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figure_3.R
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figure_3.R
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library(stochvol)
library(bayesianVARs)
library(mvtnorm)
library(colorspace)
dire <- "figures/"
if(!dir.exists(dire)) dir.create(dire)
data_sim <- function(T, M, p, PHI_setting, L_setting, SV=TRUE ,SV_setting=NULL, PHI_in =NULL, L_in = NULL) {
companion <- function(PHI, p, intercept = FALSE){
if(intercept) X <- PHI[-nrow(PHI),] else X <- PHI
M <- ncol(X)
X2 <- diag((p-1)*M)
X3 <- matrix(0, M, (p-1)*M)
companion <- cbind(X, rbind(X2,X3))
return(companion)
}
if(is.null(PHI_setting$intercept)){
K <- p*M
}else K <- p*M+1
# Coefficients
if(is.null(PHI_in)){
stable <- FALSE
while(stable == FALSE){
PHI <- matrix(0, K,M)
if(!is.null(PHI_setting$intercept)){
intercept <- rbinom(M,1, PHI_setting$intercept$p)
PHI[K,which(intercept==1)] <- rnorm(length(which(intercept==1)),PHI_setting$intercept$mu, PHI_setting$intercept$sigma)
}
for (lag in seq.int(p)) {
diagonal <- rbinom(M, 1, PHI_setting$diagonal$p/lag^PHI_setting$lag_penalizer)
diag(PHI[(M*(lag-1)+1):(M*lag), ])[which(diagonal==1)] <- rnorm(length(which(diagonal==1)), PHI_setting$diagonal$mu, PHI_setting$diagonal$sigma)
upper <- rbinom((M^2-M)/2, 1, PHI_setting$offdiagonal$p/lag^PHI_setting$lag_penalizer)
PHI[(M*(lag-1)+1):(M*lag),][upper.tri(PHI[(M*(lag-1)+1):(M*lag),])][which(upper==1)] <- rnorm(length(which(upper==1)), PHI_setting$offdiagonal$mu, PHI_setting$offdiagonal$sigma)
lower <- rbinom((M^2-M)/2, 1, PHI_setting$offdiagonal$p/lag^PHI_setting$lag_penalizer)
PHI[(M*(lag-1)+1):(M*lag),][lower.tri(PHI[(M*(lag-1)+1):(M*lag),])][which(lower==1)] <- rnorm(length(which(lower==1)),PHI_setting$offdiagonal$mu, PHI_setting$offdiagonal$sigma)
}
## check companion
PHI_comp <- companion(PHI, p, !is.null(PHI_setting$intercept))
if(max(Mod(eigen(PHI_comp, only.values = TRUE)$values)) < 0.99){
stable <- TRUE
}
}
}else{
if(nrow(PHI_in)==K | nrow(PHI_in)==(K+1)){
if(nrow(PHI_in)==(K+1)){
PHI_setting$intercept <- TRUE
}
}else{
stop("dim(PHI_in) does not coincide with p and M!")
}
PHI <- PHI_in
}
# L
if(is.null(L_in)){
L <- diag(M)
for(i in 2:(M)){
#L[i,1:(i-1)] <- rnorm(i-1)
ind <- rbinom(i-1,1,L_setting$p)
L[which(ind==1), i] <- rnorm(1,L_setting$mu, L_setting$sigma)
}
}else{
if(!identical(as.numeric((dim(L_in))), c(M,M))){
stop("dim(L_in) does not coincide with M!")
}
if(any(L_in[lower.tri(L_in)]!=0)){
stop("L_in must be an upper triangular matrix with ones on the diagonal!")
}
if(!all(diag(L_in)==1)){
stop("L_in must be an upper triangular matrix with ones on the diagonal!")
