ArimaVec_4" "Feature_1_ArimaVec_5" "Feature_1_ArimaVec_6"
## [7] "Feature_1_ArimaVec_7" "Feature_1_ArimaVec_8" "Feature_1_ArimaVec_9"
## [10] "Feature_2_ArimaVec_1" "Feature_2_ArimaVec_2" "Feature_2_ArimaVec_3"
## [13] "Feature_2_ArimaVec_4" "Feature_2_ArimaVec_5" "Feature_2_ArimaVec_6"
## [16] "Feature_2_ArimaVec_7" "Feature_2_ArimaVec_8" "Feature_2_ArimaVec_9"
## [19] "Feature_3_ArimaVec_1" "Feature_3_ArimaVec_2" "Feature_3_ArimaVec_3"
## [22] "Feature_3_ArimaVec_4" "Feature_3_ArimaVec_5" "Feature_3_ArimaVec_6"
## [25] "Feature_3_ArimaVec_7" "Feature_3_ArimaVec_8" "Feature_3_ArimaVec_9"
## [28] "Feature_4_ArimaVec_1" "Feature_4_ArimaVec_2" "Feature_4_ArimaVec_3"
## [31] "Feature_4_ArimaVec_4" "Feature_4_ArimaVec_5" "Feature_4_ArimaVec_6"
## [34] "Feature_4_ArimaVec_7" "Feature_4_ArimaVec_8" "Feature_4_ArimaVec_9"
## [37] "Feature_5_ArimaVec_1" "Feature_5_ArimaVec_2" "Feature_5_ArimaVec_3"
## [40] "Feature_5_ArimaVec_4" "Feature_5_ArimaVec_5" "Feature_5_ArimaVec_6"
## [43] "Feature_5_ArimaVec_7" "Feature_5_ArimaVec_8" "Feature_5_ArimaVec_9"
## [46] "Feature_6_ArimaVec_1" "Feature_6_ArimaVec_2" "Feature_6_ArimaVec_3"
## [49] "Feature_6_ArimaVec_4" "Feature_6_ArimaVec_5" "Feature_6_ArimaVec_6"
## [52] "Feature_6_ArimaVec_7" "Feature_6_ArimaVec_8" "Feature_6_ArimaVec_9"
## [55] "Feature_7_ArimaVec_1" "Feature_7_ArimaVec_2" "Feature_7_ArimaVec_3"
## [58] "Feature_7_ArimaVec_4" "Feature_7_ArimaVec_5" "Feature_7_ArimaVec_6"
## [61] "Feature_7_ArimaVec_7" "Feature_7_ArimaVec_8" "Feature_7_ArimaVec_9"
## [64] "Feature_8_ArimaVec_1" "Feature_8_ArimaVec_2" "Feature_8_ArimaVec_3"
## [67] "Feature_8_ArimaVec_4" "Feature_8_ArimaVec_5" "Feature_8_ArimaVec_6"
## [70] "Feature_8_ArimaVec_7" "Feature_8_ArimaVec_8" "Feature_8_ArimaVec_9"
## [73] "Feature_9_ArimaVec_1" "Feature_9_ArimaVec_2" "Feature_9_ArimaVec_3"
## [76] "Feature_9_ArimaVec_4" "Feature_9_ArimaVec_5" "Feature_9_ArimaVec_6"
## [79] "Feature_9_ArimaVec_7" "Feature_9_ArimaVec_8" "Feature_9_ArimaVec_9"
## [82] "Feature_10_ArimaVec_1" "Feature_10_ArimaVec_2" "Feature_10_ArimaVec_3"
## [85] "Feature_10_ArimaVec_4" "Feature_10_ArimaVec_5" "Feature_10_ArimaVec_6"
## [88] "Feature_10_ArimaVec_7" "Feature_10_ArimaVec_8" "Feature_10_ArimaVec_9"
## [91] "Feature_11_ArimaVec_1" "Feature_11_ArimaVec_2" "Feature_11_ArimaVec_3"
## [94] "Feature_11_ArimaVec_4" "Feature_11_ArimaVec_5" "Feature_11_ArimaVec_6"
## [97] "Feature_11_ArimaVec_7" "Feature_11_ArimaVec_8" "Feature_11_ArimaVec_9"
## [100] "Feature_12_ArimaVec_1" "Feature_12_ArimaVec_2" "Feature_12_ArimaVec_3"
## [103] "Feature_12_ArimaVec_4" "Feature_12_ArimaVec_5" "Feature_12_ArimaVec_6"
## [106] "Feature_12_ArimaVec_7" "Feature_12_ArimaVec_8" "Feature_12_ArimaVec_9"
## [109] "Feature_13_ArimaVec_1" "Feature_13_ArimaVec_2" "Feature_13_ArimaVec_3"
## [112] "Feature_13_ArimaVec_4" "Feature_13_ArimaVec_5" "Feature_13_ArimaVec_6"
## [115] "Feature_13_ArimaVec_7" "Feature_13_ArimaVec_8" "Feature_13_ArimaVec_9"
## [118] "Feature_14_ArimaVec_1" "Feature_14_ArimaVec_2" "Feature_14_ArimaVec_3"
## [121] "Feature_14_ArimaVec_4" "Feature_14_ArimaVec_5" "Feature_14_ArimaVec_6"
## [124] "Feature_14_ArimaVec_7" "Feature_14_ArimaVec_8" "Feature_14_ArimaVec_9"
## [127] "Feature_15_ArimaVec_1" "Feature_15_ArimaVec_2" "Feature_15_ArimaVec_3"
## [130] "Feature_15_ArimaVec_4" "Feature_15_ArimaVec_5" "Feature_15_ArimaVec_6"
## [133] "Feature_15_ArimaVec_7" "Feature_15_ArimaVec_8" "Feature_15_ArimaVec_9"
## [136] "Feature_16_ArimaVec_1" "Feature_16_ArimaVec_2" "Feature_16_ArimaVec_3"
## [139] "Feature_16_ArimaVec_4" "Feature_16_ArimaVec_5" "Feature_16_ArimaVec_6"
## [142] "Feature_16_ArimaVec_7" "Feature_16_ArimaVec_8" "Feature_16_ArimaVec_9"
## [145] "Feature_17_ArimaVec_1" "Feature_17_ArimaVec_2" "Feature_17_ArimaVec_3"
## [148] "Feature_17_ArimaVec_4" "Feature_17_ArimaVec_5" "Feature_17_ArimaVec_6"
## [151] "Feature_17_ArimaVec_7" "Feature_17_ArimaVec_8" "Feature_17_ArimaVec_9"
## [154] "Feature_18_ArimaVec_1" "Feature_18_ArimaVec_2" "Feature_18_ArimaVec_3"
## [157] "Feature_18_ArimaVec_4" "Feature_18_ArimaVec_5" "Feature_18_ArimaVec_6"
## [160] "Feature_18_ArimaVec_7" "Feature_18_ArimaVec_8" "Feature_18_ArimaVec_9"
## [163] "Feature_19_ArimaVec_1" "Feature_19_ArimaVec_2" "Feature_19_ArimaVec_3"
## [166] "Feature_19_ArimaVec_4" "Feature_19_ArimaVec_5" "Feature_19_ArimaVec_6"
## [169] "Feature_19_ArimaVec_7" "Feature_19_ArimaVec_8" "Feature_19_ArimaVec_9"
## [172] "Feature_20_ArimaVec_1" "Feature_20_ArimaVec_2" "Feature_20_ArimaVec_3"
## [175] "Feature_20_ArimaVec_4" "Feature_20_ArimaVec_5" "Feature_20_ArimaVec_6"
## [178] "Feature_20_ArimaVec_7" "Feature_20_ArimaVec_8" "Feature_20_ArimaVec_9"
## [181] "Feature_21_ArimaVec_1" "Feature_21_ArimaVec_2" "Feature_21_ArimaVec_3"
## [184] "Feature_21_ArimaVec_4" "Feature_21_ArimaVec_5" "Feature_21_ArimaVec_6"
## [187] "Feature_21_ArimaVec_7" "Feature_21_ArimaVec_8" "Feature_21_ArimaVec_9"
## [190] "Feature_22_ArimaVec_1" "Feature_22_ArimaVec_2" "Feature_22_ArimaVec_3"
## [193] "Feature_22_ArimaVec_4" "Feature_22_ArimaVec_5" "Feature_22_ArimaVec_6"
## [196] "Feature_22_ArimaVec_7" "Feature_22_ArimaVec_8" "Feature_22_ArimaVec_9"
## [199] "Feature_23_ArimaVec_1" "Feature_23_ArimaVec_2" "Feature_23_ArimaVec_3"
## [202] "Feature_23_ArimaVec_4" "Feature_23_ArimaVec_5" "Feature_23_ArimaVec_6"
## [205] "Feature_23_ArimaVec_7" "Feature_23_ArimaVec_8" "Feature_23_ArimaVec_9"
## [208] "Feature_24_ArimaVec_1" "Feature_24_ArimaVec_2" "Feature_24_ArimaVec_3"
## [211] "Feature_24_ArimaVec_4" "Feature_24_ArimaVec_5" "Feature_24_ArimaVec_6"
## [214] "Feature_24_ArimaVec_7" "Feature_24_ArimaVec_8" "Feature_24_ArimaVec_9"
## [217] "Feature_25_ArimaVec_1" "Feature_25_ArimaVec_2" "Feature_25_ArimaVec_3"
## [220] "Feature_25_ArimaVec_4" "Feature_25_ArimaVec_5" "Feature_25_ArimaVec_6"
## [223] "Feature_25_ArimaVec_7" "Feature_25_ArimaVec_8" "Feature_25_ArimaVec_9"
## [226] "Feature_26_ArimaVec_1" "Feature_26_ArimaVec_2" "Feature_26_ArimaVec_3"
## [229] "Feature_26_ArimaVec_4" "Feature_26_ArimaVec_5" "Feature_26_ArimaVec_6"
## [232] "Feature_26_ArimaVec_7" "Feature_26_ArimaVec_8" "Feature_26_ArimaVec_9"
## [235] "Feature_27_ArimaVec_1" "Feature_27_ArimaVec_2" "Feature_27_ArimaVec_3"
## [238] "Feature_27_ArimaVec_4" "Feature_27_ArimaVec_5" "Feature_27_ArimaVec_6"
## [241] "Feature_27_ArimaVec_7" "Feature_27_ArimaVec_8" "Feature_27_ArimaVec_9"
## [244] "Feature_28_ArimaVec_1" "Feature_28_ArimaVec_2" "Feature_28_ArimaVec_3"
## [247] "Feature_28_ArimaVec_4" "Feature_28_ArimaVec_5" "Feature_28_ArimaVec_6"
## [250] "Feature_28_ArimaVec_7" "Feature_28_ArimaVec_8" "Feature_28_ArimaVec_9"
## [253] "Feature_29_ArimaVec_1" "Feature_29_ArimaVec_2" "Feature_29_ArimaVec_3"
## [256] "Feature_29_ArimaVec_4" "Feature_29_ArimaVec_5" "Feature_29_ArimaVec_6"
## [259] "Feature_29_ArimaVec_7" "Feature_29_ArimaVec_8" "Feature_29_ArimaVec_9"
## [262] "Feature_30_ArimaVec_1" "Feature_30_ArimaVec_2" "Feature_30_ArimaVec_3"
## [265] "Feature_30_ArimaVec_4" "Feature_30_ArimaVec_5" "Feature_30_ArimaVec_6"
## [268] "Feature_30_ArimaVec_7" "Feature_30_ArimaVec_8" "Feature_30_ArimaVec_9"
## [271] "Feature_31_ArimaVec_1" "Feature_31_ArimaVec_2" "Feature_31_ArimaVec_3"
## [274] "Feature_31_ArimaVec_4" "Feature_31_ArimaVec_5" "Feature_31_ArimaVec_6"
## [277] "Feature_31_ArimaVec_7" "Feature_31_ArimaVec_8" "Feature_31_ArimaVec_9"
## [280] "Feature_32_ArimaVec_1" "Feature_32_ArimaVec_2" "Feature_32_ArimaVec_3"
## [283] "Feature_32_ArimaVec_4" "Feature_32_ArimaVec_5" "Feature_32_ArimaVec_6"
## [286] "Feature_32_ArimaVec_7" "Feature_32_ArimaVec_8" "Feature_32_ArimaVec_9"
## [289] "Feature_33_ArimaVec_1" "Feature_33_ArimaVec_2" "Feature_33_ArimaVec_3"
## [292] "Feature_33_ArimaVec_4" "Feature_33_ArimaVec_5" "Feature_33_ArimaVec_6"
## [295] "Feature_33_ArimaVec_7" "Feature_33_ArimaVec_8" "Feature_33_ArimaVec_9"
## [298] "Feature_34_ArimaVec_1" "Feature_34_ArimaVec_2" "Feature_34_ArimaVec_3"
## [301] "Feature_34_ArimaVec_4" "Feature_34_ArimaVec_5" "Feature_34_ArimaVec_6"
## [304] "Feature_34_ArimaVec_7" "Feature_34_ArimaVec_8" "Feature_34_ArimaVec_9"
## [307] "Feature_35_ArimaVec_1" "Feature_35_ArimaVec_2" "Feature_35_ArimaVec_3"
## [310] "Feature_35_ArimaVec_4" "Feature_35_ArimaVec_5" "Feature_35_ArimaVec_6"
## [313] "Feature_35_ArimaVec_7" "Feature_35_ArimaVec_8" "Feature_35_ArimaVec_9"
## [316] "Feature_36_ArimaVec_1" "Feature_36_ArimaVec_2" "Feature_36_ArimaVec_3"
## [319] "Feature_36_ArimaVec_4" "Feature_36_ArimaVec_5" "Feature_36_ArimaVec_6"
## [322] "Feature_36_ArimaVec_7" "Feature_36_ArimaVec_8" "Feature_36_ArimaVec_9"
## [325] "Feature_37_ArimaVec_1" "Feature_37_ArimaVec_2" "Feature_37_ArimaVec_3"
## [328] "Feature_37_ArimaVec_4" "Feature_37_ArimaVec_5" "Feature_37_ArimaVec_6"
## [331] "Feature_37_ArimaVec_7" "Feature_37_ArimaVec_8" "Feature_37_ArimaVec_9"
## [334] "Feature_38_ArimaVec_1" "Feature_38_ArimaVec_2" "Feature_38_ArimaVec_3"
## [337] "Feature_38_ArimaVec_4" "Feature_38_ArimaVec_5" "Feature_38_ArimaVec_6"
## [340] "Feature_38_ArimaVec_7" "Feature_38_ArimaVec_8" "Feature_38_ArimaVec_9"
## [343] "Feature_39_ArimaVec_1" "Feature_39_ArimaVec_2" "Feature_39_ArimaVec_3"
## [346] "Feature_39_ArimaVec_4" "Feature_39_ArimaVec_5" "Feature_39_ArimaVec_6"
## [349] "Feature_39_ArimaVec_7" "Feature_39_ArimaVec_8" "Feature_39_ArimaVec_9"
## [352] "Feature_40_ArimaVec_1" "Feature_40_ArimaVec_2" "Feature_40_ArimaVec_3"
## [355] "Feature_40_ArimaVec_4" "Feature_40_ArimaVec_5" "Feature_40_ArimaVec_6"
## [358] "Feature_40_ArimaVec_7" "Feature_40_ArimaVec_8" "Feature_40_ArimaVec_9"
## [361] "Feature_41_ArimaVec_1" "Feature_41_ArimaVec_2" "Feature_41_ArimaVec_3"
## [364] "Feature_41_ArimaVec_4" "Feature_41_ArimaVec_5" "Feature_41_ArimaVec_6"
## [367] "Feature_41_ArimaVec_7" "Feature_41_ArimaVec_8" "Feature_41_ArimaVec_9"
## [370] "Feature_42_ArimaVec_1" "Feature_42_ArimaVec_2" "Feature_42_ArimaVec_3"
## [373] "Feature_42_ArimaVec_4" "Feature_42_ArimaVec_5" "Feature_42_ArimaVec_6"
## [376] "Feature_42_ArimaVec_7" "Feature_42_ArimaVec_8" "Feature_42_ArimaVec_9"
## [379] "IncomeGroup" "PopSizeGroup" "ED"
## [382] "Edu" "HI" "QOL"
## [385] "PE" "Relig" "OA"# IFT_NilPhase_FT_aggregate_arima_vector[1:5, 1:4]; temp_Data[1:5, 1:4]
# 2. Perform LASSO modeling on IFT_NilPhase_FT_aggregate_arima_vector;
# report param estimates and quality metrics AIC/BIC
# library(forecast)
set.seed(123)
cvLASSO_nil_kime = cv.glmnet(data.matrix(IFT_NilPhase_FT_aggregate_arima_vector[ , 1:378]),
# IFT_NilPhase_FT_aggregate_arima_vector[ , 387], alpha = 1, parallel=TRUE)
Y, alpha = 1, parallel=TRUE)
plot(cvLASSO_nil_kime)
mtext("(Spacekime, Nil-phase) CV LASSO: Number of Nonzero (Active) Coefficients", side=3, line=2.5)
# Identify top predictors and forecast the Y=Overall (OA) Country ranking outcome
predLASSO_nil_kime <- predict(cvLASSO_nil_kime, s = cvLASSO_nil_kime$lambda.min,
newx = data.matrix(IFT_NilPhase_FT_aggregate_arima_vector[ , 1:378])); predLASSO_nil_kime## s1
## 1 17.96229
## 2 20.91197
## 3 21.16400
## 4 21.41214
## 5 30.72476
## 6 24.16388
## 7 19.64671
## 8 29.77555
## 9 18.63838
## 10 22.28967
## 11 11.75271
## 12 20.20818
## 13 33.17333
## 14 23.78775
## 15 23.15300
## 16 28.71681
## 17 28.71681
## 18 23.15300
## 19 23.78775
## 20 33.17333
## 21 20.20818
## 22 11.75271
## 23 22.28967
## 24 18.63838
## 25 29.77555
## 26 19.64671
## 27 24.16388
## 28 30.72476
## 29 21.41214
## 30 21.16400
## 31 20.91197# testMSE_LASSO_nil_kime <- mean((predLASSO_nil_kime - IFT_NilPhase_FT_aggregate_arima_vector[ , 387])^2)
# testMSE_LASSO_nil_kime
# Plot Regression Coefficients: create variable names for plotting
library("arm")
# par(mar=c(2, 13, 1, 1)) # extra large left margin # par(mar=c(5,5,5,5))
# varNames <- colnames(X); varNames; length(varNames)
#betaHatLASSO_kime = as.double(coef(cvLASSO_kime, s=cvLASSO_kime$lambda.min))
#cvLASSO_kime$lambda.1se
#
#coefplot(betaHatLASSO_kime[377:386], sd = rep(0, 10), pch=0, cex.pts = 3, col="red",
# main = "(Spacekime) LASSO-Regularized Regression Coefficient Estimates",
# varnames = varNames[377:386])
varImp(cvLASSO_nil_kime, lambda = cvLASSO_nil_kime$lambda.min)## Overall
## Feature_11_ArimaVec_4 8.561417371
## Feature_12_ArimaVec_4 5.220797419
## Feature_12_ArimaVec_8 9.312528503
## Feature_26_ArimaVec_6 1.927773216
## Feature_30_ArimaVec_4 2.623218796
## Feature_34_ArimaVec_5 1.171720009
## Feature_37_ArimaVec_2 0.004213823
## Feature_39_ArimaVec_5 1.534741405coefList_nil_kime <- coef(cvLASSO_nil_kime, s='lambda.min')
coefList_nil_kime <- data.frame(coefList_nil_kime@Dimnames[[1]][coefList_nil_kime@i+1], coefList_nil_kime@x)
names(coefList_nil_kime) <- c('Feature','EffectSize')
arrange(coefList_nil_kime, -abs(EffectSize))[1:9, ]## Feature EffectSize
## 1 (Intercept) 26.385520163
## 2 Feature_12_ArimaVec_8 -9.312528503
## 3 Feature_11_ArimaVec_4 8.561417371
## 4 Feature_12_ArimaVec_4 -5.220797419
## 5 Feature_30_ArimaVec_4 2.623218796
## 6 Feature_26_ArimaVec_6 1.927773216
## 7 Feature_39_ArimaVec_5 -1.534741405
## 8 Feature_34_ArimaVec_5 -1.171720009
## 9 Feature_37_ArimaVec_2 0.004213823# Feature EffectSize
#1 (Intercept) 26.385520159
#2 Feature_12_ArimaVec_8 -9.312528495
#3 Feature_11_ArimaVec_4 8.561417371
#4 Feature_12_ArimaVec_4 -5.220797416
#5 Feature_30_ArimaVec_4 2.623218791
#6 Feature_26_ArimaVec_6 1.927773213
#7 Feature_39_ArimaVec_5 -1.534741402
#8 Feature_34_ArimaVec_5 -1.171720008
#9 Feature_37_ArimaVec_2 0.004213823
# ARIMA-spacetime: 4=non-seasonal MA, 5=seasonal AR, 8=non-seasonal Diff
# ARIMA-spacekimeNil: 2=forecast_avg, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA, 8=non-seasonal Diff
#9 ARIMA-derived vector includes:
# (1=ts_avg, 2=forecast_avg, 3=non-seasonal AR, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA,
# 7=period, 8=non-seasonal Diff, 9=seasonal differences)
coef(cvLASSO_nil_kime, s = "lambda.min") %>%
broom::tidy() %>%
filter(row != "(Intercept)") %>%
top_n(100, wt = abs(value)) %>%
ggplot(aes(value, reorder(row, value), color = value > 0)) +
geom_point(show.legend = FALSE, aes(size = abs(value))) +
ggtitle("(Spacekime) Top 9 salient features (LASSO penalty)") +
xlab("Effect-size") +
ylab(NULL)
# pack a 31*3 DF with (predLASSO_kime, IFT_NilPhase_FT_aggregate_arima_vector_Y, Y)
validation_nil_kime <- cbind(predLASSO_nil_kime[, 1],
IFT_NilPhase_FT_aggregate_arima_vector[ , 387], Y)
colnames(validation_nil_kime) <- c("predLASSO_kime", "IFT_NilPhase_FT_Y", "Orig_Y")
rownames(validation_nil_kime)[11] <- "Germany"
head(validation_nil_kime)## predLASSO_kime IFT_NilPhase_FT_Y Orig_Y
## 1 17.96229 87.771967 18
## 2 20.91197 19.640349 19
## 3 21.16400 24.453327 38
## 4 21.41214 24.267994 28
## 5 30.72476 8.137025 50
## 6 24.16388 11.737091 25validation_nil_kime <- as.data.frame(cbind(validation_nil_kime, ifelse (validation_nil_kime[,3]<=30, 1, 0)))
colnames(validation_nil_kime)[4] <- "Top30Rank"
head(validation_nil_kime)## predLASSO_kime IFT_NilPhase_FT_Y Orig_Y Top30Rank
## 1 17.96229 87.771967 18 1
## 2 20.91197 19.640349 19 1
## 3 21.16400 24.453327 38 0
## 4 21.41214 24.267994 28 1
## 5 30.72476 8.137025 50 0
## 6 24.16388 11.737091 25 1# Prediction correlations:
# cor(validation_nil_kime[ , 1], validation_nil_kime[, 2]) # Y=predLASSO_kime OA rank vs. kime_LASSO_pred: 0.99
cor(validation_nil_kime[ , 1], validation_nil_kime[, 3]) # Y=predLASSO_kime OA rank vs. Orig_Y: 0.64## [1] 0.6430442# Plot observed Y (Overall Country ranking) vs. LASSO (9-parameters) predicted Y^
linFit1_nil_kime <- lm(predLASSO_nil_kime ~ validation_nil_kime[ , 3])
plot(predLASSO_nil_kime ~ validation_nil_kime[ , 3],
col="blue", xaxt='n', yaxt='n', pch = 16, cex=3,
xlab="Observed Country Overall Ranking", ylab="IFT_NilPhase predLASSO_kime",
main = sprintf("Observed (x) vs. IFT_NilPhase Predicted (y) Overall Country Ranking, cor=%.02f",
cor(validation_nil_kime[ , 1], validation_nil_kime[, 3])))
abline(linFit1_kime, lwd=3, col="red")
# abline(linFit1, lwd=3, col="green")
# Spacetime LASSO modeling
myPlotNilPhase <- ggplot(as.data.frame(validation_nil_kime), aes(x=Orig_Y,
y=predLASSO_nil_kime, label=rownames(validation_nil_kime))) +
geom_smooth(method='lm') +
geom_point() +
# Color by groups
# geom_text(aes(color=factor(rownames(validation_nil_kime)))) +
geom_label_repel(aes(label = rownames(validation_nil_kime),
fill = factor(Top30Rank)), color = 'black', size = 5,
point.padding = unit(0.3, "lines")) +
# theme(legend.position = "bottom") +
theme(legend.position = c(0.1, 0.9),
legend.text = element_text(colour="black", size=12, face="bold"),
legend.title = element_text(colour="black", size=14, face="bold")) +
scale_fill_discrete(name = "Country Overall Ranking",
labels = c("Below 30 Rank", "Top 30 Rank")) +
labs(title=sprintf("Spacekime LASSO Predicted, Nil-Phases (y) vs. Observed (x) Overall Country Ranking, cor=%.02f", cor(validation_nil_kime[ , 1], validation_nil_kime[, 3])),
x ="Observed Overall Country Ranking (1 is 'best')",
y = "Spacekime LASSO Predicted, using Nil-Phases")
myPlotNilPhase
Swapped Feature Phases and then synthesize the data (reconstruction)
# temp_Data <- aggregate_arima_vector_country_ranking_df
swappedPhase_FT_aggregate_arima_vector <- FT_aggregate_arima_vector_country_ranking_df$phases
dim(swappedPhase_FT_aggregate_arima_vector) # ; head(swappedPhase_FT_aggregate_arima_vector)## [1] 31 387# [1] 31 387
IFT_SwappedPhase_FT_aggregate_arima_vector <- array(complex(), c(dim(temp_Data)[1], dim(temp_Data)[2]))
set.seed(12345) # sample randomly Phase-columns for each of the 131 covariates (X)
swappedPhase_FT_aggregate_arima_vector1 <- as.data.frame(cbind(
swappedPhase_FT_aggregate_arima_vector[ ,
sample(ncol(swappedPhase_FT_aggregate_arima_vector[ , 1:378]))], # mix ARIMA signature phases
swappedPhase_FT_aggregate_arima_vector[ ,
sample(ncol(swappedPhase_FT_aggregate_arima_vector[ , 379:386]))],# mix the meta-data phases
swappedPhase_FT_aggregate_arima_vector[ , 387])) # add correct Outcome phase
swappedPhase_FT_aggregate_arima_vector <- swappedPhase_FT_aggregate_arima_vector1
colnames(swappedPhase_FT_aggregate_arima_vector) <- colnames(temp_Data)
colnames(swappedPhase_FT_aggregate_arima_vector); dim(swappedPhase_FT_aggregate_arima_vector)## [1] "Feature_1_ArimaVec_1" "Feature_1_ArimaVec_2" "Feature_1_ArimaVec_3"
## [4] "Feature_1_ArimaVec_4" "Feature_1_ArimaVec_5" "Feature_1_ArimaVec_6"
## [7] "Feature_1_ArimaVec_7" "Feature_1_ArimaVec_8" "Feature_1_ArimaVec_9"
## [10] "Feature_2_ArimaVec_1" "Feature_2_ArimaVec_2" "Feature_2_ArimaVec_3"
## [13] "Feature_2_ArimaVec_4" "Feature_2_ArimaVec_5" "Feature_2_ArimaVec_6"
## [16] "Feature_2_ArimaVec_7" "Feature_2_ArimaVec_8" "Feature_2_ArimaVec_9"
## [19] "Feature_3_ArimaVec_1" "Feature_3_ArimaVec_2" "Feature_3_ArimaVec_3"
## [22] "Feature_3_ArimaVec_4" "Feature_3_ArimaVec_5" "Feature_3_ArimaVec_6"
## [25] "Feature_3_ArimaVec_7" "Feature_3_ArimaVec_8" "Feature_3_ArimaVec_9"
## [28] "Feature_4_ArimaVec_1" "Feature_4_ArimaVec_2" "Feature_4_ArimaVec_3"
## [31] "Feature_4_ArimaVec_4" "Feature_4_ArimaVec_5" "Feature_4_ArimaVec_6"
## [34] "Feature_4_ArimaVec_7" "Feature_4_ArimaVec_8" "Feature_4_ArimaVec_9"
## [37] "Feature_5_ArimaVec_1" "Feature_5_ArimaVec_2" "Feature_5_ArimaVec_3"
## [40] "Feature_5_ArimaVec_4" "Feature_5_ArimaVec_5" "Feature_5_ArimaVec_6"
## [43] "Feature_5_ArimaVec_7" "Feature_5_ArimaVec_8" "Feature_5_ArimaVec_9"
## [46] "Feature_6_ArimaVec_1" "Feature_6_ArimaVec_2" "Feature_6_ArimaVec_3"
## [49] "Feature_6_ArimaVec_4" "Feature_6_ArimaVec_5" "Feature_6_ArimaVec_6"
## [52] "Feature_6_ArimaVec_7" "Feature_6_ArimaVec_8" "Feature_6_ArimaVec_9"
## [55] "Feature_7_ArimaVec_1" "Feature_7_ArimaVec_2" "Feature_7_ArimaVec_3"
## [58] "Feature_7_ArimaVec_4" "Feature_7_ArimaVec_5" "Feature_7_ArimaVec_6"
## [61] "Feature_7_ArimaVec_7" "Feature_7_ArimaVec_8" "Feature_7_ArimaVec_9"
## [64] "Feature_8_ArimaVec_1" "Feature_8_ArimaVec_2" "Feature_8_ArimaVec_3"
## [67] "Feature_8_ArimaVec_4" "Feature_8_ArimaVec_5" "Feature_8_ArimaVec_6"
## [70] "Feature_8_ArimaVec_7" "Feature_8_ArimaVec_8" "Feature_8_ArimaVec_9"
## [73] "Feature_9_ArimaVec_1" "Feature_9_ArimaVec_2" "Feature_9_ArimaVec_3"
## [76] "Feature_9_ArimaVec_4" "Feature_9_ArimaVec_5" "Feature_9_ArimaVec_6"
## [79] "Feature_9_ArimaVec_7" "Feature_9_ArimaVec_8" "Feature_9_ArimaVec_9"
## [82] "Feature_10_ArimaVec_1" "Feature_10_ArimaVec_2" "Feature_10_ArimaVec_3"
## [85] "Feature_10_ArimaVec_4" "Feature_10_ArimaVec_5" "Feature_10_ArimaVec_6"
## [88] "Feature_10_ArimaVec_7" "Feature_10_ArimaVec_8" "Feature_10_ArimaVec_9"
## [91] "Feature_11_ArimaVec_1" "Feature_11_ArimaVec_2" "Feature_11_ArimaVec_3"
## [94] "Feature_11_ArimaVec_4" "Feature_11_ArimaVec_5" "Feature_11_ArimaVec_6"
## [97] "Feature_11_ArimaVec_7" "Feature_11_ArimaVec_8" "Feature_11_ArimaVec_9"
## [100] "Feature_12_ArimaVec_1" "Feature_12_ArimaVec_2" "Feature_12_ArimaVec_3"
## [103] "Feature_12_ArimaVec_4" "Feature_12_ArimaVec_5" "Feature_12_ArimaVec_6"
## [106] "Feature_12_ArimaVec_7" "Feature_12_ArimaVec_8" "Feature_12_ArimaVec_9"
## [109] "Feature_13_ArimaVec_1" "Feature_13_ArimaVec_2" "Feature_13_ArimaVec_3"
## [112] "Feature_13_ArimaVec_4" "Feature_13_ArimaVec_5" "Feature_13_ArimaVec_6"
## [115] "Feature_13_ArimaVec_7" "Feature_13_ArimaVec_8" "Feature_13_ArimaVec_9"
## [118] "Feature_14_ArimaVec_1" "Feature_14_ArimaVec_2" "Feature_14_ArimaVec_3"
## [121] "Feature_14_ArimaVec_4" "Feature_14_ArimaVec_5" "Feature_14_ArimaVec_6"
## [124] "Feature_14_ArimaVec_7" "Feature_14_ArimaVec_8" "Feature_14_ArimaVec_9"
## [127] "Feature_15_ArimaVec_1" "Feature_15_ArimaVec_2" "Feature_15_ArimaVec_3"
## [130] "Feature_15_ArimaVec_4" "Feature_15_ArimaVec_5" "Feature_15_ArimaVec_6"
## [133] "Feature_15_ArimaVec_7" "Feature_15_ArimaVec_8" "Feature_15_ArimaVec_9"
## [136] "Feature_16_ArimaVec_1" "Feature_16_ArimaVec_2" "Feature_16_ArimaVec_3"
## [139] "Feature_16_ArimaVec_4" "Feature_16_ArimaVec_5" "Feature_16_ArimaVec_6"
## [142] "Feature_16_ArimaVec_7" "Feature_16_ArimaVec_8" "Feature_16_ArimaVec_9"
## [145] "Feature_17_ArimaVec_1" "Feature_17_ArimaVec_2" "Feature_17_ArimaVec_3"
## [148] "Feature_17_ArimaVec_4" "Feature_17_ArimaVec_5" "Feature_17_ArimaVec_6"
## [151] "Feature_17_ArimaVec_7" "Feature_17_ArimaVec_8" "Feature_17_ArimaVec_9"
## [154] "Feature_18_ArimaVec_1" "Feature_18_ArimaVec_2" "Feature_18_ArimaVec_3"
## [157] "Feature_18_ArimaVec_4" "Feature_18_ArimaVec_5" "Feature_18_ArimaVec_6"
## [160] "Feature_18_ArimaVec_7" "Feature_18_ArimaVec_8" "Feature_18_ArimaVec_9"
## [163] "Feature_19_ArimaVec_1" "Feature_19_ArimaVec_2" "Feature_19_ArimaVec_3"
## [166] "Feature_19_ArimaVec_4" "Feature_19_ArimaVec_5" "Feature_19_ArimaVec_6"
## [169] "Feature_19_ArimaVec_7" "Feature_19_ArimaVec_8" "Feature_19_ArimaVec_9"
## [172] "Feature_20_ArimaVec_1" "Feature_20_ArimaVec_2" "Feature_20_ArimaVec_3"
## [175] "Feature_20_ArimaVec_4" "Feature_20_ArimaVec_5" "Feature_20_ArimaVec_6"
## [178] "Feature_20_ArimaVec_7" "Feature_20_ArimaVec_8" "Feature_20_ArimaVec_9"
## [181] "Feature_21_ArimaVec_1" "Feature_21_ArimaVec_2" "Feature_21_ArimaVec_3"
## [184] "Feature_21_ArimaVec_4" "Feature_21_ArimaVec_5" "Feature_21_ArimaVec_6"
## [187] "Feature_21_ArimaVec_7" "Feature_21_ArimaVec_8" "Feature_21_ArimaVec_9"
## [190] "Feature_22_ArimaVec_1" "Feature_22_ArimaVec_2" "Feature_22_ArimaVec_3"
## [193] "Feature_22_ArimaVec_4" "Feature_22_ArimaVec_5" "Feature_22_ArimaVec_6"
## [196] "Feature_22_ArimaVec_7" "Feature_22_ArimaVec_8" "Feature_22_ArimaVec_9"
## [199] "Feature_23_ArimaVec_1" "Feature_23_ArimaVec_2" "Feature_23_ArimaVec_3"
## [202] "Feature_23_ArimaVec_4" "Feature_23_ArimaVec_5" "Feature_23_ArimaVec_6"
## [205] "Feature_23_ArimaVec_7" "Feature_23_ArimaVec_8" "Feature_23_ArimaVec_9"
## [208] "Feature_24_ArimaVec_1" "Feature_24_ArimaVec_2" "Feature_24_ArimaVec_3"
## [211] "Feature_24_ArimaVec_4" "Feature_24_ArimaVec_5" "Feature_24_ArimaVec_6"
## [214] "Feature_24_ArimaVec_7" "Feature_24_ArimaVec_8" "Feature_24_ArimaVec_9"
## [217] "Feature_25_ArimaVec_1" "Feature_25_ArimaVec_2" "Feature_25_ArimaVec_3"
## [220] "Feature_25_ArimaVec_4" "Feature_25_ArimaVec_5" "Feature_25_ArimaVec_6"
## [223] "Feature_25_ArimaVec_7" "Feature_25_ArimaVec_8" "Feature_25_ArimaVec_9"
## [226] "Feature_26_ArimaVec_1" "Feature_26_ArimaVec_2" "Feature_26_ArimaVec_3"
## [229] "Feature_26_ArimaVec_4" "Feature_26_ArimaVec_5" "Feature_26_ArimaVec_6"
## [232] "Feature_26_ArimaVec_7" "Feature_26_ArimaVec_8" "Feature_26_ArimaVec_9"
## [235] "Feature_27_ArimaVec_1" "Feature_27_ArimaVec_2" "Feature_27_ArimaVec_3"
## [238] "Feature_27_ArimaVec_4" "Feature_27_ArimaVec_5" "Feature_27_ArimaVec_6"
## [241] "Feature_27_ArimaVec_7" "Feature_27_ArimaVec_8" "Feature_27_ArimaVec_9"
## [244] "Feature_28_ArimaVec_1" "Feature_28_ArimaVec_2" "Feature_28_ArimaVec_3"
## [247] "Feature_28_ArimaVec_4" "Feature_28_ArimaVec_5" "Feature_28_ArimaVec_6"
## [250] "Feature_28_ArimaVec_7" "Feature_28_ArimaVec_8" "Feature_28_ArimaVec_9"
## [253] "Feature_29_ArimaVec_1" "Feature_29_ArimaVec_2" "Feature_29_ArimaVec_3"
## [256] "Feature_29_ArimaVec_4" "Feature_29_ArimaVec_5" "Feature_29_ArimaVec_6"
## [259] "Feature_29_ArimaVec_7" "Feature_29_ArimaVec_8" "Feature_29_ArimaVec_9"
## [262] "Feature_30_ArimaVec_1" "Feature_30_ArimaVec_2" "Feature_30_ArimaVec_3"
## [265] "Feature_30_ArimaVec_4" "Feature_30_ArimaVec_5" "Feature_30_ArimaVec_6"
## [268] "Feature_30_ArimaVec_7" "Feature_30_ArimaVec_8" "Feature_30_ArimaVec_9"
## [271] "Feature_31_ArimaVec_1" "Feature_31_ArimaVec_2" "Feature_31_ArimaVec_3"
## [274] "Feature_31_ArimaVec_4" "Feature_31_ArimaVec_5" "Feature_31_ArimaVec_6"
## [277] "Feature_31_ArimaVec_7" "Feature_31_ArimaVec_8" "Feature_31_ArimaVec_9"
## [280] "Feature_32_ArimaVec_1" "Feature_32_ArimaVec_2" "Feature_32_ArimaVec_3"
## [283] "Feature_32_ArimaVec_4" "Feature_32_ArimaVec_5" "Feature_32_ArimaVec_6"
## [286] "Feature_32_ArimaVec_7" "Feature_32_ArimaVec_8" "Feature_32_ArimaVec_9"
## [289] "Feature_33_ArimaVec_1" "Feature_33_ArimaVec_2" "Feature_33_ArimaVec_3"
## [292] "Feature_33_ArimaVec_4" "Feature_33_ArimaVec_5" "Feature_33_ArimaVec_6"
## [295] "Feature_33_ArimaVec_7" "Feature_33_ArimaVec_8" "Feature_33_ArimaVec_9"
## [298] "Feature_34_ArimaVec_1" "Feature_34_ArimaVec_2" "Feature_34_ArimaVec_3"
## [301] "Feature_34_ArimaVec_4" "Feature_34_ArimaVec_5" "Feature_34_ArimaVec_6"
## [304] "Feature_34_ArimaVec_7" "Feature_34_ArimaVec_8" "Feature_34_ArimaVec_9"
## [307] "Feature_35_ArimaVec_1" "Feature_35_ArimaVec_2" "Feature_35_ArimaVec_3"
## [310] "Feature_35_ArimaVec_4" "Feature_35_ArimaVec_5" "Feature_35_ArimaVec_6"
## [313] "Feature_35_ArimaVec_7" "Feature_35_ArimaVec_8" "Feature_35_ArimaVec_9"
## [316] "Feature_36_ArimaVec_1" "Feature_36_ArimaVec_2" "Feature_36_ArimaVec_3"
## [319] "Feature_36_ArimaVec_4" "Feature_36_ArimaVec_5" "Feature_36_ArimaVec_6"
## [322] "Feature_36_ArimaVec_7" "Feature_36_ArimaVec_8" "Feature_36_ArimaVec_9"
## [325] "Feature_37_ArimaVec_1" "Feature_37_ArimaVec_2" "Feature_37_ArimaVec_3"
## [328] "Feature_37_ArimaVec_4" "Feature_37_ArimaVec_5" "Feature_37_ArimaVec_6"
## [331] "Feature_37_ArimaVec_7" "Feature_37_ArimaVec_8" "Feature_37_ArimaVec_9"
## [334] "Feature_38_ArimaVec_1" "Feature_38_ArimaVec_2" "Feature_38_ArimaVec_3"
## [337] "Feature_38_ArimaVec_4" "Feature_38_ArimaVec_5" "Feature_38_ArimaVec_6"
## [340] "Feature_38_ArimaVec_7" "Feature_38_ArimaVec_8" "Feature_38_ArimaVec_9"
## [343] "Feature_39_ArimaVec_1" "Feature_39_ArimaVec_2" "Feature_39_ArimaVec_3"
## [346] "Feature_39_ArimaVec_4" "Feature_39_ArimaVec_5" "Feature_39_ArimaVec_6"
## [349] "Feature_39_ArimaVec_7" "Feature_39_ArimaVec_8" "Feature_39_ArimaVec_9"
## [352] "Feature_40_ArimaVec_1" "Feature_40_ArimaVec_2" "Feature_40_ArimaVec_3"
## [355] "Feature_40_ArimaVec_4" "Feature_40_ArimaVec_5" "Feature_40_ArimaVec_6"
## [358] "Feature_40_ArimaVec_7" "Feature_40_ArimaVec_8" "Feature_40_ArimaVec_9"
## [361] "Feature_41_ArimaVec_1" "Feature_41_ArimaVec_2" "Feature_41_ArimaVec_3"
## [364] "Feature_41_ArimaVec_4" "Feature_41_ArimaVec_5" "Feature_41_ArimaVec_6"
## [367] "Feature_41_ArimaVec_7" "Feature_41_ArimaVec_8" "Feature_41_ArimaVec_9"
## [370] "Feature_42_ArimaVec_1" "Feature_42_ArimaVec_2" "Feature_42_ArimaVec_3"
## [373] "Feature_42_ArimaVec_4" "Feature_42_ArimaVec_5" "Feature_42_ArimaVec_6"
## [376] "Feature_42_ArimaVec_7" "Feature_42_ArimaVec_8" "Feature_42_ArimaVec_9"
## [379] "IncomeGroup" "PopSizeGroup" "ED"
## [382] "Edu" "HI" "QOL"
## [385] "PE" "Relig" "OA"## [1] 31 387# 31 387
# Invert back to spacetime the
# FT_aggregate_arima_vector$magnitudes[ , i] signal with swapped-X-phases (Y-phase is fixed)
IFT_SwappedPhase_FT_aggregate_arima_vector <-
Re(kSpaceTransform(FT_aggregate_arima_vector_country_ranking_df$magnitudes,
TRUE, swappedPhase_FT_aggregate_arima_vector))
colnames(IFT_SwappedPhase_FT_aggregate_arima_vector) <-
colnames(aggregate_arima_vector_country_ranking_df)
rownames(IFT_SwappedPhase_FT_aggregate_arima_vector) <-
rownames(aggregate_arima_vector_country_ranking_df)
dim(IFT_SwappedPhase_FT_aggregate_arima_vector)## [1] 31 387dim(FT_aggregate_arima_vector_country_ranking_df$magnitudes)## [1] 31 387colnames(IFT_SwappedPhase_FT_aggregate_arima_vector)## [1] "Feature_1_ArimaVec_1" "Feature_1_ArimaVec_2" "Feature_1_ArimaVec_3"
## [4] "Feature_1_ArimaVec_4" "Feature_1_ArimaVec_5" "Feature_1_ArimaVec_6"
## [7] "Feature_1_ArimaVec_7" "Feature_1_ArimaVec_8" "Feature_1_ArimaVec_9"
## [10] "Feature_2_ArimaVec_1" "Feature_2_ArimaVec_2" "Feature_2_ArimaVec_3"
## [13] "Feature_2_ArimaVec_4" "Feature_2_ArimaVec_5" "Feature_2_ArimaVec_6"
## [16] "Feature_2_ArimaVec_7" "Feature_2_ArimaVec_8" "Feature_2_ArimaVec_9"
## [19] "Feature_3_ArimaVec_1" "Feature_3_ArimaVec_2" "Feature_3_ArimaVec_3"
## [22] "Feature_3_ArimaVec_4" "Feature_3_ArimaVec_5" "Feature_3_ArimaVec_6"
## [25] "Feature_3_ArimaVec_7" "Feature_3_ArimaVec_8" "Feature_3_ArimaVec_9"
## [28] "Feature_4_ArimaVec_1" "Feature_4_ArimaVec_2" "Feature_4_ArimaVec_3"
## [31] "Feature_4_ArimaVec_4" "Feature_4_ArimaVec_5" "Feature_4_ArimaVec_6"
## [34] "Feature_4_ArimaVec_7" "Feature_4_ArimaVec_8" "Feature_4_ArimaVec_9"
## [37] "Feature_5_ArimaVec_1" "Feature_5_ArimaVec_2" "Feature_5_ArimaVec_3"
## [40] "Feature_5_ArimaVec_4" "Feature_5_ArimaVec_5" "Feature_5_ArimaVec_6"
## [43] "Feature_5_ArimaVec_7" "Feature_5_ArimaVec_8" "Feature_5_ArimaVec_9"
## [46] "Feature_6_ArimaVec_1" "Feature_6_ArimaVec_2" "Feature_6_ArimaVec_3"
## [49] "Feature_6_ArimaVec_4" "Feature_6_ArimaVec_5" "Feature_6_ArimaVec_6"
## [52] "Feature_6_ArimaVec_7" "Feature_6_ArimaVec_8" "Feature_6_ArimaVec_9"
## [55] "Feature_7_ArimaVec_1" "Feature_7_ArimaVec_2" "Feature_7_ArimaVec_3"
## [58] "Feature_7_ArimaVec_4" "Feature_7_ArimaVec_5" "Feature_7_ArimaVec_6"
## [61] "Feature_7_ArimaVec_7" "Feature_7_ArimaVec_8" "Feature_7_ArimaVec_9"
## [64] "Feature_8_ArimaVec_1" "Feature_8_ArimaVec_2" "Feature_8_ArimaVec_3"
## [67] "Feature_8_ArimaVec_4" "Feature_8_ArimaVec_5" "Feature_8_ArimaVec_6"
## [70] "Feature_8_ArimaVec_7" "Feature_8_ArimaVec_8" "Feature_8_ArimaVec_9"
## [73] "Feature_9_ArimaVec_1" "Feature_9_ArimaVec_2" "Feature_9_ArimaVec_3"
## [76] "Feature_9_ArimaVec_4" "Feature_9_ArimaVec_5" "Feature_9_ArimaVec_6"
## [79] "Feature_9_ArimaVec_7" "Feature_9_ArimaVec_8" "Feature_9_ArimaVec_9"
## [82] "Feature_10_ArimaVec_1" "Feature_10_ArimaVec_2" "Feature_10_ArimaVec_3"
## [85] "Feature_10_ArimaVec_4" "Feature_10_ArimaVec_5" "Feature_10_ArimaVec_6"
## [88] "Feature_10_ArimaVec_7" "Feature_10_ArimaVec_8" "Feature_10_ArimaVec_9"
## [91] "Feature_11_ArimaVec_1" "Feature_11_ArimaVec_2" "Feature_11_ArimaVec_3"
## [94] "Feature_11_ArimaVec_4" "Feature_11_ArimaVec_5" "Feature_11_ArimaVec_6"
## [97] "Feature_11_ArimaVec_7" "Feature_11_ArimaVec_8" "Feature_11_ArimaVec_9"
## [100] "Feature_12_ArimaVec_1" "Feature_12_ArimaVec_2" "Feature_12_ArimaVec_3"
## [103] "Feature_12_ArimaVec_4" "Feature_12_ArimaVec_5" "Feature_12_ArimaVec_6"
## [106] "Feature_12_ArimaVec_7" "Feature_12_ArimaVec_8" "Feature_12_ArimaVec_9"
## [109] "Feature_13_ArimaVec_1" "Feature_13_ArimaVec_2" "Feature_13_ArimaVec_3"