}
L <- L_in
}
L_inv <- backsolve(L, diag(M))
if(SV==TRUE){
# simulate volas
vol <- matrix(as.numeric(NA), T,M)
for (m in seq.int(M)) {
mu <- SV_setting$mu
phi <- runif(1, SV_setting$phi_range[1], SV_setting$phi_range[2])
sig <- runif(1, SV_setting$sigma_range[1], SV_setting$sigma_range[2])
sv_sim <- svsim(T, mu = mu, phi = phi, sigma = sig)
vol[,m] <- sv_sim$vol
}
}else if(SV==FALSE){
D <- diag(abs(rnorm(M)))
Sigma <- t(L_inv) %*% D %*% L_inv
}
# Y
Y <- matrix(as.numeric(NA), T+p, M)
if(SV==TRUE){
Y[1:p,] <- rnorm(p*M,0,exp(SV_setting$mu))
}else{
Y[1:p,] <- rnorm(p*M,0,1)
}
for (t in (1+p):(T+p)) {
if(SV==TRUE){
Sigma_t <- t(L_inv) %*% diag(vol[t-p,]^2) %*% L_inv
}else if(SV==FALSE){
Sigma_t <- Sigma
}
if(is.null(PHI_setting$intercept)){
meanvec <- as.vector(Y[(t-p):(t-1),])%*%PHI
}else meanvec <- c(as.vector(Y[(t-p):(t-1),]), 1)%*%PHI
Y[t,] <- mvtnorm::rmvnorm(1, mean = meanvec, sigma = Sigma_t)
}
return(list(PHI=PHI, L=L, Y=Y[-(1:p),]))
}
plotPHI <- function(object, summary = "median", colorbar = TRUE, ylabels = NULL, xlabels = NULL,
add_numbers = FALSE, zlim = NULL,main="",...){
optionals <- list(...)
PHI <- apply(object, 1:2, function(x) do.call(what = summary,
args = list(x)))
PHI_star <- t(apply(PHI, 1, rev)) # image orders differently
if(add_numbers){
alpha <- .5
}else{
alpha <- 1
}
if(summary %in% c("median", "mean")){
colspace <- colorspace::diverge_hcl(1001, alpha = alpha, palette = "Blue-Red")
if(is.null(zlim)){
zlim <- c(-max(abs(PHI)),max(abs(PHI)))
}
colbreaks <- seq(zlim[1]*1.001, zlim[2]*1.001, len=1002)#[-1]
}else if(summary %in% c("sd", "var", "IQR")){
colspace <- colorspace::sequential_hcl(1001, alpha = alpha, rev = TRUE,
palette = "Reds 2")#colorspace::sequential_hcl(1000, alpha = alpha, rev = TRUE)#colorspace::sequential_hcl(5, h = 0, c = c(100, 0), l = 65, rev = TRUE, power = 1, alpha = alpha) #colorspace::sequential_hcl(1000, alpha = alpha, rev = TRUE)
if(is.null(zlim)){
zlim <- c(0,max(abs(PHI)))
}
}
M <- ncol(PHI)
Kp <- nrow(PHI)
p <- floor(Kp/M)
if(colorbar){
oldpar <- par(no.readonly = TRUE)
if(!is.null(optionals$layoutmat)){
if(optionals$layoutmat){
on.exit(par(oldpar), add = TRUE)
mat <- matrix(c(rep(1,9),2),nrow = 10)
layout(mat)
}
}else{
#oldpar <- par(no.readonly = TRUE)
on.exit(par(oldpar), add = TRUE)
mat <- matrix(c(rep(1,9),2),nrow = 10)
layout(mat)
}
mymar <- oldpar$mar
mymar[1] <- 0.1
par(mar=mymar)
}
image((PHI_star), zlim = zlim ,xaxt = "n", yaxt="n", col = colspace,
bty="n", main = main)
if((Kp-1)>M){
abline(v = seq(M,Kp-1, M)/(Kp-1) - 0.5/(Kp-1), xpd = FALSE)
}
if(is.null(xlabels)){
axis(3, labels = rownames(PHI), at = seq(0,1, length.out=Kp),
tick = FALSE, las=2, cex.axis=.75)
}else if(xlabels=="lags"){
text(seq(M,Kp, M)/(Kp-1) - 0.5/(Kp-1) - M/(2*(Kp-1)), 1 + 0.5/(M-1) ,
pos = 3, xpd = TRUE, labels = paste0("Lag ", 1:p))
}
if(is.null(ylabels)){
axis(2, at = seq(1,0, length.out=M), labels = colnames(PHI),
tick = FALSE, las = 2, cex.axis=.75)
}
if(add_numbers){
text(rep(seq(0,1, length.out=Kp),M),
sort(rep(seq(1,0, length.out=M),Kp), decreasing = TRUE),
round(as.vector(PHI),3), cex=.75)
}
if(colorbar){
mymar2 <- oldpar$mar
mymar2[3] <- .1
mymar2[1] <- 2.1
par(mar=mymar2)
plot.new()
if(summary %in% c("median", "mean")){
colbarlim <- length(which(colbreaks<min(PHI_star)))
#colbarlim <- ceiling((min(PHI_star) - zlim[1]*1.001)/(diff(zlim)+2*zlim[2]/1000)*1001)
adjustedcolspace <- colspace[-c(1:(colbarlim-1))]
if(sign(min(PHI_star))!=sign(max(PHI_star))){
llabels <- round(c(colbreaks[colbarlim],0,tail(colbreaks,1)),2)
#llabels <- round(sort(c(range(PHI_star),0)),2)
#
at <- sort(c(0,1,(0-colbreaks[colbarlim])/(tail(colbreaks,1)-colbreaks[colbarlim])))
}else{
llabels <- round(range(PHI_star),2)
at <- c(0,1)
}
}else if(summary %in% c("sd", "var", "IQR")){
adjustedcolspace <- colspace
llabels <- round(zlim,2)
at <- c(0,1)
}
len <- length(adjustedcolspace)
xxx <- seq(0,1,length=len+1)
rect(xxx[1:len], rep(0, len), xxx[-1],
rep(1, len), col = adjustedcolspace, border = adjustedcolspace)
axis(1, labels = llabels, at = at,
tick = FALSE, las=1, cex.axis=.9, line=-1.2)
}
}
T <- 100
M <- 20
p <- 1
set.seed(1675)
PHI_in <- diag(M)*runif(M, -.8,.8)
PHI_in[1,20] <- runif(1, -.8,.8)
data <- data_sim(T, M, p,
PHI_setting = NULL,
L_setting = list(p=0.1, mu=0.001, sigma = 0.001),
SV = TRUE,
SV_setting = list(mu = -10, phi_range = c(0.85, 0.98), sigma_range= c(0.1,0.3)),
PHI_in = PHI_in)
PHI_true <- data$PHI
PHI_true <- array(PHI_true,c(M,M,1))
priorPHI_global <- specify_prior_phi(data = data$Y,lags = 1L,prior = "HS", global_grouping = "global")
priorPHI_semiglobal <- specify_prior_phi(data = data$Y,lags = 1L,prior = "HS", global_grouping = "olcl-lagwise")
priorL <- specify_prior_sigma(data = data$Y, type = "cholesky", cholesky_U_prior = "HS")
burnin <- 1000L
draws <- 10000L
mod_global <- bvar(data$Y, lags = 1L, prior_intercept = FALSE,
draws = draws, burnin = burnin,
prior_phi = priorPHI_global,
prior_sigma = priorL)
mod_semiglobal <- bvar(data$Y, lags = 1L, prior_intercept = FALSE,
draws = draws, burnin = burnin,
prior_phi = priorPHI_semiglobal,
prior_sigma = priorL)
fileprefix <- paste0(dire, "figure_3")
pdf(paste0(fileprefix, "a.pdf"), height = 5, width = 5)
par(mar = c(1,1,1,1))
plotPHI(PHI_true, add_numbers = FALSE, colorbar = TRUE, #layoutmat = FALSE,
main = "", xlabels = "", ylabels = "")
mtext("True", side = 1)
dev.off()
pdf(paste0(fileprefix, "b.pdf"), height = 5, width = 5)
par(mar = c(1,1,1,1))
plotPHI(mod_global$PHI, add_numbers = FALSE, colorbar = TRUE, #layoutmat = FALSE,
main = "", xlabels = "", ylabels = "")
mtext("Posterior median", side = 1)
dev.off()
pdf(paste0(fileprefix, "c.pdf"), height = 5, width = 5)
par(mar = c(1,1,1,1))
plotPHI(mod_global$PHI,"IQR", add_numbers = FALSE, colorbar = TRUE, #layoutmat = FALSE,
xlabels = "", ylabels = "")
mtext("Posterior interquartile range", side = 1)
dev.off()
pdf(paste0(fileprefix, "d.pdf"), height = 5, width = 5)
par(mar = c(1,1,1,1))
plotPHI(mod_semiglobal$PHI, add_numbers = FALSE, colorbar = TRUE, #layoutmat = FALSE,
main = "",xlabels = "", ylabels = "")
mtext("Posterior median", side = 1)
dev.off()
pdf(paste0(fileprefix, "e.pdf"), height = 5, width = 5)
par(mar = c(1,1,1,1))
plotPHI(mod_semiglobal$PHI,"IQR", add_numbers = FALSE, colorbar = TRUE, #layoutmat = FALSE,
xlabels = "", ylabels = "")
mtext("Posterior interquartile range", side = 1)
dev.off()