## [112] "Feature_13_ArimaVec_4" "Feature_13_ArimaVec_5" "Feature_13_ArimaVec_6"
## [115] "Feature_13_ArimaVec_7" "Feature_13_ArimaVec_8" "Feature_13_ArimaVec_9"
## [118] "Feature_14_ArimaVec_1" "Feature_14_ArimaVec_2" "Feature_14_ArimaVec_3"
## [121] "Feature_14_ArimaVec_4" "Feature_14_ArimaVec_5" "Feature_14_ArimaVec_6"
## [124] "Feature_14_ArimaVec_7" "Feature_14_ArimaVec_8" "Feature_14_ArimaVec_9"
## [127] "Feature_15_ArimaVec_1" "Feature_15_ArimaVec_2" "Feature_15_ArimaVec_3"
## [130] "Feature_15_ArimaVec_4" "Feature_15_ArimaVec_5" "Feature_15_ArimaVec_6"
## [133] "Feature_15_ArimaVec_7" "Feature_15_ArimaVec_8" "Feature_15_ArimaVec_9"
## [136] "Feature_16_ArimaVec_1" "Feature_16_ArimaVec_2" "Feature_16_ArimaVec_3"
## [139] "Feature_16_ArimaVec_4" "Feature_16_ArimaVec_5" "Feature_16_ArimaVec_6"
## [142] "Feature_16_ArimaVec_7" "Feature_16_ArimaVec_8" "Feature_16_ArimaVec_9"
## [145] "Feature_17_ArimaVec_1" "Feature_17_ArimaVec_2" "Feature_17_ArimaVec_3"
## [148] "Feature_17_ArimaVec_4" "Feature_17_ArimaVec_5" "Feature_17_ArimaVec_6"
## [151] "Feature_17_ArimaVec_7" "Feature_17_ArimaVec_8" "Feature_17_ArimaVec_9"
## [154] "Feature_18_ArimaVec_1" "Feature_18_ArimaVec_2" "Feature_18_ArimaVec_3"
## [157] "Feature_18_ArimaVec_4" "Feature_18_ArimaVec_5" "Feature_18_ArimaVec_6"
## [160] "Feature_18_ArimaVec_7" "Feature_18_ArimaVec_8" "Feature_18_ArimaVec_9"
## [163] "Feature_19_ArimaVec_1" "Feature_19_ArimaVec_2" "Feature_19_ArimaVec_3"
## [166] "Feature_19_ArimaVec_4" "Feature_19_ArimaVec_5" "Feature_19_ArimaVec_6"
## [169] "Feature_19_ArimaVec_7" "Feature_19_ArimaVec_8" "Feature_19_ArimaVec_9"
## [172] "Feature_20_ArimaVec_1" "Feature_20_ArimaVec_2" "Feature_20_ArimaVec_3"
## [175] "Feature_20_ArimaVec_4" "Feature_20_ArimaVec_5" "Feature_20_ArimaVec_6"
## [178] "Feature_20_ArimaVec_7" "Feature_20_ArimaVec_8" "Feature_20_ArimaVec_9"
## [181] "Feature_21_ArimaVec_1" "Feature_21_ArimaVec_2" "Feature_21_ArimaVec_3"
## [184] "Feature_21_ArimaVec_4" "Feature_21_ArimaVec_5" "Feature_21_ArimaVec_6"
## [187] "Feature_21_ArimaVec_7" "Feature_21_ArimaVec_8" "Feature_21_ArimaVec_9"
## [190] "Feature_22_ArimaVec_1" "Feature_22_ArimaVec_2" "Feature_22_ArimaVec_3"
## [193] "Feature_22_ArimaVec_4" "Feature_22_ArimaVec_5" "Feature_22_ArimaVec_6"
## [196] "Feature_22_ArimaVec_7" "Feature_22_ArimaVec_8" "Feature_22_ArimaVec_9"
## [199] "Feature_23_ArimaVec_1" "Feature_23_ArimaVec_2" "Feature_23_ArimaVec_3"
## [202] "Feature_23_ArimaVec_4" "Feature_23_ArimaVec_5" "Feature_23_ArimaVec_6"
## [205] "Feature_23_ArimaVec_7" "Feature_23_ArimaVec_8" "Feature_23_ArimaVec_9"
## [208] "Feature_24_ArimaVec_1" "Feature_24_ArimaVec_2" "Feature_24_ArimaVec_3"
## [211] "Feature_24_ArimaVec_4" "Feature_24_ArimaVec_5" "Feature_24_ArimaVec_6"
## [214] "Feature_24_ArimaVec_7" "Feature_24_ArimaVec_8" "Feature_24_ArimaVec_9"
## [217] "Feature_25_ArimaVec_1" "Feature_25_ArimaVec_2" "Feature_25_ArimaVec_3"
## [220] "Feature_25_ArimaVec_4" "Feature_25_ArimaVec_5" "Feature_25_ArimaVec_6"
## [223] "Feature_25_ArimaVec_7" "Feature_25_ArimaVec_8" "Feature_25_ArimaVec_9"
## [226] "Feature_26_ArimaVec_1" "Feature_26_ArimaVec_2" "Feature_26_ArimaVec_3"
## [229] "Feature_26_ArimaVec_4" "Feature_26_ArimaVec_5" "Feature_26_ArimaVec_6"
## [232] "Feature_26_ArimaVec_7" "Feature_26_ArimaVec_8" "Feature_26_ArimaVec_9"
## [235] "Feature_27_ArimaVec_1" "Feature_27_ArimaVec_2" "Feature_27_ArimaVec_3"
## [238] "Feature_27_ArimaVec_4" "Feature_27_ArimaVec_5" "Feature_27_ArimaVec_6"
## [241] "Feature_27_ArimaVec_7" "Feature_27_ArimaVec_8" "Feature_27_ArimaVec_9"
## [244] "Feature_28_ArimaVec_1" "Feature_28_ArimaVec_2" "Feature_28_ArimaVec_3"
## [247] "Feature_28_ArimaVec_4" "Feature_28_ArimaVec_5" "Feature_28_ArimaVec_6"
## [250] "Feature_28_ArimaVec_7" "Feature_28_ArimaVec_8" "Feature_28_ArimaVec_9"
## [253] "Feature_29_ArimaVec_1" "Feature_29_ArimaVec_2" "Feature_29_ArimaVec_3"
## [256] "Feature_29_ArimaVec_4" "Feature_29_ArimaVec_5" "Feature_29_ArimaVec_6"
## [259] "Feature_29_ArimaVec_7" "Feature_29_ArimaVec_8" "Feature_29_ArimaVec_9"
## [262] "Feature_30_ArimaVec_1" "Feature_30_ArimaVec_2" "Feature_30_ArimaVec_3"
## [265] "Feature_30_ArimaVec_4" "Feature_30_ArimaVec_5" "Feature_30_ArimaVec_6"
## [268] "Feature_30_ArimaVec_7" "Feature_30_ArimaVec_8" "Feature_30_ArimaVec_9"
## [271] "Feature_31_ArimaVec_1" "Feature_31_ArimaVec_2" "Feature_31_ArimaVec_3"
## [274] "Feature_31_ArimaVec_4" "Feature_31_ArimaVec_5" "Feature_31_ArimaVec_6"
## [277] "Feature_31_ArimaVec_7" "Feature_31_ArimaVec_8" "Feature_31_ArimaVec_9"
## [280] "Feature_32_ArimaVec_1" "Feature_32_ArimaVec_2" "Feature_32_ArimaVec_3"
## [283] "Feature_32_ArimaVec_4" "Feature_32_ArimaVec_5" "Feature_32_ArimaVec_6"
## [286] "Feature_32_ArimaVec_7" "Feature_32_ArimaVec_8" "Feature_32_ArimaVec_9"
## [289] "Feature_33_ArimaVec_1" "Feature_33_ArimaVec_2" "Feature_33_ArimaVec_3"
## [292] "Feature_33_ArimaVec_4" "Feature_33_ArimaVec_5" "Feature_33_ArimaVec_6"
## [295] "Feature_33_ArimaVec_7" "Feature_33_ArimaVec_8" "Feature_33_ArimaVec_9"
## [298] "Feature_34_ArimaVec_1" "Feature_34_ArimaVec_2" "Feature_34_ArimaVec_3"
## [301] "Feature_34_ArimaVec_4" "Feature_34_ArimaVec_5" "Feature_34_ArimaVec_6"
## [304] "Feature_34_ArimaVec_7" "Feature_34_ArimaVec_8" "Feature_34_ArimaVec_9"
## [307] "Feature_35_ArimaVec_1" "Feature_35_ArimaVec_2" "Feature_35_ArimaVec_3"
## [310] "Feature_35_ArimaVec_4" "Feature_35_ArimaVec_5" "Feature_35_ArimaVec_6"
## [313] "Feature_35_ArimaVec_7" "Feature_35_ArimaVec_8" "Feature_35_ArimaVec_9"
## [316] "Feature_36_ArimaVec_1" "Feature_36_ArimaVec_2" "Feature_36_ArimaVec_3"
## [319] "Feature_36_ArimaVec_4" "Feature_36_ArimaVec_5" "Feature_36_ArimaVec_6"
## [322] "Feature_36_ArimaVec_7" "Feature_36_ArimaVec_8" "Feature_36_ArimaVec_9"
## [325] "Feature_37_ArimaVec_1" "Feature_37_ArimaVec_2" "Feature_37_ArimaVec_3"
## [328] "Feature_37_ArimaVec_4" "Feature_37_ArimaVec_5" "Feature_37_ArimaVec_6"
## [331] "Feature_37_ArimaVec_7" "Feature_37_ArimaVec_8" "Feature_37_ArimaVec_9"
## [334] "Feature_38_ArimaVec_1" "Feature_38_ArimaVec_2" "Feature_38_ArimaVec_3"
## [337] "Feature_38_ArimaVec_4" "Feature_38_ArimaVec_5" "Feature_38_ArimaVec_6"
## [340] "Feature_38_ArimaVec_7" "Feature_38_ArimaVec_8" "Feature_38_ArimaVec_9"
## [343] "Feature_39_ArimaVec_1" "Feature_39_ArimaVec_2" "Feature_39_ArimaVec_3"
## [346] "Feature_39_ArimaVec_4" "Feature_39_ArimaVec_5" "Feature_39_ArimaVec_6"
## [349] "Feature_39_ArimaVec_7" "Feature_39_ArimaVec_8" "Feature_39_ArimaVec_9"
## [352] "Feature_40_ArimaVec_1" "Feature_40_ArimaVec_2" "Feature_40_ArimaVec_3"
## [355] "Feature_40_ArimaVec_4" "Feature_40_ArimaVec_5" "Feature_40_ArimaVec_6"
## [358] "Feature_40_ArimaVec_7" "Feature_40_ArimaVec_8" "Feature_40_ArimaVec_9"
## [361] "Feature_41_ArimaVec_1" "Feature_41_ArimaVec_2" "Feature_41_ArimaVec_3"
## [364] "Feature_41_ArimaVec_4" "Feature_41_ArimaVec_5" "Feature_41_ArimaVec_6"
## [367] "Feature_41_ArimaVec_7" "Feature_41_ArimaVec_8" "Feature_41_ArimaVec_9"
## [370] "Feature_42_ArimaVec_1" "Feature_42_ArimaVec_2" "Feature_42_ArimaVec_3"
## [373] "Feature_42_ArimaVec_4" "Feature_42_ArimaVec_5" "Feature_42_ArimaVec_6"
## [376] "Feature_42_ArimaVec_7" "Feature_42_ArimaVec_8" "Feature_42_ArimaVec_9"
## [379] "IncomeGroup" "PopSizeGroup" "ED"
## [382] "Edu" "HI" "QOL"
## [385] "PE" "Relig" "OA"# IFT_SwappedPhase_FT_aggregate_arima_vector[1:5, 1:4]; temp_Data[1:5, 1:4]
# 2. Perform LASSO modeling on IFT_SwappedPhase_FT_aggregate_arima_vector;
# report param estimates and quality metrics AIC/BIC
set.seed(12)
cvLASSO_kime_swapped =
cv.glmnet(data.matrix(IFT_SwappedPhase_FT_aggregate_arima_vector[ , 1:378]),
# IFT_SwappedPhase_FT_aggregate_arima_vector[ , 387], alpha = 1, parallel=TRUE)
Y, alpha = 1, parallel=TRUE)
plot(cvLASSO_kime_swapped)
mtext("(Spacekime, Swapped-Phases) CV LASSO: Number of Nonzero (Active) Coefficients", side=3, line=2.5)
# Identify top predictors and forecast the Y=Overall (OA) Country ranking outcome
predLASSO_kime_swapped <- predict(cvLASSO_kime_swapped, s = 3, # cvLASSO_kime_swapped$lambda.min,
newx = data.matrix(IFT_SwappedPhase_FT_aggregate_arima_vector[ , 1:378]))
# testMSE_LASSO_kime_swapped <-
# mean((predLASSO_kime_swapped - IFT_SwappedPhase_FT_aggregate_arima_vector[ , 387])^2)
# testMSE_LASSO_kime_swapped
predLASSO_kime_swapped## s1
## 1 23.26124
## 2 25.33788
## 3 25.68937
## 4 25.09766
## 5 30.84766
## 6 23.01836
## 7 22.75197
## 8 27.90027
## 9 11.20383
## 10 17.19234
## 11 17.16636
## 12 25.39744
## 13 29.60808
## 14 30.95488
## 15 22.94134
## 16 24.41465
## 17 26.94810
## 18 30.79167
## 19 16.88240
## 20 35.03674
## 21 12.69022
## 22 14.85075
## 23 23.56948
## 24 23.06139
## 25 25.09476
## 26 29.47846
## 27 20.75416
## 28 21.64873
## 29 20.34044
## 30 18.32573
## 31 14.74365# Plot Regression Coefficients: create variable names for plotting
betaHatLASSO_kime_swapped = as.double(coef(cvLASSO_kime_swapped,
s=3)) # cvLASSO_kime_swapped$lambda.min))
#cvLASSO_kime_swapped$lambda.1se
#coefplot(betaHatLASSO_kime_swapped[377:386], sd = rep(0, 10), pch=0, cex.pts = 3, col="red",
# main = "(Spacekime, Swapped-Phases) LASSO-Regularized Regression Coefficient Estimates",
# varnames = varNames[377:386])
varImp(cvLASSO_kime_swapped, lambda = 3) #cvLASSO_kime_swapped$lambda.min)## Overall
## Feature_1_ArimaVec_1 0.0001581607
## Feature_3_ArimaVec_8 5.4414240889
## Feature_6_ArimaVec_3 0.2052325091
## Feature_7_ArimaVec_1 0.0007922646
## Feature_7_ArimaVec_6 1.6317407164
## Feature_24_ArimaVec_1 0.0002003192
## Feature_24_ArimaVec_5 4.9895032906
## Feature_41_ArimaVec_3 0.4666980893
## Feature_41_ArimaVec_6 1.7580440109
## Feature_42_ArimaVec_3 0.4100416326coefList_kime_swapped <- coef(cvLASSO_kime_swapped, s=3) # 'lambda.min')
coefList_kime_swapped <- data.frame(coefList_kime_swapped@Dimnames[[1]][coefList_kime_swapped@i+1], coefList_kime_swapped@x)
names(coefList_kime_swapped) <- c('Feature','EffectSize')
arrange(coefList_kime_swapped, -abs(EffectSize))[2:10, ]## Feature EffectSize
## 2 Feature_3_ArimaVec_8 5.4414240889
## 3 Feature_24_ArimaVec_5 -4.9895032906
## 4 Feature_41_ArimaVec_6 1.7580440109
## 5 Feature_7_ArimaVec_6 -1.6317407164
## 6 Feature_41_ArimaVec_3 -0.4666980893
## 7 Feature_42_ArimaVec_3 0.4100416326
## 8 Feature_6_ArimaVec_3 -0.2052325091
## 9 Feature_7_ArimaVec_1 -0.0007922646
## 10 Feature_24_ArimaVec_1 -0.0002003192# Feature EffectSize
#2 Feature_3_ArimaVec_8 5.4414240889
#3 Feature_24_ArimaVec_5 -4.9895032906
#4 Feature_41_ArimaVec_6 1.7580440109
#5 Feature_7_ArimaVec_6 -1.6317407164
#6 Feature_41_ArimaVec_3 -0.4666980893
#7 Feature_42_ArimaVec_3 0.4100416326
#8 Feature_6_ArimaVec_3 -0.2052325091
#9 Feature_7_ArimaVec_1 -0.0007922646
#10 Feature_24_ArimaVec_1 -0.0002003192
#
# ARIMA-spacetime: 4=non-seasonal MA, 5=seasonal AR, 8=non-seasonal Diff
# ARIMA-spacekime_nill: 3=non-seasonal AR, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA
# ARIMA-spacekime_swapped: 3=non-seasonal AR, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA
# 9 ARIMA-derived vector includes:
# (1=ts_avg, 2=forecast_avg, 3=non-seasonal AR, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA,
# 7=period, 8=non-seasonal Diff, 9=seasonal differences)
coef(cvLASSO_kime_swapped, s = 3) %>% # "lambda.min") %>%
broom::tidy() %>%
filter(row != "(Intercept)") %>%
top_n(100, wt = abs(value)) %>%
ggplot(aes(value, reorder(row, value), color = value > 0)) +
geom_point(show.legend = FALSE, aes(size = abs(value))) +
ggtitle("(Spacekime, Swapped-Phases) Top 9 salient features (LASSO penalty)") +
xlab("Effect-size") +
ylab(NULL)
# pack a 31*4 DF with (predLASSO_kime, IFT_NilPhase_FT_aggregate_arima_vector_Y,
# IFT_SwappedPhase_FT_aggregate_arima_vector_Y, Y)
validation_kime_swapped <- cbind(predLASSO_lim[, 1], predLASSO_nil_kime[, 1],
predLASSO_kime_swapped[ , 1], Y)
colnames(validation_kime_swapped) <- c("predLASSO (spacetime)", "predLASSO_IFT_NilPhase",
"predLASSO_IFT_SwappedPhase", "Orig_Y")
head(validation_kime_swapped); dim(validation_kime_swapped)## predLASSO (spacetime) predLASSO_IFT_NilPhase
## Austria 20.21660 17.96229
## Belgium 24.57457 20.91197
## Bulgaria 27.42736 21.16400
## Croatia 25.84568 21.41214
## Cyprus 27.80166 30.72476
## Czech Republic 24.17704 24.16388
## predLASSO_IFT_SwappedPhase Orig_Y
## Austria 23.26124 18
## Belgium 25.33788 19
## Bulgaria 25.68937 38
## Croatia 25.09766 28
## Cyprus 30.84766 50
## Czech Republic 23.01836 25## [1] 31 4# Prediction correlations:
cor(validation_kime_swapped[ , 3], validation_kime_swapped[, 4]) ## [1] 0.8644778# predLASSO_IFT_SwappedPhase OA rank vs. predLASSO_spacekime: 0.7
cor(validation_kime_swapped[ , 1], validation_kime_swapped[, 3]) ## [1] 0.8600452# predLASSO (spacetime) vs. predLASSO_IFT_SwappedPhase OA rank: 0.83
# Plot observed Y (Overall Country ranking), x-axis vs. Kime-Swapped LASSO (9-parameters) predicted Y^
linFit1_kime_swapped <- lm(validation_kime_swapped[ , 3] ~ validation_kime_swapped[ , 4])
plot(validation_kime_swapped[ , 3] ~ validation_kime_swapped[ , 4],
col="blue", xaxt='n', yaxt='n', pch = 16, cex=3,
xlab="predLASSO_IFT_SwappedPhase_FT_Y", ylab="predLASSO_spacekime_swapped Country Overall Ranking",
main = sprintf("Observed (x) vs. Kime IFT_SwappedPhase_FT_Y (y) Overall Country Ranking, cor=%.02f",
cor(validation_kime_swapped[ , 3], validation_kime_swapped[, 4])))
abline(linFit1_kime_swapped, lwd=3, col="red")
#abline(linFit1_kime, lwd=3, col="green")
# Plot Spacetime LASSO forecasting
# Plot observed Y (Overall Country ranking), x-axis vs. LASSO (9-parameters) predicted Y^, y-axis
linFit1_spacetime <- lm(validation_kime_swapped[ , 3] ~ validation_kime_swapped[ , 4])
plot(validation_kime_swapped[ , 3] ~ validation_kime_swapped[ , 4],
col="blue", xaxt='n', yaxt='n', pch = 16, cex=3,
xlab="Observed Country Overall Ranking", ylab="predLASSO_spacetime",
main = sprintf("Predicted (y) vs. Observed (x) Overall Country Ranking, cor=%.02f",
cor(validation_kime_swapped[ , 3], validation_kime_swapped[, 4])))
abline(linFit1_spacetime, lwd=3, col="red")
# add Top_30_Ranking_Indicator
validation_kime_swapped <- as.data.frame(cbind(validation_kime_swapped, ifelse (validation_kime_swapped[,4]<=30, 1, 0)))
colnames(validation_kime_swapped)[5] <- "Top30Rank"
rownames(validation_kime_swapped)[11] <- "Germany"
head(validation_kime_swapped)## predLASSO (spacetime) predLASSO_IFT_NilPhase
## Austria 20.21660 17.96229
## Belgium 24.57457 20.91197
## Bulgaria 27.42736 21.16400
## Croatia 25.84568 21.41214
## Cyprus 27.80166 30.72476
## Czech Republic 24.17704 24.16388
## predLASSO_IFT_SwappedPhase Orig_Y Top30Rank
## Austria 23.26124 18 1
## Belgium 25.33788 19 1
## Bulgaria 25.68937 38 0
## Croatia 25.09766 28 1
## Cyprus 30.84766 50 0
## Czech Republic 23.01836 25 1# Spacetime LASSO modeling
myPlotSwappedPhase <- ggplot(as.data.frame(validation_kime_swapped), aes(x=Orig_Y,
y=validation_kime_swapped[, 3], label=rownames(validation_kime_swapped))) +
geom_smooth(method='lm') +
geom_point() +
# Color by groups
# geom_text(aes(color=factor(rownames(validation_kime_swapped)))) +
geom_label_repel(aes(label = rownames(validation_kime_swapped),
fill = factor(Top30Rank)), color = 'black', size = 5,
point.padding = unit(0.3, "lines")) +
# theme(legend.position = "bottom") +
theme(legend.position = c(0.1, 0.9),
legend.text = element_text(colour="black", size=12, face="bold"),
legend.title = element_text(colour="black", size=14, face="bold")) +
scale_fill_discrete(name = "Country Overall Ranking",
labels = c("Below 30 Rank", "Top 30 Rank")) +
labs(title=sprintf("Spacekime LASSO Predicted, Swapped-Phases (y) vs. Observed (x) Overall Country Ranking, cor=%.02f", cor(validation_kime_swapped[ , 3], validation_kime_swapped[, 4])),
x ="Observed Overall Country Ranking (1 is 'best')",
y = "Spacekime LASSO Predicted, using Swapped-Phases")
myPlotSwappedPhase
12.3.3 Stronger Signal Analytics
Using all 386 features (378 ARIMA signatures + 8 meta-data).
12.3.3.0.1 Space-Time Analytics
# 1. LASSO regression/feature extraction
library(glmnet)
library(arm)
library(knitr)
# subset test data
Y = aggregate_arima_vector_country_ranking_df$OA
X = aggregate_arima_vector_country_ranking_df[ , 1:386]
# remove columns containing NAs
X = X[ , colSums(is.na(X)) == 0]; dim(X) # [1] 31 378## [1] 31 386#### 10-fold cross validation: for the LASSO
set.seed(4321)
cvLASSO_lim_all = cv.glmnet(data.matrix(X), Y, alpha = 1, parallel=TRUE)
plot(cvLASSO_lim)
mtext("CV LASSO (using only Timeseries data): Number of Nonzero (Active) Coefficients", side=3, line=2.5)
# Identify top predictors and forecast the Y=Overall (OA) Country ranking outcome
predLASSO_lim_all <- predict(cvLASSO_lim_all, s = 1.1, # cvLASSO_lim$lambda.min,
newx = data.matrix(X))
coefList_lim_all <- coef(cvLASSO_lim_all, s='lambda.min')
coefList_lim_all <- data.frame(coefList_lim_all@Dimnames[[1]][coefList_lim_all@i+1],coefList_lim_all@x)
names(coefList_lim_all) <- c('Feature','EffectSize')
arrange(coefList_lim_all, -abs(EffectSize))[2:10, ]## Feature EffectSize
## 2 ED -0.48113754
## 3 Feature_19_ArimaVec_8 0.45588201
## 4 QOL -0.41158771
## 5 PE -0.31722273
## 6 Feature_37_ArimaVec_6 -0.29115396
## 7 HI -0.14139165
## 8 Feature_22_ArimaVec_4 -0.12244068
## 9 Edu -0.09526626
## 10 Feature_41_ArimaVec_4 0.04273808cor(Y, predLASSO_lim_all[, 1]) # 0.9974121## [1] 0.9929494varImp(cvLASSO_lim_all, lambda = 1.1) # cvLASSO_lim_all$lambda.min)## Overall
## ED 0.51375256
## HI 0.07009496
## QOL 0.44007667
## PE 0.28142873#Feature_1_ArimaVec_8 2.7518241
#Feature_9_ArimaVec_4 0.2662136
#Feature_9_ArimaVec_8 1.0871240
#Feature_20_ArimaVec_8 1.6851990
#Feature_25_ArimaVec_5 0.5113345
#IncomeGroup 1.1787811
#ED 0.7508295
#QOL 0.2057181
#PE 0.5131427
coef(cvLASSO_lim_all, s = 1.1) %>% #"lambda.min") %>%
broom::tidy() %>%
filter(row != "(Intercept)") %>%
top_n(100, wt = abs(value)) %>%
ggplot(aes(value, reorder(row, value), color = value > 0)) +
geom_point(show.legend = FALSE, aes(size = abs(value))) +
ggtitle("Top 9 salient features (LASSO penalty)") +
xlab("Effect-size") +
ylab(NULL)
countryNames[11] <- "Germany"
validation_lim_all <- data.frame(matrix(NA, nrow = dim(predLASSO_lim_all)[1], ncol=2), row.names=countryNames)
validation_lim_all [ , 1] <- Y; validation_lim_all[ , 2] <- predLASSO_lim_all[, 1]
colnames(validation_lim_all) <- c("Orig_Y", "LASSO")
dim(validation_lim_all); head(validation_lim_all)## [1] 31 2## Orig_Y LASSO
## Austria 18 17.08080
## Belgium 19 16.39025
## Bulgaria 38 34.78236
## Croatia 28 28.34703
## Cyprus 50 47.62993
## Czech Republic 25 26.65363# add Top_30_Ranking_Indicator
validation_lim_all <- as.data.frame(cbind(validation_lim_all, ifelse (validation_lim_all[, 1]<=30, 1, 0)))
colnames(validation_lim_all)[3] <- "Top30Rank"
head(validation_lim_all)## Orig_Y LASSO Top30Rank
## Austria 18 17.08080 1
## Belgium 19 16.39025 1
## Bulgaria 38 34.78236 0
## Croatia 28 28.34703 1
## Cyprus 50 47.62993 0
## Czech Republic 25 26.65363 1# Prediction correlations:
cor(validation_lim_all[ , 1], validation_lim_all[, 2]) # Y=observed OA rank vs. LASSO-pred 0.98 (lim) 0.84## [1] 0.9929494# Plot observed Y (Overall Country ranking) vs. LASSO (9-parameters) predicted Y^
linFit_lim_all <- lm(validation_lim_all[ , 1] ~ validation_lim_all[, 2])
plot(validation_lim_all[ , 1] ~ validation_lim_all[, 2],
col="blue", xaxt='n', yaxt='n', pch = 16, cex=3,
xlab="Observed Country Overall Ranking", ylab="LASSO (42*9 +8) param model",
main = sprintf("Observed (X) vs. LASSO-Predicted (Y) Overall Country Ranking, cor=%.02f",
cor(validation_lim_all[ , 1], validation_lim_all[, 2])))
abline(linFit_lim_all, lwd=3, col="red")
# Plot
myPlot_all <- ggplot(as.data.frame(validation_lim_all), aes(x=validation_lim_all[ , 1],
y=validation_lim_all[ , 2], label=rownames(validation_lim_all))) +
geom_smooth(method='lm') +
geom_point() +
# Color by groups
# geom_text(aes(color=factor(rownames(validation_lim_all)))) +
geom_label_repel(aes(label = rownames(validation_lim_all),
fill = factor(Top30Rank)), color = 'black', size = 5,
point.padding = unit(0.3, "lines")) +
# theme(legend.position = "bottom") +
theme(legend.position = c(0.1, 0.9),
legend.text = element_text(colour="black", size=12, face="bold"),
legend.title = element_text(colour="black", size=14, face="bold")) +
scale_fill_discrete(name = "Country Overall Ranking",
labels = c("Below 30 Rank", "Top 30 Rank")) +
labs(title=sprintf("Spacetime LASSO Predicted (y) vs. Observed (x) Overall Country Ranking, cor=%.02f", cor(validation_lim_all[ , 1], validation_lim_all[, 2])),
x ="Observed Overall Country Ranking (1 is 'best')",
y = "Spacetime LASSO Predicted")
myPlot_all
12.3.3.0.2 Space-Kime Analytics
Nil-Phase Synthesis and LASSO model estimation …
library(glmnet)
# Generic function to Transform Data ={all predictors (X) and outcome (Y)} to k-space (Fourier domain): kSpaceTransform(data, inverse = FALSE, reconPhases = NULL)
# ForwardFT (rawData, FALSE, NULL)
# InverseFT(magnitudes, TRUE, reconPhasesToUse) or InverseFT(FT_data, TRUE, NULL)
# DATA
# subset test data
Y = aggregate_arima_vector_country_ranking_df$OA
X = aggregate_arima_vector_country_ranking_df[ , 1:386]
# remove columns containing NAs
# X = X[ , colSums(is.na(X)) == 0]; dim(X) # [1] 31 386
length(Y); dim(X)## [1] 31## [1] 31 386FT_aggregate_arima_vector_country_ranking_df <-
kSpaceTransform(aggregate_arima_vector_country_ranking_df, inverse = FALSE, reconPhases = NULL)
## Kime-Phase Distributions
# Examine the Kime-direction Distributions of the Phases for all *Belgium* features (predictors + outcome). Define a generic function that plots the Phase distributions.
# plotPhaseDistributions(dataFT, dataColnames)
plotPhaseDistributions(FT_aggregate_arima_vector_country_ranking_df,
colnames(aggregate_arima_vector_country_ranking_df), size=4, cex=0.1)
IFT_FT_aggregate_arima_vector_country_ranking_df <-
kSpaceTransform(FT_aggregate_arima_vector_country_ranking_df$magnitudes,
TRUE, FT_aggregate_arima_vector_country_ranking_df$phases)
# Check IFT(FT) == I:
# ifelse(aggregate_arima_vector_country_ranking_df[5,4] -
# Re(IFT_FT_aggregate_arima_vector_country_ranking_df[5,4]) < 0.001, "Perfect Synthesis", "Problems!!!")
##############################################
# Nil-Phase Synthesis and LASSO model estimation
# 1. Nil-Phase data synthesis (reconstruction)
temp_Data <- aggregate_arima_vector_country_ranking_df
nilPhase_FT_aggregate_arima_vector <-
array(complex(real=0, imaginary=0), c(dim(temp_Data)[1], dim(temp_Data)[2]))
dim(nilPhase_FT_aggregate_arima_vector) # ; head(nilPhase_FT_aggregate_arima_vector)## [1] 31 387# [1] 31 387
IFT_NilPhase_FT_aggregate_arima_vector <- array(complex(), c(dim(temp_Data)[1], dim(temp_Data)[2]))
# Invert back to spacetime the
# FT_aggregate_arima_vector_country_ranking_df$magnitudes[ , i] signal with nil-phase
IFT_NilPhase_FT_aggregate_arima_vector <-
Re(kSpaceTransform(FT_aggregate_arima_vector_country_ranking_df$magnitudes,
TRUE, nilPhase_FT_aggregate_arima_vector))
colnames(IFT_NilPhase_FT_aggregate_arima_vector) <-
colnames(aggregate_arima_vector_country_ranking_df)
rownames(IFT_NilPhase_FT_aggregate_arima_vector) <-
rownames(aggregate_arima_vector_country_ranking_df)
dim(IFT_NilPhase_FT_aggregate_arima_vector)## [1] 31 387dim(FT_aggregate_arima_vector_country_ranking_df$magnitudes)## [1] 31 387colnames(IFT_NilPhase_FT_aggregate_arima_vector)## [1] "Feature_1_ArimaVec_1" "Feature_1_ArimaVec_2" "Feature_1_ArimaVec_3"
## [4] "Feature_1_ArimaVec_4" "Feature_1_ArimaVec_5" "Feature_1_ArimaVec_6"
## [7] "Feature_1_ArimaVec_7" "Feature_1_ArimaVec_8" "Feature_1_ArimaVec_9"
## [10] "Feature_2_ArimaVec_1" "Feature_2_ArimaVec_2" "Feature_2_ArimaVec_3"
## [13] "Feature_2_ArimaVec_4" "Feature_2_ArimaVec_5" "Feature_2_ArimaVec_6"
## [16] "Feature_2_ArimaVec_7" "Feature_2_ArimaVec_8" "Feature_2_ArimaVec_9"
## [19] "Feature_3_ArimaVec_1" "Feature_3_ArimaVec_2" "Feature_3_ArimaVec_3"
## [22] "Feature_3_ArimaVec_4" "Feature_3_ArimaVec_5" "Feature_3_ArimaVec_6"
## [25] "Feature_3_ArimaVec_7" "Feature_3_ArimaVec_8" "Feature_3_ArimaVec_9"
## [28] "Feature_4_ArimaVec_1" "Feature_4_ArimaVec_2" "Feature_4_ArimaVec_3"
## [31] "Feature_4_ArimaVec_4" "Feature_4_ArimaVec_5" "Feature_4_ArimaVec_6"
## [34] "Feature_4_ArimaVec_7" "Feature_4_ArimaVec_8" "Feature_4_ArimaVec_9"
## [37] "Feature_5_ArimaVec_1" "Feature_5_ArimaVec_2" "Feature_5_ArimaVec_3"
## [40] "Feature_5_ArimaVec_4" "Feature_5_ArimaVec_5" "Feature_5_ArimaVec_6"
## [43] "Feature_5_ArimaVec_7" "Feature_5_ArimaVec_8" "Feature_5_ArimaVec_9"
## [46] "Feature_6_ArimaVec_1" "Feature_6_ArimaVec_2" "Feature_6_ArimaVec_3"
## [49] "Feature_6_ArimaVec_4" "Feature_6_ArimaVec_5" "Feature_6_ArimaVec_6"
## [52] "Feature_6_ArimaVec_7" "Feature_6_ArimaVec_8" "Feature_6_ArimaVec_9"
## [55] "Feature_7_ArimaVec_1" "Feature_7_ArimaVec_2" "Feature_7_ArimaVec_3"
## [58] "Feature_7_ArimaVec_4" "Feature_7_ArimaVec_5" "Feature_7_ArimaVec_6"
## [61] "Feature_7_ArimaVec_7" "Feature_7_ArimaVec_8" "Feature_7_ArimaVec_9"
## [64] "Feature_8_ArimaVec_1" "Feature_8_ArimaVec_2" "Feature_8_ArimaVec_3"
## [67] "Feature_8_ArimaVec_4" "Feature_8_ArimaVec_5" "Feature_8_ArimaVec_6"
## [70] "Feature_8_ArimaVec_7" "Feature_8_ArimaVec_8" "Feature_8_ArimaVec_9"
## [73] "Feature_9_ArimaVec_1" "Feature_9_ArimaVec_2" "Feature_9_ArimaVec_3"
## [76] "Feature_9_ArimaVec_4" "Feature_9_ArimaVec_5" "Feature_9_ArimaVec_6"
## [79] "Feature_9_ArimaVec_7" "Feature_9_ArimaVec_8" "Feature_9_ArimaVec_9"
## [82] "Feature_10_ArimaVec_1" "Feature_10_ArimaVec_2" "Feature_10_ArimaVec_3"
## [85] "Feature_10_ArimaVec_4" "Feature_10_ArimaVec_5" "Feature_10_ArimaVec_6"
## [88] "Feature_10_ArimaVec_7" "Feature_10_ArimaVec_8" "Feature_10_ArimaVec_9"
## [91] "Feature_11_ArimaVec_1" "Feature_11_ArimaVec_2" "Feature_11_ArimaVec_3"
## [94] "Feature_11_ArimaVec_4" "Feature_11_ArimaVec_5" "Feature_11_ArimaVec_6"
## [97] "Feature_11_ArimaVec_7" "Feature_11_ArimaVec_8" "Feature_11_ArimaVec_9"
## [100] "Feature_12_ArimaVec_1" "Feature_12_ArimaVec_2" "Feature_12_ArimaVec_3"
## [103] "Feature_12_ArimaVec_4" "Feature_12_ArimaVec_5" "Feature_12_ArimaVec_6"
## [106] "Feature_12_ArimaVec_7" "Feature_12_ArimaVec_8" "Feature_12_ArimaVec_9"
## [109] "Feature_13_ArimaVec_1" "Feature_13_ArimaVec_2" "Feature_13_ArimaVec_3"
## [112] "Feature_13_ArimaVec_4" "Feature_13_ArimaVec_5" "Feature_13_ArimaVec_6"
## [115] "Feature_13_ArimaVec_7" "Feature_13_ArimaVec_8" "Feature_13_ArimaVec_9"
## [118] "Feature_14_ArimaVec_1" "Feature_14_ArimaVec_2" "Feature_14_ArimaVec_3"
## [121] "Feature_14_ArimaVec_4" "Feature_14_ArimaVec_5" "Feature_14_ArimaVec_6"
## [124] "Feature_14_ArimaVec_7" "Feature_14_ArimaVec_8" "Feature_14_ArimaVec_9"
## [127] "Feature_15_ArimaVec_1" "Feature_15_ArimaVec_2" "Feature_15_ArimaVec_3"
## [130] "Feature_15_ArimaVec_4" "Feature_15_ArimaVec_5" "Feature_15_ArimaVec_6"
## [133] "Feature_15_ArimaVec_7" "Feature_15_ArimaVec_8" "Feature_15_ArimaVec_9"
## [136] "Feature_16_ArimaVec_1" "Feature_16_ArimaVec_2" "Feature_16_ArimaVec_3"
## [139] "Feature_16_ArimaVec_4" "Feature_16_ArimaVec_5" "Feature_16_ArimaVec_6"
## [142] "Feature_16_ArimaVec_7" "Feature_16_ArimaVec_8" "Feature_16_ArimaVec_9"
## [145] "Feature_17_ArimaVec_1" "Feature_17_ArimaVec_2" "Feature_17_ArimaVec_3"
## [148] "Feature_17_ArimaVec_4" "Feature_17_ArimaVec_5" "Feature_17_ArimaVec_6"
## [151] "Feature_17_ArimaVec_7" "Feature_17_ArimaVec_8" "Feature_17_ArimaVec_9"
## [154] "Feature_18_ArimaVec_1" "Feature_18_ArimaVec_2" "Feature_18_ArimaVec_3"
## [157] "Feature_18_ArimaVec_4" "Feature_18_ArimaVec_5" "Feature_18_ArimaVec_6"
## [160] "Feature_18_ArimaVec_7" "Feature_18_ArimaVec_8" "Feature_18_ArimaVec_9"
## [163] "Feature_19_ArimaVec_1" "Feature_19_ArimaVec_2" "Feature_19_ArimaVec_3"
## [166] "Feature_19_ArimaVec_4" "Feature_19_ArimaVec_5" "Feature_19_ArimaVec_6"
## [169] "Feature_19_ArimaVec_7" "Feature_19_ArimaVec_8" "Feature_19_ArimaVec_9"
## [172] "Feature_20_ArimaVec_1" "Feature_20_ArimaVec_2" "Feature_20_ArimaVec_3"
## [175] "Feature_20_ArimaVec_4" "Feature_20_ArimaVec_5" "Feature_20_ArimaVec_6"
## [178] "Feature_20_ArimaVec_7" "Feature_20_ArimaVec_8" "Feature_20_ArimaVec_9"
## [181] "Feature_21_ArimaVec_1" "Feature_21_ArimaVec_2" "Feature_21_ArimaVec_3"
## [184] "Feature_21_ArimaVec_4" "Feature_21_ArimaVec_5" "Feature_21_ArimaVec_6"
## [187] "Feature_21_ArimaVec_7" "Feature_21_ArimaVec_8" "Feature_21_ArimaVec_9"
## [190] "Feature_22_ArimaVec_1" "Feature_22_ArimaVec_2" "Feature_22_ArimaVec_3"
## [193] "Feature_22_ArimaVec_4" "Feature_22_ArimaVec_5" "Feature_22_ArimaVec_6"
## [196] "Feature_22_ArimaVec_7" "Feature_22_ArimaVec_8" "Feature_22_ArimaVec_9"
## [199] "Feature_23_ArimaVec_1" "Feature_23_ArimaVec_2" "Feature_23_ArimaVec_3"
## [202] "Feature_23_ArimaVec_4" "Feature_23_ArimaVec_5" "Feature_23_ArimaVec_6"
## [205] "Feature_23_ArimaVec_7" "Feature_23_ArimaVec_8" "Feature_23_ArimaVec_9"
## [208] "Feature_24_ArimaVec_1" "Feature_24_ArimaVec_2" "Feature_24_ArimaVec_3"
## [211] "Feature_24_ArimaVec_4" "Feature_24_ArimaVec_5" "Feature_24_ArimaVec_6"
## [214] "Feature_24_ArimaVec_7" "Feature_24_ArimaVec_8" "Feature_24_ArimaVec_9"
## [217] "Feature_25_ArimaVec_1" "Feature_25_ArimaVec_2" "Feature_25_ArimaVec_3"
## [220] "Feature_25_ArimaVec_4" "Feature_25_ArimaVec_5" "Feature_25_ArimaVec_6"
## [223] "Feature_25_ArimaVec_7" "Feature_25_ArimaVec_8" "Feature_25_ArimaVec_9"
## [226] "Feature_26_ArimaVec_1" "Feature_26_ArimaVec_2" "Feature_26_ArimaVec_3"
## [229] "Feature_26_ArimaVec_4" "Feature_26_ArimaVec_5" "Feature_26_ArimaVec_6"
## [232] "Feature_26_ArimaVec_7" "Feature_26_ArimaVec_8" "Feature_26_ArimaVec_9"
## [235] "Feature_27_ArimaVec_1" "Feature_27_ArimaVec_2" "Feature_27_ArimaVec_3"
## [238] "Feature_27_ArimaVec_4" "Feature_27_ArimaVec_5" "Feature_27_ArimaVec_6"
## [241] "Feature_27_ArimaVec_7" "Feature_27_ArimaVec_8" "Feature_27_ArimaVec_9"
## [244] "Feature_28_ArimaVec_1" "Feature_28_ArimaVec_2" "Feature_28_ArimaVec_3"
## [247] "Feature_28_ArimaVec_4" "Feature_28_ArimaVec_5" "Feature_28_ArimaVec_6"
## [250] "Feature_28_ArimaVec_7" "Feature_28_ArimaVec_8" "Feature_28_ArimaVec_9"
## [253] "Feature_29_ArimaVec_1" "Feature_29_ArimaVec_2" "Feature_29_ArimaVec_3"
## [256] "Feature_29_ArimaVec_4" "Feature_29_ArimaVec_5" "Feature_29_ArimaVec_6"
## [259] "Feature_29_ArimaVec_7" "Feature_29_ArimaVec_8" "Feature_29_ArimaVec_9"
## [262] "Feature_30_ArimaVec_1" "Feature_30_ArimaVec_2" "Feature_30_ArimaVec_3"
## [265] "Feature_30_ArimaVec_4" "Feature_30_ArimaVec_5" "Feature_30_ArimaVec_6"
## [268] "Feature_30_ArimaVec_7" "Feature_30_ArimaVec_8" "Feature_30_ArimaVec_9"
## [271] "Feature_31_ArimaVec_1" "Feature_31_ArimaVec_2" "Feature_31_ArimaVec_3"
## [274] "Feature_31_ArimaVec_4" "Feature_31_ArimaVec_5" "Feature_31_ArimaVec_6"
## [277] "Feature_31_ArimaVec_7" "Feature_31_ArimaVec_8" "Feature_31_ArimaVec_9"
## [280] "Feature_32_ArimaVec_1" "Feature_32_ArimaVec_2" "Feature_32_ArimaVec_3"
## [283] "Feature_32_ArimaVec_4" "Feature_32_ArimaVec_5" "Feature_32_ArimaVec_6"
## [286] "Feature_32_ArimaVec_7" "Feature_32_ArimaVec_8" "Feature_32_ArimaVec_9"
## [289] "Feature_33_ArimaVec_1" "Feature_33_ArimaVec_2" "Feature_33_ArimaVec_3"
## [292] "Feature_33_ArimaVec_4" "Feature_33_ArimaVec_5" "Feature_33_ArimaVec_6"
## [295] "Feature_33_ArimaVec_7" "Feature_33_ArimaVec_8" "Feature_33_ArimaVec_9"
## [298] "Feature_34_ArimaVec_1" "Feature_34_ArimaVec_2" "Feature_34_ArimaVec_3"
## [301] "Feature_34_ArimaVec_4" "Feature_34_ArimaVec_5" "Feature_34_ArimaVec_6"
## [304] "Feature_34_ArimaVec_7" "Feature_34_ArimaVec_8" "Feature_34_ArimaVec_9"
## [307] "Feature_35_ArimaVec_1" "Feature_35_ArimaVec_2" "Feature_35_ArimaVec_3"
## [310] "Feature_35_ArimaVec_4" "Feature_35_ArimaVec_5" "Feature_35_ArimaVec_6"
## [313] "Feature_35_ArimaVec_7" "Feature_35_ArimaVec_8" "Feature_35_ArimaVec_9"
## [316] "Feature_36_ArimaVec_1" "Feature_36_ArimaVec_2" "Feature_36_ArimaVec_3"
## [319] "Feature_36_ArimaVec_4" "Feature_36_ArimaVec_5" "Feature_36_ArimaVec_6"
## [322] "Feature_36_ArimaVec_7" "Feature_36_ArimaVec_8" "Feature_36_ArimaVec_9"
## [325] "Feature_37_ArimaVec_1" "Feature_37_ArimaVec_2" "Feature_37_ArimaVec_3"
## [328] "Feature_37_ArimaVec_4" "Feature_37_ArimaVec_5" "Feature_37_ArimaVec_6"
## [331] "Feature_37_ArimaVec_7" "Feature_37_ArimaVec_8" "Feature_37_ArimaVec_9"
## [334] "Feature_38_ArimaVec_1" "Feature_38_ArimaVec_2" "Feature_38_ArimaVec_3"
## [337] "Feature_38_ArimaVec_4" "Feature_38_ArimaVec_5" "Feature_38_ArimaVec_6"
## [340] "Feature_38_ArimaVec_7" "Feature_38_ArimaVec_8" "Feature_38_ArimaVec_9"
## [343] "Feature_39_ArimaVec_1" "Feature_39_ArimaVec_2" "Feature_39_ArimaVec_3"
## [346] "Feature_39_ArimaVec_4" "Feature_39_ArimaVec_5" "Feature_39_ArimaVec_6"
## [349] "Feature_39_ArimaVec_7" "Feature_39_ArimaVec_8" "Feature_39_ArimaVec_9"
## [352] "Feature_40_ArimaVec_1" "Feature_40_ArimaVec_2" "Feature_40_ArimaVec_3"
## [355] "Feature_40_ArimaVec_4" "Feature_40_ArimaVec_5" "Feature_40_ArimaVec_6"
## [358] "Feature_40_ArimaVec_7" "Feature_40_ArimaVec_8" "Feature_40_ArimaVec_9"
## [361] "Feature_41_ArimaVec_1" "Feature_41_ArimaVec_2" "Feature_41_ArimaVec_3"
## [364] "Feature_41_ArimaVec_4" "Feature_41_ArimaVec_5" "Feature_41_ArimaVec_6"
## [367] "Feature_41_ArimaVec_7" "Feature_41_ArimaVec_8" "Feature_41_ArimaVec_9"
## [370] "Feature_42_ArimaVec_1" "Feature_42_ArimaVec_2" "Feature_42_ArimaVec_3"
## [373] "Feature_42_ArimaVec_4" "Feature_42_ArimaVec_5" "Feature_42_ArimaVec_6"
## [376] "Feature_42_ArimaVec_7" "Feature_42_ArimaVec_8" "Feature_42_ArimaVec_9"
## [379] "IncomeGroup" "PopSizeGroup" "ED"
## [382] "Edu" "HI" "QOL"
## [385] "PE" "Relig" "OA"# IFT_NilPhase_FT_aggregate_arima_vector[1:5, 1:4]; temp_Data[1:5, 1:4]
# 2. Perform LASSO modeling on IFT_NilPhase_FT_aggregate_arima_vector;
# report param estimates and quality metrics AIC/BIC
# library(forecast)
set.seed(123)
cvLASSO_nil_kime_all = cv.glmnet(data.matrix(IFT_NilPhase_FT_aggregate_arima_vector[ , 1:386]),
# IFT_NilPhase_FT_aggregate_arima_vector[ , 387], alpha = 1, parallel=TRUE)
Y, alpha = 1, parallel=TRUE)
plot(cvLASSO_nil_kime_all)
mtext("(Spacekime, Nil-phase) CV LASSO: Number of Nonzero (Active) Coefficients", side=3, line=2.5)
# Identify top predictors and forecast the Y=Overall (OA) Country ranking outcome
predLASSO_nil_kime_all <- predict(cvLASSO_nil_kime_all, s = exp(-1/4), # cvLASSO_nil_kime$lambda.min,
newx = data.matrix(IFT_NilPhase_FT_aggregate_arima_vector[ , 1:386])); predLASSO_nil_kime_all## s1
## 1 17.85361
## 2 20.99808
## 3 20.91310
## 4 20.62338
## 5 31.45441
## 6 24.42391
## 7 19.43468
## 8 30.45423
## 9 17.99855
## 10 22.10649
## 11 11.14070
## 12 19.65189
## 13 34.49169
## 14 23.59418
## 15 23.22100
## 16 29.06692
## 17 29.06692
## 18 23.22100
## 19 23.59418
## 20 34.49169
## 21 19.65189
## 22 11.14070
## 23 22.10649
## 24 17.99855
## 25 30.45423
## 26 19.43468
## 27 24.42391
## 28 31.45441
## 29 20.62338
## 30 20.91310
## 31 20.99808# testMSE_LASSO_nil_kime <- mean((predLASSO_nil_kime - IFT_NilPhase_FT_aggregate_arima_vector[ , 387])^2)
# testMSE_LASSO_nil_kime
varImp(cvLASSO_nil_kime_all, lambda = exp(-1/4)) # cvLASSO_nil_kime_all$lambda.min)## Overall
## Feature_2_ArimaVec_6 0.07190024
## Feature_6_ArimaVec_6 0.49799326
## Feature_11_ArimaVec_4 8.45132661
## Feature_12_ArimaVec_4 5.38002499
## Feature_12_ArimaVec_8 10.37633956
## Feature_26_ArimaVec_6 2.06530937
## Feature_30_ArimaVec_4 3.29579474
## Feature_34_ArimaVec_5 0.96507673
## Feature_37_ArimaVec_2 0.01033978
## Feature_39_ArimaVec_5 2.08659578coefList_nil_kime_all <- coef(cvLASSO_nil_kime_all, s=exp(-1/4)) # 'lambda.min')
coefList_nil_kime_all <- data.frame(coefList_nil_kime_all@Dimnames[[1]][coefList_nil_kime_all@i+1],
coefList_nil_kime_all@x)
names(coefList_nil_kime_all) <- c('Feature','EffectSize')
arrange(coefList_nil_kime_all, -abs(EffectSize))[1:9, ]## Feature EffectSize
## 1 (Intercept) 26.6921768
## 2 Feature_12_ArimaVec_8 -10.3763396
## 3 Feature_11_ArimaVec_4 8.4513266
## 4 Feature_12_ArimaVec_4 -5.3800250
## 5 Feature_30_ArimaVec_4 3.2957947
## 6 Feature_39_ArimaVec_5 -2.0865958
## 7 Feature_26_ArimaVec_6 2.0653094
## 8 Feature_34_ArimaVec_5 -0.9650767
## 9 Feature_6_ArimaVec_6 -0.4979933# Feature EffectSize
#1 (Intercept) 26.385520159
#Feature_2_ArimaVec_6 0.07190025
#Feature_6_ArimaVec_6 0.49799326
#Feature_11_ArimaVec_4 8.45132661
#Feature_12_ArimaVec_4 5.38002499
#Feature_12_ArimaVec_8 10.37633956
#Feature_26_ArimaVec_6 2.06530937
#Feature_30_ArimaVec_4 3.29579474
#Feature_34_ArimaVec_5 0.96507673
#Feature_37_ArimaVec_2 0.01033978
#Feature_39_ArimaVec_5 2.08659578
# ARIMA-spacetime: 4=non-seasonal MA, 5=seasonal AR, 8=non-seasonal Diff
# ARIMA-spacekimeNil: 2=forecast_avg, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA, 8=non-seasonal Diff
#9 ARIMA-derived vector includes:
# (1=ts_avg, 2=forecast_avg, 3=non-seasonal AR, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA,
# 7=period, 8=non-seasonal Diff, 9=seasonal differences)
coef(cvLASSO_nil_kime_all, s = exp(-1/4)) %>% # "lambda.min") %>%
broom::tidy() %>%
filter(row != "(Intercept)") %>%
top_n(100, wt = abs(value)) %>%
ggplot(aes(value, reorder(row, value), color = value > 0)) +
geom_point(show.legend = FALSE, aes(size = abs(value))) +
ggtitle("(Spacekime) Top 9 salient features (LASSO penalty)") +
xlab("Effect-size") +
ylab(NULL)
# pack a 31*3 DF with (predLASSO_kime, IFT_NilPhase_FT_aggregate_arima_vector_Y, Y)
validation_nil_kime_all <- cbind(predLASSO_nil_kime_all[, 1],
IFT_NilPhase_FT_aggregate_arima_vector[ , 387], Y)
colnames(validation_nil_kime_all) <- c("predLASSO_kime", "IFT_NilPhase_FT_Y", "Orig_Y")
rownames(validation_nil_kime_all)[11] <- "Germany"
head(validation_nil_kime_all)## predLASSO_kime IFT_NilPhase_FT_Y Orig_Y
## 1 17.85361 87.771967 18
## 2 20.99808 19.640349 19
## 3 20.91310 24.453327 38
## 4 20.62338 24.267994 28
## 5 31.45441 8.137025 50
## 6 24.42391 11.737091 25validation_nil_kime_all <- as.data.frame(cbind(validation_nil_kime_all,
ifelse (validation_nil_kime_all[,3]<=30, 1, 0)))
colnames(validation_nil_kime_all)[4] <- "Top30Rank"
head(validation_nil_kime_all)## predLASSO_kime IFT_NilPhase_FT_Y Orig_Y Top30Rank
## 1 17.85361 87.771967 18 1
## 2 20.99808 19.640349 19 1
## 3 20.91310 24.453327 38 0
## 4 20.62338 24.267994 28 1
## 5 31.45441 8.137025 50 0
## 6 24.42391 11.737091 25 1# Prediction correlations:
# cor(validation_nil_kime[ , 1], validation_nil_kime[, 2]) # Y=predLASSO_kime OA rank vs. kime_LASSO_pred: 0.99
cor(validation_nil_kime_all[ , 1], validation_nil_kime_all[, 3]) # Y=predLASSO_kime OA rank vs. Orig_Y: 0.64## [1] 0.6493571# Plot observed Y (Overall Country ranking) vs. LASSO (9-parameters) predicted Y^
linFit1_nil_kime_all <- lm(predLASSO_nil_kime_all ~ validation_nil_kime_all[ , 3])
plot(predLASSO_nil_kime_all ~ validation_nil_kime_all[ , 3],
col="blue", xaxt='n', yaxt='n', pch = 16, cex=3,
xlab="Observed Country Overall Ranking", ylab="IFT_NilPhase predLASSO_kime",
main = sprintf("Observed (x) vs. IFT_NilPhase Predicted (y) Overall Country Ranking, cor=%.02f",
cor(validation_nil_kime_all[ , 1], validation_nil_kime_all[, 3])))
abline(linFit1_nil_kime_all, lwd=3, col="red")
# abline(linFit1, lwd=3, col="green")
# Spacetime LASSO modeling
myPlotNilPhase_all <- ggplot(as.data.frame(validation_nil_kime_all), aes(x=Orig_Y,
y=predLASSO_nil_kime_all, label=rownames(validation_nil_kime_all))) +
geom_smooth(method='lm') +
geom_point() +
# Color by groups
# geom_text(aes(color=factor(rownames(validation_nil_kime)))) +
geom_label_repel(aes(label = rownames(validation_nil_kime_all),
fill = factor(Top30Rank)), color = 'black', size = 5,
point.padding = unit(0.3, "lines")) +
# theme(legend.position = "bottom") +
theme(legend.position = c(0.1, 0.9),
legend.text = element_text(colour="black", size=12, face="bold"),
legend.title = element_text(colour="black", size=14, face="bold")) +
scale_fill_discrete(name = "Country Overall Ranking",
labels = c("Below 30 Rank", "Top 30 Rank")) +
labs(title=sprintf("Spacekime LASSO Predicted, Nil-Phases (y) vs. Observed (x) Overall Country Ranking, cor=%.02f", cor(validation_nil_kime_all[ , 1], validation_nil_kime_all[, 3])),
x ="Observed Overall Country Ranking (1 is 'best')",
y = "Spacekime LASSO Predicted, using Nil-Phases")
myPlotNilPhase_all
Swapped Feature Phases and then synthesize the data (reconstruction)
# temp_Data <- aggregate_arima_vector_country_ranking_df
swappedPhase_FT_aggregate_arima_vector <- FT_aggregate_arima_vector_country_ranking_df$phases
dim(swappedPhase_FT_aggregate_arima_vector) # ; head(swappedPhase_FT_aggregate_arima_vector)## [1] 31 387# [1] 31 387
IFT_SwappedPhase_FT_aggregate_arima_vector <- array(complex(), c(dim(temp_Data)[1], dim(temp_Data)[2]))
set.seed(1234) # sample randomly Phase-columns for each of the 131 covariates (X)
swappedPhase_FT_aggregate_arima_vector1 <- as.data.frame(cbind(
swappedPhase_FT_aggregate_arima_vector[ ,
sample(ncol(swappedPhase_FT_aggregate_arima_vector[ , 1:378]))], # mix ARIMA signature phases
swappedPhase_FT_aggregate_arima_vector[ ,
sample(ncol(swappedPhase_FT_aggregate_arima_vector[ , 379:386]))],# mix the meta-data phases
swappedPhase_FT_aggregate_arima_vector[ , 387])) # add correct Outcome phase
swappedPhase_FT_aggregate_arima_vector <- swappedPhase_FT_aggregate_arima_vector1
colnames(swappedPhase_FT_aggregate_arima_vector) <- colnames(temp_Data)
colnames(swappedPhase_FT_aggregate_arima_vector); dim(swappedPhase_FT_aggregate_arima_vector)## [1] "Feature_1_ArimaVec_1" "Feature_1_ArimaVec_2" "Feature_1_ArimaVec_3"
## [4] "Feature_1_ArimaVec_4" "Feature_1_ArimaVec_5" "Feature_1_ArimaVec_6"
## [7] "Feature_1_ArimaVec_7" "Feature_1_ArimaVec_8" "Feature_1_ArimaVec_9"
## [10] "Feature_2_ArimaVec_1" "Feature_2_ArimaVec_2" "Feature_2_ArimaVec_3"
## [13] "Feature_2_ArimaVec_4" "Feature_2_ArimaVec_5" "Feature_2_ArimaVec_6"
## [16] "Feature_2_ArimaVec_7" "Feature_2_ArimaVec_8" "Feature_2_ArimaVec_9"
## [19] "Feature_3_ArimaVec_1" "Feature_3_ArimaVec_2" "Feature_3_ArimaVec_3"
## [22] "Feature_3_ArimaVec_4" "Feature_3_ArimaVec_5" "Feature_3_ArimaVec_6"
## [25] "Feature_3_ArimaVec_7" "Feature_3_ArimaVec_8" "Feature_3_ArimaVec_9"
## [28] "Feature_4_ArimaVec_1" "Feature_4_ArimaVec_2" "Feature_4_ArimaVec_3"
## [31] "Feature_4_ArimaVec_4" "Feature_4_ArimaVec_5" "Feature_4_ArimaVec_6"
## [34] "Feature_4_ArimaVec_7" "Feature_4_ArimaVec_8" "Feature_4_ArimaVec_9"
## [37] "Feature_5_ArimaVec_1" "Feature_5_ArimaVec_2" "Feature_5_ArimaVec_3"
## [40] "Feature_5_ArimaVec_4" "Feature_5_ArimaVec_5" "Feature_5_ArimaVec_6"
## [43] "Feature_5_ArimaVec_7" "Feature_5_ArimaVec_8" "Feature_5_ArimaVec_9"
## [46] "Feature_6_ArimaVec_1" "Feature_6_ArimaVec_2" "Feature_6_ArimaVec_3"
## [49] "Feature_6_ArimaVec_4" "Feature_6_ArimaVec_5" "Feature_6_ArimaVec_6"
## [52] "Feature_6_ArimaVec_7" "Feature_6_ArimaVec_8" "Feature_6_ArimaVec_9"
## [55] "Feature_7_ArimaVec_1" "Feature_7_ArimaVec_2" "Feature_7_ArimaVec_3"
## [58] "Feature_7_ArimaVec_4" "Feature_7_ArimaVec_5" "Feature_7_ArimaVec_6"
## [61] "Feature_7_ArimaVec_7" "Feature_7_ArimaVec_8" "Feature_7_ArimaVec_9"
## [64] "Feature_8_ArimaVec_1" "Feature_8_ArimaVec_2" "Feature_8_ArimaVec_3"
## [67] "Feature_8_ArimaVec_4" "Feature_8_ArimaVec_5" "Feature_8_ArimaVec_6"
## [70] "Feature_8_ArimaVec_7" "Feature_8_ArimaVec_8" "Feature_8_ArimaVec_9"
## [73] "Feature_9_ArimaVec_1" "Feature_9_ArimaVec_2" "Feature_9_ArimaVec_3"
## [76] "Feature_9_ArimaVec_4" "Feature_9_ArimaVec_5" "Feature_9_ArimaVec_6"
## [79] "Feature_9_ArimaVec_7" "Feature_9_ArimaVec_8" "Feature_9_ArimaVec_9"
## [82] "Feature_10_ArimaVec_1" "Feature_10_ArimaVec_2" "Feature_10_ArimaVec_3"
## [85] "Feature_10_ArimaVec_4" "Feature_10_ArimaVec_5" "Feature_10_ArimaVec_6"
## [88] "Feature_10_ArimaVec_7" "Feature_10_ArimaVec_8" "Feature_10_ArimaVec_9"
## [91] "Feature_11_ArimaVec_1" "Feature_11_ArimaVec_2" "Feature_11_ArimaVec_3"
## [94] "Feature_11_ArimaVec_4" "Feature_11_ArimaVec_5" "Feature_11_ArimaVec_6"
## [97] "Feature_11_ArimaVec_7" "Feature_11_ArimaVec_8" "Feature_11_ArimaVec_9"
## [100] "Feature_12_ArimaVec_1" "Feature_12_ArimaVec_2" "Feature_12_ArimaVec_3"
## [103] "Feature_12_ArimaVec_4" "Feature_12_ArimaVec_5" "Feature_12_ArimaVec_6"
## [106] "Feature_12_ArimaVec_7" "Feature_12_ArimaVec_8" "Feature_12_ArimaVec_9"
## [109] "Feature_13_ArimaVec_1" "Feature_13_ArimaVec_2" "Feature_13_ArimaVec_3"
## [112] "Feature_13_ArimaVec_4" "Feature_13_ArimaVec_5" "Feature_13_ArimaVec_6"
## [115] "Feature_13_ArimaVec_7" "Feature_13_ArimaVec_8" "Feature_13_ArimaVec_9"
## [118] "Feature_14_ArimaVec_1" "Feature_14_ArimaVec_2" "Feature_14_ArimaVec_3"
## [121] "Feature_14_ArimaVec_4" "Feature_14_ArimaVec_5" "Feature_14_ArimaVec_6"
## [124] "Feature_14_ArimaVec_7" "Feature_14_ArimaVec_8" "Feature_14_ArimaVec_9"
## [127] "Feature_15_ArimaVec_1" "Feature_15_ArimaVec_2" "Feature_15_ArimaVec_3"
## [130] "Feature_15_ArimaVec_4" "Feature_15_ArimaVec_5" "Feature_15_ArimaVec_6"
## [133] "Feature_15_ArimaVec_7" "Feature_15_ArimaVec_8" "Feature_15_ArimaVec_9"
## [136] "Feature_16_ArimaVec_1" "Feature_16_ArimaVec_2" "Feature_16_ArimaVec_3"
## [139] "Feature_16_ArimaVec_4" "Feature_16_ArimaVec_5" "Feature_16_ArimaVec_6"
## [142] "Feature_16_ArimaVec_7" "Feature_16_ArimaVec_8" "Feature_16_ArimaVec_9"
## [145] "Feature_17_ArimaVec_1" "Feature_17_ArimaVec_2" "Feature_17_ArimaVec_3"
## [148] "Feature_17_ArimaVec_4" "Feature_17_ArimaVec_5" "Feature_17_ArimaVec_6"
## [151] "Feature_17_ArimaVec_7" "Feature_17_ArimaVec_8" "Feature_17_ArimaVec_9"
## [154] "Feature_18_ArimaVec_1" "Feature_18_ArimaVec_2" "Feature_18_ArimaVec_3"
## [157] "Feature_18_ArimaVec_4" "Feature_18_ArimaVec_5" "Feature_18_ArimaVec_6"
## [160] "Feature_18_ArimaVec_7" "Feature_18_ArimaVec_8" "Feature_18_ArimaVec_9"
## [163] "Feature_19_ArimaVec_1" "Feature_19_ArimaVec_2" "Feature_19_ArimaVec_3"
## [166] "Feature_19_ArimaVec_4" "Feature_19_ArimaVec_5" "Feature_19_ArimaVec_6"
## [169] "Feature_19_ArimaVec_7" "Feature_19_ArimaVec_8" "Feature_19_ArimaVec_9"
## [172] "Feature_20_ArimaVec_1" "Feature_20_ArimaVec_2" "Feature_20_ArimaVec_3"
## [175] "Feature_20_ArimaVec_4" "Feature_20_ArimaVec_5" "Feature_20_ArimaVec_6"
## [178] "Feature_20_ArimaVec_7" "Feature_20_ArimaVec_8" "Feature_20_ArimaVec_9"
## [181] "Feature_21_ArimaVec_1" "Feature_21_ArimaVec_2" "Feature_21_ArimaVec_3"
## [184] "Feature_21_ArimaVec_4" "Feature_21_ArimaVec_5" "Feature_21_ArimaVec_6"
## [187] "Feature_21_ArimaVec_7" "Feature_21_ArimaVec_8" "Feature_21_ArimaVec_9"
## [190] "Feature_22_ArimaVec_1" "Feature_22_ArimaVec_2" "Feature_22_ArimaVec_3"
## [193] "Feature_22_ArimaVec_4" "Feature_22_ArimaVec_5" "Feature_22_ArimaVec_6"
## [196] "Feature_22_ArimaVec_7" "Feature_22_ArimaVec_8" "Feature_22_ArimaVec_9"
## [199] "Feature_23_ArimaVec_1" "Feature_23_ArimaVec_2" "Feature_23_ArimaVec_3"
## [202] "Feature_23_ArimaVec_4" "Feature_23_ArimaVec_5" "Feature_23_ArimaVec_6"
## [205] "Feature_23_ArimaVec_7" "Feature_23_ArimaVec_8" "Feature_23_ArimaVec_9"
## [208] "Feature_24_ArimaVec_1" "Feature_24_ArimaVec_2" "Feature_24_ArimaVec_3"
## [211] "Feature_24_ArimaVec_4" "Feature_24_ArimaVec_5" "Feature_24_ArimaVec_6"
## [214] "Feature_24_ArimaVec_7" "Feature_24_ArimaVec_8" "Feature_24_ArimaVec_9"
## [217] "Feature_25_ArimaVec_1" "Feature_25_ArimaVec_2" "Feature_25_ArimaVec_3"
## [220] "Feature_25_ArimaVec_4" "Feature_25_ArimaVec_5" "Feature_25_ArimaVec_6"
## [223] "Feature_25_ArimaVec_7" "Feature_25_ArimaVec_8" "Feature_25_ArimaVec_9"
## [226] "Feature_26_ArimaVec_1" "Feature_26_ArimaVec_2" "Feature_26_ArimaVec_3"
## [229] "Feature_26_ArimaVec_4" "Feature_26_ArimaVec_5" "Feature_26_ArimaVec_6"
## [232] "Feature_26_ArimaVec_7" "Feature_26_ArimaVec_8" "Feature_26_ArimaVec_9"
## [235] "Feature_27_ArimaVec_1" "Feature_27_ArimaVec_2" "Feature_27_ArimaVec_3"
## [238] "Feature_27_ArimaVec_4" "Feature_27_ArimaVec_5" "Feature_27_ArimaVec_6"
## [241] "Feature_27_ArimaVec_7" "Feature_27_ArimaVec_8" "Feature_27_ArimaVec_9"
## [244] "Feature_28_ArimaVec_1" "Feature_28_ArimaVec_2" "Feature_28_ArimaVec_3"
## [247] "Feature_28_ArimaVec_4" "Feature_28_ArimaVec_5" "Feature_28_ArimaVec_6"
## [250] "Feature_28_ArimaVec_7" "Feature_28_ArimaVec_8" "Feature_28_ArimaVec_9"
## [253] "Feature_29_ArimaVec_1" "Feature_29_ArimaVec_2" "Feature_29_ArimaVec_3"
## [256] "Feature_29_ArimaVec_4" "Feature_29_ArimaVec_5" "Feature_29_ArimaVec_6"
## [259] "Feature_29_ArimaVec_7" "Feature_29_ArimaVec_8" "Feature_29_ArimaVec_9"
## [262] "Feature_30_ArimaVec_1" "Feature_30_ArimaVec_2" "Feature_30_ArimaVec_3"
## [265] "Feature_30_ArimaVec_4" "Feature_30_ArimaVec_5" "Feature_30_ArimaVec_6"
## [268] "Feature_30_ArimaVec_7" "Feature_30_ArimaVec_8" "Feature_30_ArimaVec_9"
## [271] "Feature_31_ArimaVec_1" "Feature_31_ArimaVec_2" "Feature_31_ArimaVec_3"
## [274] "Feature_31_ArimaVec_4" "Feature_31_ArimaVec_5" "Feature_31_ArimaVec_6"
## [277] "Feature_31_ArimaVec_7" "Feature_31_ArimaVec_8" "Feature_31_ArimaVec_9"
## [280] "Feature_32_ArimaVec_1" "Feature_32_ArimaVec_2" "Feature_32_ArimaVec_3"
## [283] "Feature_32_ArimaVec_4" "Feature_32_ArimaVec_5" "Feature_32_ArimaVec_6"
## [286] "Feature_32_ArimaVec_7" "Feature_32_ArimaVec_8" "Feature_32_ArimaVec_9"
## [289] "Feature_33_ArimaVec_1" "Feature_33_ArimaVec_2" "Feature_33_ArimaVec_3"
## [292] "Feature_33_ArimaVec_4" "Feature_33_ArimaVec_5" "Feature_33_ArimaVec_6"
## [295] "Feature_33_ArimaVec_7" "Feature_33_ArimaVec_8" "Feature_33_ArimaVec_9"
## [298] "Feature_34_ArimaVec_1" "Feature_34_ArimaVec_2" "Feature_34_ArimaVec_3"
## [301] "Feature_34_ArimaVec_4" "Feature_34_ArimaVec_5" "Feature_34_ArimaVec_6"
## [304] "Feature_34_ArimaVec_7" "Feature_34_ArimaVec_8" "Feature_34_ArimaVec_9"
## [307] "Feature_35_ArimaVec_1" "Feature_35_ArimaVec_2" "Feature_35_ArimaVec_3"
## [310] "Feature_35_ArimaVec_4" "Feature_35_ArimaVec_5" "Feature_35_ArimaVec_6"
## [313] "Feature_35_ArimaVec_7" "Feature_35_ArimaVec_8" "Feature_35_ArimaVec_9"
## [316] "Feature_36_ArimaVec_1" "Feature_36_ArimaVec_2" "Feature_36_ArimaVec_3"
## [319] "Feature_36_ArimaVec_4" "Feature_36_ArimaVec_5" "Feature_36_ArimaVec_6"
## [322] "Feature_36_ArimaVec_7" "Feature_36_ArimaVec_8" "Feature_36_ArimaVec_9"
## [325] "Feature_37_ArimaVec_1" "Feature_37_ArimaVec_2" "Feature_37_ArimaVec_3"
## [328] "Feature_37_ArimaVec_4" "Feature_37_ArimaVec_5" "Feature_37_ArimaVec_6"
## [331] "Feature_37_ArimaVec_7" "Feature_37_ArimaVec_8" "Feature_37_ArimaVec_9"
## [334] "Feature_38_ArimaVec_1" "Feature_38_ArimaVec_2" "Feature_38_ArimaVec_3"
## [337] "Feature_38_ArimaVec_4" "Feature_38_ArimaVec_5" "Feature_38_ArimaVec_6"
## [340] "Feature_38_ArimaVec_7" "Feature_38_ArimaVec_8" "Feature_38_ArimaVec_9"
## [343] "Feature_39_ArimaVec_1" "Feature_39_ArimaVec_2" "Feature_39_ArimaVec_3"
## [346] "Feature_39_ArimaVec_4" "Feature_39_ArimaVec_5" "Feature_39_ArimaVec_6"
## [349] "Feature_39_ArimaVec_7" "Feature_39_ArimaVec_8" "Feature_39_ArimaVec_9"
## [352] "Feature_40_ArimaVec_1" "Feature_40_ArimaVec_2" "Feature_40_ArimaVec_3"
## [355] "Feature_40_ArimaVec_4" "Feature_40_ArimaVec_5" "Feature_40_ArimaVec_6"
## [358] "Feature_40_ArimaVec_7" "Feature_40_ArimaVec_8" "Feature_40_ArimaVec_9"
## [361] "Feature_41_ArimaVec_1" "Feature_41_ArimaVec_2" "Feature_41_ArimaVec_3"
## [364] "Feature_41_ArimaVec_4" "Feature_41_ArimaVec_5" "Feature_41_ArimaVec_6"
## [367] "Feature_41_ArimaVec_7" "Feature_41_ArimaVec_8" "Feature_41_ArimaVec_9"
## [370] "Feature_42_ArimaVec_1" "Feature_42_ArimaVec_2" "Feature_42_ArimaVec_3"
## [373] "Feature_42_ArimaVec_4" "Feature_42_ArimaVec_5" "Feature_42_ArimaVec_6"
## [376] "Feature_42_ArimaVec_7" "Feature_42_ArimaVec_8" "Feature_42_ArimaVec_9"
## [379] "IncomeGroup" "PopSizeGroup" "ED"
## [382] "Edu" "HI" "QOL"
## [385] "PE" "Relig" "OA"## [1] 31 387# 31 387
# Invert back to spacetime the
# FT_aggregate_arima_vector$magnitudes[ , i] signal with swapped-X-phases (Y-phase is fixed)
IFT_SwappedPhase_FT_aggregate_arima_vector <-
Re(kSpaceTransform(FT_aggregate_arima_vector_country_ranking_df$magnitudes,
TRUE, swappedPhase_FT_aggregate_arima_vector))
# Save IFT_SwappedPhase_FT_aggregate_arima_vector out for PCA/t-SNE SpaceKime modeling
#options(digits = 2)
#write.table(format(IFT_SwappedPhase_FT_aggregate_arima_vector[ , 1:386]),
# #scientific=FALSE), #, digits=2),
# fileEncoding = "UTF-16LE", append = FALSE, quote = FALSE, sep = "\t",
# eol = "\n", na = "NA", dec = ".", row.names = FALSE, col.names = FALSE,
# "E:/Ivo.dir/Research/UMichigan/Publications_Books/2018/others/4D_Time_Space_Book_Ideas/ARIMAX_EU_DataAnalytics/EU_Econ_TensorData_31Countries_By_386Features_SpaceKime_SwappedPhase.txt")
colnames(IFT_SwappedPhase_FT_aggregate_arima_vector) <-
colnames(aggregate_arima_vector_country_ranking_df)
rownames(IFT_SwappedPhase_FT_aggregate_arima_vector) <-
rownames(aggregate_arima_vector_country_ranking_df)
dim(IFT_SwappedPhase_FT_aggregate_arima_vector)## [1] 31 387dim(FT_aggregate_arima_vector_country_ranking_df$magnitudes)## [1] 31 387colnames(IFT_SwappedPhase_FT_aggregate_arima_vector)## [1] "Feature_1_ArimaVec_1" "Feature_1_ArimaVec_2" "Feature_1_ArimaVec_3"
## [4] "Feature_1_ArimaVec_4" "Feature_1_ArimaVec_5" "Feature_1_ArimaVec_6"
## [7] "Feature_1_ArimaVec_7" "Feature_1_ArimaVec_8" "Feature_1_ArimaVec_9"
## [10] "Feature_2_ArimaVec_1" "Feature_2_ArimaVec_2" "Feature_2_ArimaVec_3"
## [13] "Feature_2_ArimaVec_4" "Feature_2_ArimaVec_5" "Feature_2_ArimaVec_6"
## [16] "Feature_2_ArimaVec_7" "Feature_2_ArimaVec_8" "Feature_2_ArimaVec_9"
## [19] "Feature_3_ArimaVec_1" "Feature_3_ArimaVec_2" "Feature_3_ArimaVec_3"
## [22] "Feature_3_ArimaVec_4" "Feature_3_ArimaVec_5" "Feature_3_ArimaVec_6"
## [25] "Feature_3_ArimaVec_7" "Feature_3_ArimaVec_8" "Feature_3_ArimaVec_9"
## [28] "Feature_4_ArimaVec_1" "Feature_4_ArimaVec_2" "Feature_4_ArimaVec_3"
## [31] "Feature_4_ArimaVec_4" "Feature_4_ArimaVec_5" "Feature_4_ArimaVec_6"
## [34] "Feature_4_ArimaVec_7" "Feature_4_ArimaVec_8" "Feature_4_ArimaVec_9"
## [37] "Feature_5_ArimaVec_1" "Feature_5_ArimaVec_2" "Feature_5_ArimaVec_3"
## [40] "Feature_5_ArimaVec_4" "Feature_5_ArimaVec_5" "Feature_5_ArimaVec_6"
## [43] "Feature_5_ArimaVec_7" "Feature_5_ArimaVec_8" "Feature_5_ArimaVec_9"
## [46] "Feature_6_ArimaVec_1" "Feature_6_ArimaVec_2" "Feature_6_ArimaVec_3"
## [49] "Feature_6_ArimaVec_4" "Feature_6_ArimaVec_5" "Feature_6_ArimaVec_6"
## [52] "Feature_6_ArimaVec_7" "Feature_6_ArimaVec_8" "Feature_6_ArimaVec_9"
## [55] "Feature_7_ArimaVec_1" "Feature_7_ArimaVec_2" "Feature_7_ArimaVec_3"
## [58] "Feature_7_ArimaVec_4" "Feature_7_ArimaVec_5" "Feature_7_ArimaVec_6"
## [61] "Feature_7_ArimaVec_7" "Feature_7_ArimaVec_8" "Feature_7_ArimaVec_9"
## [64] "Feature_8_ArimaVec_1" "Feature_8_ArimaVec_2" "Feature_8_ArimaVec_3"
## [67] "Feature_8_ArimaVec_4" "Feature_8_ArimaVec_5" "Feature_8_ArimaVec_6"
## [70] "Feature_8_ArimaVec_7" "Feature_8_ArimaVec_8" "Feature_8_ArimaVec_9"
## [73] "Feature_9_ArimaVec_1" "Feature_9_ArimaVec_2" "Feature_9_ArimaVec_3"
## [76] "Feature_9_ArimaVec_4" "Feature_9_ArimaVec_5" "Feature_9_ArimaVec_6"
## [79] "Feature_9_ArimaVec_7" "Feature_9_ArimaVec_8" "Feature_9_ArimaVec_9"
## [82] "Feature_10_ArimaVec_1" "Feature_10_ArimaVec_2" "Feature_10_ArimaVec_3"
## [85] "Feature_10_ArimaVec_4" "Feature_10_ArimaVec_5" "Feature_10_ArimaVec_6"
## [88] "Feature_10_ArimaVec_7" "Feature_10_ArimaVec_8" "Feature_10_ArimaVec_9"
## [91] "Feature_11_ArimaVec_1" "Feature_11_ArimaVec_2" "Feature_11_ArimaVec_3"
## [94] "Feature_11_ArimaVec_4" "Feature_11_ArimaVec_5" "Feature_11_ArimaVec_6"
## [97] "Feature_11_ArimaVec_7" "Feature_11_ArimaVec_8" "Feature_11_ArimaVec_9"
## [100] "Feature_12_ArimaVec_1" "Feature_12_ArimaVec_2" "Feature_12_ArimaVec_3"
## [103] "Feature_12_ArimaVec_4" "Feature_12_ArimaVec_5" "Feature_12_ArimaVec_6"
## [106] "Feature_12_ArimaVec_7" "Feature_12_ArimaVec_8" "Feature_12_ArimaVec_9"
## [109] "Feature_13_ArimaVec_1" "Feature_13_ArimaVec_2" "Feature_13_ArimaVec_3"
## [112] "Feature_13_ArimaVec_4" "Feature_13_ArimaVec_5" "Feature_13_ArimaVec_6"
## [115] "Feature_13_ArimaVec_7" "Feature_13_ArimaVec_8" "Feature_13_ArimaVec_9"
## [118] "Feature_14_ArimaVec_1" "Feature_14_ArimaVec_2" "Feature_14_ArimaVec_3"
## [121] "Feature_14_ArimaVec_4" "Feature_14_ArimaVec_5" "Feature_14_ArimaVec_6"
## [124] "Feature_14_ArimaVec_7" "Feature_14_ArimaVec_8" "Feature_14_ArimaVec_9"
## [127] "Feature_15_ArimaVec_1" "Feature_15_ArimaVec_2" "Feature_15_ArimaVec_3"
## [130] "Feature_15_ArimaVec_4" "Feature_15_ArimaVec_5" "Feature_15_ArimaVec_6"
## [133] "Feature_15_ArimaVec_7" "Feature_15_ArimaVec_8" "Feature_15_ArimaVec_9"
## [136] "Feature_16_ArimaVec_1" "Feature_16_ArimaVec_2" "Feature_16_ArimaVec_3"
## [139] "Feature_16_ArimaVec_4" "Feature_16_ArimaVec_5" "Feature_16_ArimaVec_6"
## [142] "Feature_16_ArimaVec_7" "Feature_16_ArimaVec_8" "Feature_16_ArimaVec_9"
## [145] "Feature_17_ArimaVec_1" "Feature_17_ArimaVec_2" "Feature_17_ArimaVec_3"
## [148] "Feature_17_ArimaVec_4" "Feature_17_ArimaVec_5" "Feature_17_ArimaVec_6"
## [151] "Feature_17_ArimaVec_7" "Feature_17_ArimaVec_8" "Feature_17_ArimaVec_9"
## [154] "Feature_18_ArimaVec_1" "Feature_18_ArimaVec_2" "Feature_18_ArimaVec_3"
## [157] "Feature_18_ArimaVec_4" "Feature_18_ArimaVec_5" "Feature_18_ArimaVec_6"
## [160] "Feature_18_ArimaVec_7" "Feature_18_ArimaVec_8" "Feature_18_ArimaVec_9"
## [163] "Feature_19_ArimaVec_1" "Feature_19_ArimaVec_2" "Feature_19_ArimaVec_3"
## [166] "Feature_19_ArimaVec_4" "Feature_19_ArimaVec_5" "Feature_19_ArimaVec_6"
## [169] "Feature_19_ArimaVec_7" "Feature_19_ArimaVec_8" "Feature_19_ArimaVec_9"
## [172] "Feature_20_ArimaVec_1" "Feature_20_ArimaVec_2" "Feature_20_ArimaVec_3"
## [175] "Feature_20_ArimaVec_4" "Feature_20_ArimaVec_5" "Feature_20_ArimaVec_6"
## [178] "Feature_20_ArimaVec_7" "Feature_20_ArimaVec_8" "Feature_20_ArimaVec_9"
## [181] "Feature_21_ArimaVec_1" "Feature_21_ArimaVec_2" "Feature_21_ArimaVec_3"
## [184] "Feature_21_ArimaVec_4" "Feature_21_ArimaVec_5" "Feature_21_ArimaVec_6"
## [187] "Feature_21_ArimaVec_7" "Feature_21_ArimaVec_8" "Feature_21_ArimaVec_9"
## [190] "Feature_22_ArimaVec_1" "Feature_22_ArimaVec_2" "Feature_22_ArimaVec_3"
## [193] "Feature_22_ArimaVec_4" "Feature_22_ArimaVec_5" "Feature_22_ArimaVec_6"
## [196] "Feature_22_ArimaVec_7" "Feature_22_ArimaVec_8" "Feature_22_ArimaVec_9"
## [199] "Feature_23_ArimaVec_1" "Feature_23_ArimaVec_2" "Feature_23_ArimaVec_3"
## [202] "Feature_23_ArimaVec_4" "Feature_23_ArimaVec_5" "Feature_23_ArimaVec_6"
## [205] "Feature_23_ArimaVec_7" "Feature_23_ArimaVec_8" "Feature_23_ArimaVec_9"
## [208] "Feature_24_ArimaVec_1" "Feature_24_ArimaVec_2" "Feature_24_ArimaVec_3"
## [211] "Feature_24_ArimaVec_4" "Feature_24_ArimaVec_5" "Feature_24_ArimaVec_6"
## [214] "Feature_24_ArimaVec_7" "Feature_24_ArimaVec_8" "Feature_24_ArimaVec_9"
## [217] "Feature_25_ArimaVec_1" "Feature_25_ArimaVec_2" "Feature_25_ArimaVec_3"
## [220] "Feature_25_ArimaVec_4" "Feature_25_ArimaVec_5" "Feature_25_ArimaVec_6"
## [223] "Feature_25_ArimaVec_7" "Feature_25_ArimaVec_8" "Feature_25_ArimaVec_9"
## [226] "Feature_26_ArimaVec_1" "Feature_26_ArimaVec_2" "Feature_26_ArimaVec_3"
## [229] "Feature_26_ArimaVec_4" "Feature_26_ArimaVec_5" "Feature_26_ArimaVec_6"
## [232] "Feature_26_ArimaVec_7" "Feature_26_ArimaVec_8" "Feature_26_ArimaVec_9"
## [235] "Feature_27_ArimaVec_1" "Feature_27_ArimaVec_2" "Feature_27_ArimaVec_3"
## [238] "Feature_27_ArimaVec_4" "Feature_27_ArimaVec_5" "Feature_27_ArimaVec_6"
## [241] "Feature_27_ArimaVec_7" "Feature_27_ArimaVec_8" "Feature_27_ArimaVec_9"
## [244] "Feature_28_ArimaVec_1" "Feature_28_ArimaVec_2" "Feature_28_ArimaVec_3"
## [247] "Feature_28_ArimaVec_4" "Feature_28_ArimaVec_5" "Feature_28_ArimaVec_6"
## [250] "Feature_28_ArimaVec_7" "Feature_28_ArimaVec_8" "Feature_28_ArimaVec_9"
## [253] "Feature_29_ArimaVec_1" "Feature_29_ArimaVec_2" "Feature_29_ArimaVec_3"
## [256] "Feature_29_ArimaVec_4" "Feature_29_ArimaVec_5" "Feature_29_ArimaVec_6"
## [259] "Feature_29_ArimaVec_7" "Feature_29_ArimaVec_8" "Feature_29_ArimaVec_9"
## [262] "Feature_30_ArimaVec_1" "Feature_30_ArimaVec_2" "Feature_30_ArimaVec_3"
## [265] "Feature_30_ArimaVec_4" "Feature_30_ArimaVec_5" "Feature_30_ArimaVec_6"
## [268] "Feature_30_ArimaVec_7" "Feature_30_ArimaVec_8" "Feature_30_ArimaVec_9"
## [271] "Feature_31_ArimaVec_1" "Feature_31_ArimaVec_2" "Feature_31_ArimaVec_3"
## [274] "Feature_31_ArimaVec_4" "Feature_31_ArimaVec_5" "Feature_31_ArimaVec_6"
## [277] "Feature_31_ArimaVec_7" "Feature_31_ArimaVec_8" "Feature_31_ArimaVec_9"
## [280] "Feature_32_ArimaVec_1" "Feature_32_ArimaVec_2" "Feature_32_ArimaVec_3"
## [283] "Feature_32_ArimaVec_4" "Feature_32_ArimaVec_5" "Feature_32_ArimaVec_6"
## [286] "Feature_32_ArimaVec_7" "Feature_32_ArimaVec_8" "Feature_32_ArimaVec_9"
## [289] "Feature_33_ArimaVec_1" "Feature_33_ArimaVec_2" "Feature_33_ArimaVec_3"
## [292] "Feature_33_ArimaVec_4" "Feature_33_ArimaVec_5" "Feature_33_ArimaVec_6"
## [295] "Feature_33_ArimaVec_7" "Feature_33_ArimaVec_8" "Feature_33_ArimaVec_9"
## [298] "Feature_34_ArimaVec_1" "Feature_34_ArimaVec_2" "Feature_34_ArimaVec_3"
## [301] "Feature_34_ArimaVec_4" "Feature_34_ArimaVec_5" "Feature_34_ArimaVec_6"
## [304] "Feature_34_ArimaVec_7" "Feature_34_ArimaVec_8" "Feature_34_ArimaVec_9"
## [307] "Feature_35_ArimaVec_1" "Feature_35_ArimaVec_2" "Feature_35_ArimaVec_3"
## [310] "Feature_35_ArimaVec_4" "Feature_35_ArimaVec_5" "Feature_35_ArimaVec_6"
## [313] "Feature_35_ArimaVec_7" "Feature_35_ArimaVec_8" "Feature_35_ArimaVec_9"
## [316] "Feature_36_ArimaVec_1" "Feature_36_ArimaVec_2" "Feature_36_ArimaVec_3"
## [319] "Feature_36_ArimaVec_4" "Feature_36_ArimaVec_5" "Feature_36_ArimaVec_6"
## [322] "Feature_36_ArimaVec_7" "Feature_36_ArimaVec_8" "Feature_36_ArimaVec_9"
## [325] "Feature_37_ArimaVec_1" "Feature_37_ArimaVec_2" "Feature_37_ArimaVec_3"
## [328] "Feature_37_ArimaVec_4" "Feature_37_ArimaVec_5" "Feature_37_ArimaVec_6"
## [331] "Feature_37_ArimaVec_7" "Feature_37_ArimaVec_8" "Feature_37_ArimaVec_9"
## [334] "Feature_38_ArimaVec_1" "Feature_38_ArimaVec_2" "Feature_38_ArimaVec_3"
## [337] "Feature_38_ArimaVec_4" "Feature_38_ArimaVec_5" "Feature_38_ArimaVec_6"
## [340] "Feature_38_ArimaVec_7" "Feature_38_ArimaVec_8" "Feature_38_ArimaVec_9"
## [343] "Feature_39_ArimaVec_1" "Feature_39_ArimaVec_2" "Feature_39_ArimaVec_3"
## [346] "Feature_39_ArimaVec_4" "Feature_39_ArimaVec_5" "Feature_39_ArimaVec_6"
## [349] "Feature_39_ArimaVec_7" "Feature_39_ArimaVec_8" "Feature_39_ArimaVec_9"
## [352] "Feature_40_ArimaVec_1" "Feature_40_ArimaVec_2" "Feature_40_ArimaVec_3"
## [355] "Feature_40_ArimaVec_4" "Feature_40_ArimaVec_5" "Feature_40_ArimaVec_6"
## [358] "Feature_40_ArimaVec_7" "Feature_40_ArimaVec_8" "Feature_40_ArimaVec_9"
## [361] "Feature_41_ArimaVec_1" "Feature_41_ArimaVec_2" "Feature_41_ArimaVec_3"
## [364] "Feature_41_ArimaVec_4" "Feature_41_ArimaVec_5" "Feature_41_ArimaVec_6"
## [367] "Feature_41_ArimaVec_7" "Feature_41_ArimaVec_8" "Feature_41_ArimaVec_9"
## [370] "Feature_42_ArimaVec_1" "Feature_42_ArimaVec_2" "Feature_42_ArimaVec_3"
## [373] "Feature_42_ArimaVec_4" "Feature_42_ArimaVec_5" "Feature_42_ArimaVec_6"
## [376] "Feature_42_ArimaVec_7" "Feature_42_ArimaVec_8" "Feature_42_ArimaVec_9"
## [379] "IncomeGroup" "PopSizeGroup" "ED"
## [382] "Edu" "HI" "QOL"
## [385] "PE" "Relig" "OA"# IFT_SwappedPhase_FT_aggregate_arima_vector[1:5, 1:4]; temp_Data[1:5, 1:4]
# 2. Perform LASSO modeling on IFT_SwappedPhase_FT_aggregate_arima_vector;
# report param estimates and quality metrics AIC/BIC
set.seed(12)
cvLASSO_kime_swapped =
cv.glmnet(data.matrix(IFT_SwappedPhase_FT_aggregate_arima_vector[ , 1:378]),
Y, alpha = 1, parallel=TRUE)
plot(cvLASSO_kime_swapped)
mtext("(Spacekime, Swapped-Phases) CV LASSO: Number of Nonzero (Active) Coefficients", side=3, line=2.5)
# Identify top predictors and forecast the Y=Overall (OA) Country ranking outcome
predLASSO_kime_swapped <- predict(cvLASSO_kime_swapped, s = cvLASSO_kime_swapped$lambda.min,
newx = data.matrix(IFT_SwappedPhase_FT_aggregate_arima_vector[ , 1:378]))
# testMSE_LASSO_kime_swapped <-
# mean((predLASSO_kime_swapped - IFT_SwappedPhase_FT_aggregate_arima_vector[ , 387])^2)
# testMSE_LASSO_kime_swapped
predLASSO_kime_swapped## s1
## 1 21.40840
## 2 23.47920
## 3 25.89234
## 4 23.44779
## 5 23.70241
## 6 23.40227
## 7 21.84031
## 8 24.93078
## 9 22.40592
## 10 20.66644
## 11 22.47175
## 12 25.25671
## 13 24.46827
## 14 20.91749
## 15 21.26995
## 16 26.03118
## 17 23.69678
## 18 26.87516
## 19 20.10879
## 20 26.20338
## 21 22.97204
## 22 21.65921
## 23 25.10388
## 24 21.23313
## 25 23.69988
## 26 23.12448
## 27 21.23837
## 28 22.71054
## 29 22.84611
## 30 22.76365
## 31 21.17338# Plot Regression Coefficients: create variable names for plotting
betaHatLASSO_kime_swapped = as.double(coef(cvLASSO_kime_swapped,
s=cvLASSO_kime_swapped$lambda.min))
#cvLASSO_kime_swapped$lambda.1se
#coefplot(betaHatLASSO_kime_swapped[377:386], sd = rep(0, 10), pch=0, cex.pts = 3, col="red",
# main = "(Spacekime, Swapped-Phases) LASSO-Regularized Regression Coefficient Estimates",
# varnames = varNames[377:386])
varImp(cvLASSO_kime_swapped, lambda = cvLASSO_kime_swapped$lambda.min)## Overall
## Feature_27_ArimaVec_6 2.720954coefList_kime_swapped <- coef(cvLASSO_kime_swapped, s='lambda.min')
coefList_kime_swapped <- data.frame(coefList_kime_swapped@Dimnames[[1]][coefList_kime_swapped@i+1], coefList_kime_swapped@x)
names(coefList_kime_swapped) <- c('Feature','EffectSize')
arrange(coefList_kime_swapped, -abs(EffectSize))[2:10, ]## Feature EffectSize
## 2 Feature_27_ArimaVec_6 2.720954
## NA <NA> NA
## NA.1 <NA> NA
## NA.2 <NA> NA
## NA.3 <NA> NA
## NA.4 <NA> NA
## NA.5 <NA> NA
## NA.6 <NA> NA
## NA.7 <NA> NA# Feature EffectSize
#2 Feature_2_ArimaVec_8 1.484856e+15
#3 Feature_42_ArimaVec_7 1.970862e+14
#4 Feature_23_ArimaVec_7 -2.467246e+13
#5 Feature_37_ArimaVec_5 -2.983216e+00
#6 Feature_34_ArimaVec_4 -1.382639e+00
#7 Feature_36_ArimaVec_3 -1.198157e+00
#8 Feature_6_ArimaVec_3 1.106294e-01
#9 Feature_38_ArimaVec_2 -1.058259e-02
#10 Feature_38_ArimaVec_1 -1.124584e-03
#
# ARIMA-spacetime: 4=non-seasonal MA, 5=seasonal AR, 8=non-seasonal Diff
# ARIMA-spacekime_nill: 3=non-seasonal AR, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA
# ARIMA-spacekime_swapped: 3=non-seasonal AR, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA
# 9 ARIMA-derived vector includes:
# (1=ts_avg, 2=forecast_avg, 3=non-seasonal AR, 4=non-seasonal MA, 5=seasonal AR, 6=seasonal MA,
# 7=period, 8=non-seasonal Diff, 9=seasonal differences)
coef(cvLASSO_kime_swapped, s = "lambda.min") %>%
broom::tidy() %>%
filter(row != "(Intercept)") %>%
top_n(100, wt = abs(value)) %>%
ggplot(aes(value, reorder(row, value), color = value > 0)) +
geom_point(show.legend = FALSE, aes(size = abs(value))) +
ggtitle("(Spacekime, Swapped-Phases) Top 9 salient features (LASSO penalty)") +
xlab("Effect-size") +
ylab(NULL)
# pack a 31*4 DF with (predLASSO_kime, IFT_NilPhase_FT_aggregate_arima_vector_Y,
# IFT_SwappedPhase_FT_aggregate_arima_vector_Y, Y)
validation_kime_swapped <- cbind(predLASSO[, 1], predLASSO_nil_kime_all[, 1],
predLASSO_kime_swapped[ , 1], Y)
colnames(validation_kime_swapped) <- c("predLASSO (spacetime)", "predLASSO_IFT_NilPhase",
"predLASSO_IFT_SwappedPhase", "Orig_Y")
head(validation_kime_swapped); dim(validation_kime_swapped)## predLASSO (spacetime) predLASSO_IFT_NilPhase predLASSO_IFT_SwappedPhase
## 1 16.57141 17.85361 21.40840
## 2 16.07527 20.99808 23.47920
## 3 35.87831 20.91310 25.89234
## 4 28.53495 20.62338 23.44779
## 5 48.71516 31.45441 23.70241
## 6 26.09735 24.42391 23.40227
## Orig_Y
## 1 18
## 2 19
## 3 38
## 4 28
## 5 50
## 6 25## [1] 31 4# Prediction correlations:
cor(validation_kime_swapped[ , 3], validation_kime_swapped[, 4]) ## [1] 0.5504575# predLASSO_IFT_SwappedPhase OA rank vs. predLASSO_spacekime: 0.7
cor(validation_kime_swapped[ , 1], validation_kime_swapped[, 3]) ## [1] 0.5587323# predLASSO (spacetime) vs. predLASSO_IFT_SwappedPhase OA rank: 0.83
# Plot observed Y (Overall Country ranking), x-axis vs. Kime-Swapped LASSO (9-parameters) predicted Y^
linFit1_kime_swapped <- lm(validation_kime_swapped[ , 3] ~ validation_kime_swapped[ , 4])
plot(validation_kime_swapped[ , 3] ~ validation_kime_swapped[ , 4],
col="blue", xaxt='n', yaxt='n', pch = 16, cex=3,
xlab="predLASSO_IFT_SwappedPhase_FT_Y", ylab="predLASSO_spacekime_swapped Country Overall Ranking",
main = sprintf("Observed (x) vs. Kime IFT_SwappedPhase_FT_Y (y) Overall Country Ranking, cor=%.02f",
cor(validation_kime_swapped[ , 3], validation_kime_swapped[, 4])))
abline(linFit1_kime_swapped, lwd=3, col="red")
#abline(linFit1_kime, lwd=3, col="green")
# Plot Spacetime LASSO forecasting
# Plot observed Y (Overall Country ranking), x-axis vs. LASSO (9-parameters) predicted Y^, y-axis
linFit1_spacetime <- lm(validation_kime_swapped[ , 3] ~ validation_kime_swapped[ , 4])
plot(validation_kime_swapped[ , 3] ~ validation_kime_swapped[ , 4],
col="blue", xaxt='n', yaxt='n', pch = 16, cex=3,
xlab="Observed Country Overall Ranking", ylab="predLASSO_spacetime",
main = sprintf("Predicted (y) vs. Observed (x) Overall Country Ranking, cor=%.02f",
cor(validation_kime_swapped[ , 3], validation_kime_swapped[, 4])))
abline(linFit1_spacetime, lwd=3, col="red")
# add Top_30_Ranking_Indicator
validation_kime_swapped <- as.data.frame(cbind(validation_kime_swapped, ifelse (validation_kime_swapped[,4]<=30, 1, 0)))
colnames(validation_kime_swapped)[5] <- "Top30Rank"
rownames(validation_kime_swapped)[11] <- "Germany"
head(validation_kime_swapped)## predLASSO (spacetime) predLASSO_IFT_NilPhase predLASSO_IFT_SwappedPhase
## 1 16.57141 17.85361 21.40840
## 2 16.07527 20.99808 23.47920
## 3 35.87831 20.91310 25.89234
## 4 28.53495 20.62338 23.44779
## 5 48.71516 31.45441 23.70241
## 6 26.09735 24.42391 23.40227
## Orig_Y Top30Rank
## 1 18 1
## 2 19 1
## 3 38 0
## 4 28 1
## 5 50 0
## 6 25 1# Write out the Binary top-30/Not-Top-30 labels
df_top30 <- cbind(countryNames, validation_kime_swapped[ , 5])
colnames(df_top30) <- c("Country", "Top-30-Label")
write.table(df_top30,
fileEncoding = "UTF-16LE", append = FALSE, quote = FALSE, sep = "\t",
eol = "\n", na = "NA", dec = ".", row.names = FALSE, col.names = TRUE,
"E:/Ivo.dir/Research/UMichigan/Publications_Books/2018/others/4D_Time_Space_Book_Ideas/ARIMAX_EU_DataAnalytics/EU_Econ_Labels_31Countries_Top_30_BinaryOutcome.txt")
# Spacetime LASSO modeling
myPlotSwappedPhase <- ggplot(as.data.frame(validation_kime_swapped), aes(x=Orig_Y,
y=validation_kime_swapped[, 3], label=rownames(validation_kime_swapped))) +
geom_smooth(method='lm') +
geom_point() +
# Color by groups
# geom_text(aes(color=factor(rownames(validation_kime_swapped)))) +
geom_label_repel(aes(label = rownames(validation_kime_swapped),
fill = factor(Top30Rank)), color = 'black', size = 5,
point.padding = unit(0.3, "lines")) +
# theme(legend.position = "bottom") +
theme(legend.position = c(0.1, 0.9),
legend.text = element_text(colour="black", size=12, face="bold"),
legend.title = element_text(colour="black", size=14, face="bold")) +
scale_fill_discrete(name = "Country Overall Ranking",
labels = c("Below 30 Rank", "Top 30 Rank")) +
labs(title=sprintf("Spacekime LASSO Predicted, Swapped-Phases (y) vs. Observed (x) Overall Country Ranking, cor=%.02f", cor(validation_kime_swapped[ , 3], validation_kime_swapped[, 4])),
x ="Observed Overall Country Ranking (1 is 'best')",
y = "Spacekime LASSO Predicted, using Swapped-Phases")
myPlotSwappedPhase
12.3.3.1 Overall Plots
myPlotNilPhase <- ggplot(as.data.frame(validation_kime_swapped), aes(x=Orig_Y,
y=predLASSO_kime, label=rownames(validation_kime_swapped))) +
geom_smooth(method='lm') +
geom_point() +
# Color by groups
# geom_text(aes(color=factor(rownames(validation_kime_swapped)))) +
geom_label_repel(aes(label = rownames(validation_kime_swapped),
fill = factor(Top30Rank)), color = 'black', size = 5,
point.padding = unit(0.3, "lines")) +
# theme(legend.position = "bottom") +
theme(legend.position = c(0.1, 0.9),
legend.text = element_text(colour="black", size=12, face="bold"),
legend.title = element_text(colour="black", size=14, face="bold")) +
scale_fill_discrete(name = "Country Overall Ranking",
labels = c("Below 30 Rank", "Top 30 Rank")) +
labs(title=sprintf("Spacekime LASSO Predicted, Nil-Phases, (y) vs. Observed (x) Overall Country Ranking, cor=%.02f", cor(validation_kime_swapped[ , 2], validation_kime_swapped[, 4])),
x ="Observed Overall Country Ranking (1 is 'best')",
y = "Spacekime LASSO Predicted, using Nil-Phases")
myPlotNilPhase
countryNames[11]<-"Germany"
aggregateResults <- (rbind(cbind(as.character(countryNames), "predLASSO_spacetime_386", as.numeric(predLASSO)),
cbind(as.character(countryNames), "predLASSO_spacetime_378", predLASSO_lim),
cbind(as.character(countryNames), "predLASSO_nil_kime_386", predLASSO_nil_kime_all),
cbind(as.character(countryNames), "predLASSO_nil_kime_378", predLASSO_nil_kime),
cbind(as.character(countryNames), "predLASSO_swapped_kime_386", predLASSO_kime_swapped),
cbind(as.character(countryNames), "predLASSO_swapped_kime_378", predLASSO_kime_swapped_lim),
cbind(as.character(countryNames), "observed", Y)
))
aggregateResults <- data.frame(aggregateResults[ , -3], as.numeric(aggregateResults[,3]))
colnames(aggregateResults) <- c("country", "estimate_method", "ranking")
ggplot(aggregateResults, aes(x=country, y=ranking, color=estimate_method)) +
geom_point(aes(shape=estimate_method, color=estimate_method, size=estimate_method)) +
geom_point(size = 5) +
geom_line(data = aggregateResults[aggregateResults$estimate_method == "observed", ],
aes(group = estimate_method), size=2, linetype = "dashed") +
theme(axis.text.x = element_text(angle=90, hjust=1, vjust=.5)) +
# theme(legend.position = "bottom") +
# scale_shape_manual(values = as.factor(aggregateResults$estimate_method)) +
# scale_color_gradientn(colours = rainbow(7)) +
theme(text = element_text(size = 15), legend.position = c(0.3, 0.85),
axis.text=element_text(size=16),
legend.text = element_text(colour="black", size=12, face="bold"),
legend.title = element_text(colour="black", size=14, face="bold"))
library(plotly)
plot_ly(aggregateResults) %>%
add_markers(x = ~country, y = ~ranking, type = "scatter",
color = ~estimate_method, colors = c("black", "red", "blue", "green", "purple", "orange", "yellow"),
mode = "markers", marker = list(size = ~ranking, opacity=~(1-(ranking-1)/49),
line = list(color = "black", width = 2))) %>%
layout(title="Spacekime Analytics - Country Ranking using Different Phase Estimators",
legend = list(orientation = "h", # show legend horizontally
xanchor = "center", # use center of legend as anchor
x = 0)) # put legend in center of x-axis)12.3.4 Unsupervised clustering
Use hierarchical, k-means and spectral clustering to generate derived-computed phenotypes of countries. Do these derived labels relate (correspond to) the overall (OA) country ranking?
load("E:/Ivo.dir/Research/UMichigan/Publications_Books/2018/others/4D_Time_Space_Book_Ideas/ARIMAX_EU_DataAnalytics/EU_Econ_SpaceKime.RData")
# View(aggregate_arima_vector_country_ranking_df)
dim(aggregate_arima_vector_country_ranking_df) ## [1] 31 387# 31(countries) 387(features)
# Features = country-index + 386 features (378 time-series derivatives + 8 meta-data features)12.3.4.1 Spacetime analytics
- 1.1 Lasso features selection
eudata <- aggregate_arima_vector_country_ranking_df
colnames(eudata) <- c("country",colnames(eudata[,-1]))
eudata <- eudata[ , -ncol(eudata)]
Y<-aggregate_arima_vector_country_ranking_df$OA
# Complete data 386 features (378 + 8)
X<-eudata[,-ncol(eudata)]; dim(X)## [1] 31 385# TS-derivative features only (378)
X378 <- X[, -c(379:386)]; dim(X378)## [1] 31 378countryinfo<-as.character(X[,1])
countryinfo[11]<-"Germany"
X<-X[,-1]
keeplist<-NULL
for (i in 1:ncol(X)) {
if(FALSE %in% (X[,i]==mean(X[,i]))) {keeplist<-c(keeplist,i)}
}
X<-X[,keeplist]; dim(X)## [1] 31 290# Reduced to 378 features
#countryinfo<-as.character(X378[,1])
#countryinfo[11]<-"Germany"
#X378<-X378[,-1]
#keeplist<-NULL
#for (i in 1:ncol(X378)) {
# if(FALSE %in% (X378[,i]==mean(X378[,i]))) {keeplist<-c(keeplist,i)}
#}
#X378<-X378[,keeplist]; dim(X378)
library(glmnet)
fitLASSO <- glmnet(as.matrix(X), Y, alpha = 1)
library(doParallel)
registerDoParallel(5)
#cross-validation
cvLASSO = cv.glmnet(data.matrix(X), Y, alpha = 1, parallel=TRUE)
# fitLASSO <- glmnet(as.matrix(X378), Y, alpha = 1)
#library(doParallel)
#registerDoParallel(5)
#cross-validation
#cvLASSO = cv.glmnet(data.matrix(X378), Y, alpha = 1, parallel=TRUE)
# To choose features we like to have based on lasso
chooselambda <- function(cvlasso, option, k=NULL) {
lambmat<-cbind(cvlasso$glmnet.fit$df,cvlasso$glmnet.fit$lambda)
result<-tapply(lambmat[,2],lambmat[,1],max)
kresult<-result[which(names(result)==as.factor(k))]
if(option==1) {return(result)}
else if (option==2) {return(kresult)}
else (return("Not a valid option"))
}
showfeatures <- function(object, lambda, k ,...) {
lam<-lambda[which(names(lambda)==as.factor(k))]
beta <- predict(object, s = lam, type = "coef")
if(is.list(beta)) {
out <- do.call("cbind", lapply(beta, function(x) x[,1]))
out <- as.data.frame(out)
s <- rowSums(out)
out <- out[which(s)!=0,,drop=FALSE]
} else {out<-data.frame(Overall = beta[,1])
out<-out[which(out!=0),,drop=FALSE]
}
out <- abs(out[rownames(out) != "(Intercept)",,drop = FALSE])
out
}- ** 1.2 Comparison of different ML algorithms of different feature numbers**
#test training data setup
randchoose <- function(matr) {
leng<-nrow(matr)
se<-seq(1:leng)
sam<-sample(se,as.integer(leng*0.6))
return(sam)
}
eusample<-X
eusample$Rank<-as.factor(ifelse(Y<30, 1, 0))
set.seed(1234)
eutrain<-eusample[randchoose(eusample), ]
set.seed(1234)
eutest<-eusample[-randchoose(eusample), ]
eusample378 <- X378
eusample378$Rank <- as.factor(ifelse(Y<30, 1, 0))
set.seed(1234)
eutrain378 <- eusample378[randchoose(eusample378), ]
set.seed(1234)
eutest378 <- eusample378[-randchoose(eusample378), ]
# Load Libraries
library(e1071)
library("randomForest")
library(ada); library(adabag)
library(caret)
library(kernlab)
library(cluster)
library(ipred)
library(ggplot2)
MLcomp <- function(fitlas, cvlas, trn, test, option=1) {
allfeat<-as.numeric(names(chooselambda(cvlasso = cvlas, option = 1)))
allfeat<-allfeat[which(allfeat>4)]
trainlist<-as.list(NULL)
for (i in 1:length(allfeat)) {
trainlist[[i]]<-trn[,which(colnames(trn) %in%
c(row.names(showfeatures(fitlas, chooselambda(cvlas = cvlas,1), allfeat[i])), "Rank"))]
}
resultframe<-data.frame(origin=rep(NA,length(allfeat)))
rownames(resultframe)<-allfeat
resultframe$Decision_tree_bagging<-rep(NA,length(allfeat))
for (i in 1:length(allfeat)) {
set.seed(1234)
eubag<-ipred::bagging(Rank~.,data = trainlist[[i]],nbagg=100)
bagtest<-predict(eubag, eutest)
bagagg<-bagtest==eutest$Rank
accuracy<-prop.table(table(bagagg))[c("TRUE")]
resultframe$Decision_tree_bagging[i]<-accuracy
}
resultframe$Random_forest<-rep(NA,length(allfeat))
for (i in 1:length(allfeat)) {
set.seed(1234)
eurf<-randomForest(Rank~.,data=trainlist[[i]])
rftest<-predict(eurf,eutest)
rfagg<-rftest==eutest$Rank
accuracy<-prop.table(table(rfagg))[c("TRUE")]
resultframe$Random_forest[i]<-accuracy
}
resultframe$Decision_tree_adaboost<-rep(NA,length(allfeat))
for (i in 1:length(allfeat)) {
set.seed(1234)
enada<-ada(Rank~.,data = trainlist[[i]],iter=50)
adatest<-predict(enada,eutest)
adaagg<-adatest==eutest$Rank
accuracy<-prop.table(table(adaagg))[c("TRUE")]
resultframe$Decision_tree_adaboost[i]<-accuracy
}
resultframe$GLM<-rep(NA,length(allfeat))
for (i in 1:length(allfeat)) {
euglm<-glm(Rank~.,data = trainlist[[i]],family = "binomial")
glmtest<-predict(euglm,eutest)
glmtest<-ifelse(glmtest<0,0,1)
glmagg<-glmtest==eutest$Rank
accuracy<-prop.table(table(glmagg))[c("TRUE")]
resultframe$GLM[i]<-accuracy
}
resultframe$SVM_best_Gamma_Cost<-rep(NA,length(allfeat))
for (i in 1:length(allfeat)) {
set.seed(1234)
svmtune<-tune.svm(Rank~.,data = trainlist[[i]],gamma = 10^(-6:1),cost = 10^(-10:10))
svmed<-svm(Rank~.,data=trainlist[[i]],gamma=svmtune$best.parameters[1],cost=svmtune$best.parameters[2])
svmtest<-predict(svmed,eutest)
svmagg<-svmtest==eutest$Rank
accuracy<-prop.table(table(svmagg))[c("TRUE")]
resultframe$SVM_best_Gamma_Cost[i]<-accuracy
}
resultframe$origin<-NULL
if(option==1){return(resultframe)}
}
resultframe <- MLcomp(fitLASSO, cvLASSO, eutrain, eutest, 1)
resultframe_386_ST <- resultframe
# View(resultframe_386_ST)
# resultframe_378_ST <- MLcomp(fitLASSO, cvLASSO, eutrain378, eutest378, 1)
# Display results
resultframe$features<-as.factor(as.numeric(rownames(resultframe)))
ppframe<-data.frame(NULL)
for (i in 1:5) {
FM <- data.frame(resultframe[,i], resultframe$features,
Methods<-rep(colnames(resultframe)[i], nrow(resultframe)))
ppframe<-rbind(ppframe, FM)
}
colnames(ppframe)<-c("Accuracy", "Features", "Methods")
ggplot(ppframe, aes(x=Features, y=Accuracy, colour=Methods,
group=Methods, shape=Methods))+
geom_line(position=position_dodge(0.2), lwd=2)+
ylim(0.2, 1.0) +
geom_point(size=5, position=position_dodge(0.2))+
theme(legend.position="top", legend.text=element_text(size=16))+
ggtitle("Spacetime (386 features): Compare ML Forecasting Results")+
theme(
axis.text=element_text(size=16),
plot.title = element_text(size=18, face="bold.italic"),
axis.title.x = element_text(size=14, face="bold"),
axis.title.y = element_text(size=14, face="bold"))
# spacetime (ST) 378_ST
resultframe_378_ST$features<-as.factor(as.numeric(rownames(resultframe_378_ST)))
ppframe_378_ST<-data.frame(NULL)
for (i in 1:5) {
FM_378_ST <- data.frame(resultframe_378_ST[,i], resultframe_378_ST$features,
Methods<-rep(colnames(resultframe_378_ST)[i], nrow(resultframe_378_ST)))
ppframe_378_ST<-rbind(ppframe_378_ST, FM_378_ST)
}
colnames(ppframe_378_ST)<-c("Accuracy", "Features", "Methods")
ggplot(ppframe_378_ST, aes(x=Features, y=Accuracy, colour=Methods,
group=Methods, shape=Methods))+
geom_line(position=position_dodge(0.2), lwd=2)+
ylim(0.2, 1.0) +
geom_point(size=5, position=position_dodge(0.2))+
theme(legend.position="top", legend.text=element_text(size=16))+
ggtitle("Spacetime (386 features): Compare ML Forecasting Results")+
theme(
axis.text=element_text(size=16),
plot.title = element_text(size=18, face="bold.italic"),
axis.title.x = element_text(size=14, face="bold"),
axis.title.y = element_text(size=14, face="bold"))
- 1.3 Clustering
showfeatures(fitLASSO, chooselambda(cvLASSO,1), 10)## Overall
## Feature_1_ArimaVec_8 5.256360e-01
## Feature_16_ArimaVec_4 6.716879e-01
## Feature_19_ArimaVec_8 3.949426e-01
## Feature_22_ArimaVec_4 1.796214e+00
## Feature_25_ArimaVec_1 9.911928e-04
## Feature_25_ArimaVec_4 4.972196e-01
## Feature_25_ArimaVec_5 3.717699e-01
## Feature_27_ArimaVec_3 1.693775e-02
## Feature_35_ArimaVec_4 9.390697e-01
## IncomeGroup 1.252439e+01feat_5 <- predict(fitLASSO, s = chooselambda(cvLASSO,2,10), newx = data.matrix(X))
df1 <- as.data.frame(rbind(as.numeric(feat_5),Y),
row.names = c("Predicted Rank","OA Rank"))
colnames(df1) <- countryNames
df1 # View(t(df1))## Austria Belgium Bulgaria Croatia Cyprus Czech Republic
## Predicted Rank 21.48021 22.01051 32.74413 21.15846 34.84274 21.90391
## OA Rank 18.00000 19.00000 38.00000 28.00000 50.00000 25.00000
## Denmark Estonia Finland France Germany Greece Hungary
## Predicted Rank 17.78768 21.21233 15.60224 16.10767 14.64532 21.15785 24.47112
## OA Rank 10.00000 32.00000 1.00000 16.00000 12.00000 26.00000 33.00000
## Iceland Ireland Italy Latvia Lithuania Luxembourg Malta
## Predicted Rank 35.20295 21.07326 20.1141 33.74456 35.48394 19.53351 35.39727
## OA Rank 36.00000 17.00000 23.0000 36.00000 34.00000 5.00000 50.00000
## Netherlands Norway Poland Portugal Romania Slovakia
## Predicted Rank 16.31461 11.33358 33.08849 22.12424 35.33505 20.73411
## OA Rank 8.00000 6.00000 29.00000 26.00000 39.00000 31.00000
## Slovenia Spain Sweden Switzerland United Kingdom
## Predicted Rank 22.59695 19.70497 18.95008 14.89101 16.25316
## OA Rank 24.00000 26.00000 3.00000 2.00000 14.00000# Clustering
cluster5 <- X[, which(colnames(X) %in%
row.names(showfeatures(fitLASSO, chooselambda(cvLASSO,1), 10)))]
rownames(cluster5) <- countryNames # countryinfo
#1. hierarchical clustering
scaled_cluster5 <- scale(cluster5)
##deal with NAN values
#scaled_country<-scaled_country[,which(is.nan(scaled_country[1,])==FALSE)]
dis_SC5 <- dist(scaled_cluster5)
H_clust_SC5 <- hclust(dis_SC5)
library("factoextra")
library("FactoMineR")
H_clust_SC5 <- eclust(scaled_cluster5, k=5, "hclust")
fviz_dend(H_clust_SC5, rect = TRUE, cex=0.5)
# fviz_dend(H_clust_SC5, lwd=2, rect = TRUE)
# ST 378
cluster5_378_ST <- X378[, which(colnames(X378) %in%
row.names(showfeatures(fitLASSO, chooselambda(cvLASSO,1), 10)))]
rownames(cluster5_378_ST) <- countryNames # countryinfo
#1. hierarchical clustering
scaled_cluster5_378_ST <- scale(cluster5_378_ST)
dis_SC5_378_ST <- dist(scaled_cluster5_378_ST)
H_clust_SC5_378_ST <- hclust(dis_SC5_378_ST)
H_clust_SC5_378_ST <- eclust(scaled_cluster5_378_ST, k=5, "hclust")
fviz_dend(H_clust_SC5_378_ST,rect = TRUE, cex=0.5)
12.3.4.2 Spacekime - Nil-Phase
** 2.1 Lasso features selection**
** 2.2 Comparison of different ML algorithms of different feature numbers**
** 2.3 Clustering**
12.3.4.3 Spacekime - Swapped-Phase
- ** 3.1 Lasso features selection**
dim(IFT_SwappedPhase_FT_aggregate_arima_vector)## [1] 31 387# [1] 31 387
eudata_SwappedPhase <- IFT_SwappedPhase_FT_aggregate_arima_vector
colnames(eudata_SwappedPhase) <- c("country", colnames(eudata_SwappedPhase[,-1]))
eudata_SwappedPhase <- as.data.frame(eudata_SwappedPhase[ , -ncol(eudata_SwappedPhase)])
Y <- as.data.frame(IFT_SwappedPhase_FT_aggregate_arima_vector)$OA
# Complete data 386 features (378 + 8)
X <- eudata_SwappedPhase
countryinfo<-as.character(X[,1])
countryinfo[11]<-"Germany"
X<-X[,-1]
keeplist<-NULL
for (i in 1:ncol(X)) {
if(FALSE %in% (X[,i]==mean(X[,i]))) {keeplist<-c(keeplist,i)}
}
X<-X[,keeplist]; dim(X) # 31 343## [1] 31 343# Reduced to 378 features
# TS-derivative features only (378)
# X378 <- X[, -c(379:386)]; dim(X378)
#countryinfo<-as.character(X378[,1])
#countryinfo[11]<-"Germany"
#X378<-X378[,-1]
#keeplist<-NULL
#for (i in 1:ncol(X378)) {
# if(FALSE %in% (X378[,i]==mean(X378[,i]))) {keeplist<-c(keeplist,i)}
#}
#X378<-X378[,keeplist]; dim(X378)
library(glmnet)
fitLASSO_X <- glmnet(as.matrix(X), Y, alpha = 1)
library(doParallel)
registerDoParallel(5)
#cross-validation
cvLASSO_X = cv.glmnet(data.matrix(X), Y, alpha = 1, parallel=TRUE)
# fitLASSO_X <- glmnet(as.matrix(X378), Y, alpha = 1)
#library(doParallel)
#registerDoParallel(5)
#cross-validation
#cvLASSO_X = cv.glmnet(data.matrix(X378), Y, alpha = 1, parallel=TRUE)
# To choose features we like to have based on lasso
chooselambda <- function(cvlasso, option, k=NULL) {
lambmat<-cbind(cvlasso$glmnet.fit$df,cvlasso$glmnet.fit$lambda)
result<-tapply(lambmat[,2],lambmat[,1],max)
kresult<-result[which(names(result)==as.factor(k))]
if(option==1) {return(result)}
else if (option==2) {return(kresult)}
else (return("Not a valid option"))
}
showfeatures <- function(object, lambda, k ,...) {
lam<-lambda[which(names(lambda)==as.factor(k))]
beta <- predict(object, s = lam, type = "coef")
if(is.list(beta)) {
out <- do.call("cbind", lapply(beta, function(x) x[,1]))
out <- as.data.frame(out)
s <- rowSums(out)
out <- out[which(s)!=0,,drop=FALSE]
} else {out<-data.frame(Overall = beta[,1])
out<-out[which(out!=0),,drop=FALSE]
}
out <- abs(out[rownames(out) != "(Intercept)",,drop = FALSE])
out
}- ** 3.2 Comparison of different ML algorithms of different feature numbers**
#test training data setup
randchoose <- function(matr) {
leng<-nrow(matr)
se<-seq(1:leng)
sam<-sample(se,as.integer(leng*0.6))
return(sam)
}
Xsample <- X
Xsample$Rank <- as.factor(ifelse(Y<30, 1, 0))
set.seed(1234)
Xtrain <- Xsample[randchoose(Xsample), ]
set.seed(1234)
Xtest <- Xsample[-randchoose(Xsample), ]
#Xsample378 <- X378
#Xsample378$Rank <- as.factor(ifelse(Y<30, 1, 0))
#set.seed(1234)
#Xtrain378 <- Xsample378[randchoose(Xsample378), ]
#set.seed(1234)
#Xtest378 <- Xsample378[-randchoose(Xsample378), ]
# Load Libraries
library(e1071)
library("randomForest")
library(ada); library(adabag)
library(caret)
library(kernlab)
library(cluster)
library(ipred)
library(ggplot2)
# resultXframe <- MLcomp(fitLASSO, cvLASSO, Xtrain, Xtest, 1)
MLcompX <- function(fitlas, cvlas, trn, test, option=1) {
allfeat<-as.numeric(names(chooselambda(cvlasso = cvlas, option = 1)))
allfeat<-allfeat[which(allfeat>4)]
trainlist<-as.list(NULL)
for (i in 1:length(allfeat)) {
trainlist[[i]]<-trn[,which(colnames(trn) %in%
c(row.names(showfeatures(fitlas, chooselambda(cvlas = cvlas,1), allfeat[i])), "Rank"))]
}
resultXframe<-data.frame(origin=rep(NA,length(allfeat)))
rownames(resultXframe)<-allfeat
resultXframe$Decision_tree_bagging<-rep(NA,length(allfeat))
for (i in 1:length(allfeat)) {
#ERROR HANDLING
possibleError <- tryCatch(
function () {
set.seed(1234)
Xbag<-ipred::bagging(Rank~ . ,data = trainlist[[i]], nbagg=100,
control=rpart.control(minsplit=2, cp=0.1, xval=10))
bagtest<-predict(Xbag, Xtest)
bagagg<-bagtest==Xtest$Rank
accuracy<-prop.table(table(bagagg))[c("TRUE")]
resultXframe$Decision_tree_bagging[i]<-accuracy
},
error=function(e) e
)
if(inherits(possibleError, "error")) next
# print(i)
}
resultXframe$Random_forest<-rep(NA,length(allfeat))
for (i in 1:length(allfeat)) {
set.seed(1234)
Xrf<-randomForest(Rank~.,data=trainlist[[i]])
rftest<-predict(Xrf,test)
rfagg<-rftest==test$Rank
accuracy<-prop.table(table(rfagg))[c("TRUE")]
resultXframe$Random_forest[i]<-accuracy
}
resultXframe$Decision_tree_adaboost<-rep(NA,length(allfeat))
for (i in 1:length(allfeat)) {
set.seed(1234)
Xada<-ada(Rank~.,data = trainlist[[i]],iter=50)
adatest<-predict(Xada,test)
adaagg<-adatest==test$Rank
accuracy<-prop.table(table(adaagg))[c("TRUE")]
resultXframe$Decision_tree_adaboost[i]<-accuracy
}
resultXframe$GLM<-rep(NA,length(allfeat))
for (i in 1:length(allfeat)) {
euglm<-glm(Rank~.,data = trainlist[[i]],family = "binomial")
glmtest<-predict(euglm,test)
glmtest<-ifelse(glmtest<0,0,1)
glmagg<-glmtest==test$Rank
accuracy<-prop.table(table(glmagg))[c("TRUE")]
resultXframe$GLM[i]<-accuracy
}
resultXframe$SVM_best_Gamma_Cost<-rep(NA,length(allfeat))
for (i in 1:length(allfeat)) {
set.seed(1234)
svmtune<-tune.svm(Rank~.,data = trainlist[[i]],gamma = 10^(-6:1),cost = 10^(-10:10))
svmed<-svm(Rank~.,data=trainlist[[i]],gamma=svmtune$best.parameters[1],cost=svmtune$best.parameters[2])
svmtest<-predict(svmed,test)
svmagg<-svmtest==test$Rank
accuracy<-prop.table(table(svmagg))[c("TRUE")]
resultXframe$SVM_best_Gamma_Cost[i]<-accuracy
}
resultXframe$origin<-NULL
if(option==1){return(resultXframe)}
}
resultXframe <- MLcompX(fitLASSO_X, cvLASSO_X, Xtrain, Xtest, 1)
resultXframe_386_SK_Swapped <- resultXframe
# View(resultXframe_386_SK_Swapped)
# resultXframe_378_SK_Swapped <- MLcompX(fitLASSO_X, cvLASSO_X, Xtrain378, Xtest378, 1)
# Display results
resultXframe$features<-as.factor(as.numeric(rownames(resultXframe)))
ppframeX<-data.frame(NULL)
for (i in 1:5) {
FM <- data.frame(resultXframe[,i], resultXframe$features,
Methods<-rep(colnames(resultXframe)[i], nrow(resultXframe)))
ppframeX<-rbind(ppframeX, FM)
}
colnames(ppframeX)<-c("Accuracy", "Features", "Methods")
ggplot(ppframeX, aes(x=Features, y=Accuracy, colour=Methods,
group=Methods, shape=Methods))+
geom_line(position=position_dodge(0.2), lwd=2)+
ylim(0.2, 1.0) +
geom_point(size=5, position=position_dodge(0.2))+
theme(legend.position="top", legend.text=element_text(size=16))+
ggtitle("Spacekime Swapped-Phases (386 features): Compare ML Forecasting Results")+
theme(
axis.text=element_text(size=16),
plot.title = element_text(size=18, face="bold.italic"),
axis.title.x = element_text(size=14, face="bold"),
axis.title.y = element_text(size=14, face="bold"))
# spacetime (ST) 378_ST
resultframe_378_ST$features<-as.factor(as.numeric(rownames(resultframe_378_ST)))
ppframe_378_ST<-data.frame(NULL)
for (i in 1:5) {
FM_378_ST <- data.frame(resultframe_378_ST[,i], resultframe_378_ST$features,
Methods<-rep(colnames(resultframe_378_ST)[i], nrow(resultframe_378_ST)))
ppframe_378_ST<-rbind(ppframe_378_ST, FM_378_ST)
}
colnames(ppframe_378_ST)<-c("Accuracy", "Features", "Methods")
ggplot(ppframe_378_ST, aes(x=Features, y=Accuracy, colour=Methods,
group=Methods, shape=Methods))+
geom_line(position=position_dodge(0.2), lwd=2)+
ylim(0.2, 1.0) +
geom_point(size=5, position=position_dodge(0.2))+
theme(legend.position="top", legend.text=element_text(size=16))+
ggtitle("Spacetime (386 features): Compare ML Forecasting Results")+
theme(
axis.text=element_text(size=16),
plot.title = element_text(size=18, face="bold.italic"),
axis.title.x = element_text(size=14, face="bold"),
axis.title.y = element_text(size=14, face="bold"))
##################### for resultXframe_378_SK_Swapped
resultXframe_378_SK_Swapped$features<-as.factor(as.numeric(rownames(resultXframe_378_SK_Swapped)))
ppframeX<-data.frame(NULL)
for (i in 1:5) {
FM <- data.frame(resultXframe_378_SK_Swapped[, i], resultXframe_378_SK_Swapped$features,
Methods<-rep(colnames(resultXframe_378_SK_Swapped)[i], nrow(resultXframe_378_SK_Swapped)))
ppframeX<-rbind(ppframeX, FM)
}
colnames(ppframeX)<-c("Accuracy", "Features", "Methods")
ggplot(ppframeX, aes(x=Features, y=Accuracy, colour=Methods,
group=Methods, shape=Methods))+
geom_line(position=position_dodge(0.2), lwd=2)+
ylim(0.2, 1.0) +
geom_point(size=5, position=position_dodge(0.2))+
theme(legend.position="top", legend.text=element_text(size=16))+
ggtitle("Spacekime Swapped-Phases (386 features): Compare ML Forecasting Results")+
theme(
axis.text=element_text(size=16),
plot.title = element_text(size=18, face="bold.italic"),
axis.title.x = element_text(size=14, face="bold"),
axis.title.y = element_text(size=14, face="bold"))
- ** 3.3 Clustering**
showfeatures(fitLASSO_X, chooselambda(cvLASSO_X, 1), 10)## Overall
## Feature_2_ArimaVec_8 1.235405e+15
## Feature_23_ArimaVec_7 4.550363e+13
## Feature_29_ArimaVec_2 9.442348e-06
## Feature_34_ArimaVec_4 1.176612e+00
## Feature_36_ArimaVec_3 2.950920e-02
## Feature_37_ArimaVec_5 2.057147e+00
## Feature_38_ArimaVec_2 8.574547e-03
## Feature_41_ArimaVec_5 5.030549e-03
## Feature_42_ArimaVec_7 1.945926e+14
## HI 6.324360e-01feat_5 <- predict(fitLASSO_X, s = chooselambda(cvLASSO_X, 2, 10), newx = data.matrix(X))
df1 <- as.data.frame(rbind(as.numeric(feat_5), Y),
row.names = c("Predicted Rank","OA Rank"))
colnames(df1) <- countryNames
df1 # View(t(df1))## Austria Belgium Bulgaria Croatia Cyprus Czech Republic
## Predicted Rank 17.28923 22.68372 29.93736 27.06854 34.19145 24.83282
## OA Rank 18.00000 19.00000 38.00000 28.00000 50.00000 25.00000
## Denmark Estonia Finland France Germany Greece Hungary
## Predicted Rank 17.01317 27.27495 16.15511 15.36158 15.28928 25.50112 28.71318
## OA Rank 10.00000 32.00000 1.00000 16.00000 12.00000 26.00000 33.00000
## Iceland Ireland Italy Latvia Lithuania Luxembourg Malta
## Predicted Rank 29.12328 22.9181 26.61231 29.25168 32.2068 14.0985 39.44405
## OA Rank 36.00000 17.0000 23.00000 36.00000 34.0000 5.0000 50.00000
## Netherlands Norway Poland Portugal Romania Slovakia
## Predicted Rank 14.72146 15.72675 26.03445 21.26028 28.77042 21.64072
## OA Rank 8.00000 6.00000 29.00000 26.00000 39.00000 31.00000
## Slovenia Spain Sweden Switzerland United Kingdom
## Predicted Rank 21.50078 20.36478 16.76813 13.03486 15.82017
## OA Rank 24.00000 26.00000 3.00000 2.00000 14.00000# Clustering
cluster5 <- X[, which(colnames(X) %in%
row.names(showfeatures(fitLASSO_X, chooselambda(cvLASSO_X, 1), 10)))]
rownames(cluster5) <- countryNames # countryinfo
#1. hierarchical clustering
scaled_cluster5 <- scale(cluster5)
##deal with NAN values
#scaled_country<-scaled_country[,which(is.nan(scaled_country[1,])==FALSE)]
dis_SC5 <- dist(scaled_cluster5)
H_clust_SC5 <- hclust(dis_SC5)
library("factoextra")
library("FactoMineR")
H_clust_SC5 <- eclust(scaled_cluster5, k=5, "hclust")
fviz_dend(H_clust_SC5, rect = TRUE, cex=0.5)
# fviz_dend(H_clust_SC5, lwd=2, rect = TRUE)
# ST 378
cluster5_378_SK <- X378[, which(colnames(X378) %in%
row.names(showfeatures(fitLASSO_X, chooselambda(cvLASSO_X, 1), 10)))]
rownames(cluster5_378_SK) <- countryNames # countryinfo
#1. hierarchical clustering
scaled_cluster5_378_SK <- scale(cluster5_378_SK)
dis_SC5_378_SK <- dist(scaled_cluster5_378_SK)
H_clust_SC5_378_SK <- hclust(dis_SC5_378_SK)
H_clust_SC5_378_SK <- eclust(scaled_cluster5_378_SK, k=5, "hclust")
fviz_dend(H_clust_SC5_378_SK,rect = TRUE, cex=0.5)
13 Save Workspace
# Save this entire Computed Workspace as an image:
# save.image("E:/Ivo.dir/Research/UMichigan/Publications_Books/2018/others/4D_Time_Space_Book_Ideas/ARIMAX_EU_DataAnalytics/EU_Econ_SpaceKime.RData")