######################################################
# Time-varying covariance modeling
#
# Copyright by Hedibert Freitas Lopes, PhD
# Date: March 22th 2019.
######################################################
# install.packages("bayesDccGarch")
# install.packages("stochvol")
# install.packages("factorstochvol")
library("bayesDccGarch")
library("factorstochvol")
library("stochvol")

data  = read.table("pbr-vale-google.txt",header=TRUE)
price = data[,4:6]
y     = apply(log(price),2,diff)
n     = nrow(y)
names = c("Petrobras","Vale","Google")

pdf(file="dccgarch-fsv.pdf",width=12,height=7)
par(mfrow=c(1,3))
for (i in 1:3)
  ts.plot(y[,i],ylim=range(y),xlab="days",main=names[i],ylab="Log-returns")

# Fitting univariate and multivariate 
# time-varying covariance models
fit.garch1 = bayesDccGarch(y[,1])
fit.garch2 = bayesDccGarch(y[,2])
fit.garch3 = bayesDccGarch(y[,3])
fit.dccgarch = bayesDccGarch(y)

fit.sv1 = svsample(y[,1])
fit.sv2 = svsample(y[,2])
fit.sv3 = svsample(y[,3])
fit.fsv = fsvsample(y,runningstore=5)

par(mfrow=c(1,1))
ts.plot(sqrt(fit.garch1$H[,1]),xlab="days",ylab="standard deviation")
lines(apply(exp(fit.sv2$latent/2),2,median),col=2)
lines(sqrt(fit.dccgarch$H[,1]),col=3)
lines(sqrt(fit.fsv$runningstore$cov[,1,1]),col=4)
legend("topleft",legend=c("garch","sv","dccgarch","fsv"),col=1:4,lty=1)
title("Petrobras")

par(mfrow=c(1,1))
ts.plot(sqrt(fit.garch2$H[,1]),xlab="days",ylab="standard deviation")
lines(apply(exp(fit.sv2$latent/2),2,median),col=2)
lines(sqrt(fit.dccgarch$H[,5]),col=3)
lines(sqrt(fit.fsv$runningstore$cov[,4,1]),col=4)
legend("topleft",legend=c("garch","sv","dccgarch","fsv"),col=1:4,lty=1)
title("Vale")


par(mfrow=c(1,1))
ts.plot(sqrt(fit.garch3$H[,1]),xlab="days",ylab="standard deviation")
lines(apply(exp(fit.sv3$latent/2),2,median),col=2)
lines(sqrt(fit.dccgarch$H[,9]),col=3)
lines(sqrt(fit.fsv$runningstore$cov[,6,1]),col=4)
legend("topleft",legend=c("garch","sv","dccgarch","fsv"),col=1:4,lty=1)
title("Google")


cor.dccgarch1 = fit.dccgarch$H[,2]/sqrt(fit.dccgarch$H[,1]*fit.dccgarch$H[,5])
cor.dccgarch2 = fit.dccgarch$H[,3]/sqrt(fit.dccgarch$H[,1]*fit.dccgarch$H[,9])
cor.dccgarch3 = fit.dccgarch$H[,6]/sqrt(fit.dccgarch$H[,5]*fit.dccgarch$H[,9])


Sy = cov(y)
Ry = cor(y)

par(mfrow=c(2,3))
ts.plot(fit.dccgarch$H[,2],ylab="covariance")
lines(fit.fsv$runningstore$cov[,2,1],col=2)
title(paste(names[1]," x ",names[2],sep=""))
legend("topright",legend=c("dccgarch","fsv"),col=1:2,lty=1)
abline(h=Sy[1,2],lty=2,col=3)

ts.plot(fit.dccgarch$H[,3],ylab="covariance")
lines(fit.fsv$runningstore$cov[,3,1],col=2)
title(paste(names[1]," x ",names[3],sep=""))
abline(h=Sy[1,3],lty=2,col=3)

ts.plot(fit.dccgarch$H[,6],ylab="covariance")
lines(fit.fsv$runningstore$cov[,5,1],col=2)
title(paste(names[2]," x ",names[3],sep=""))
abline(h=Sy[2,3],lty=2,col=3)

ts.plot(cor.dccgarch1,ylab="correlation",ylim=c(-0.2,1))
lines(fit.fsv$runningstore$cor[,1,1],col=2)
abline(h=Ry[1,2],lty=2,col=3)

ts.plot(cor.dccgarch2,ylab="correlation",ylim=c(-0.2,1))
lines(fit.fsv$runningstore$cor[,2,1],col=2)
abline(h=Ry[1,3],lty=2,col=3)

ts.plot(cor.dccgarch3,ylab="correlation",ylim=c(-0.2,1))
lines(fit.fsv$runningstore$cor[,3,1],col=2)
abline(h=Ry[2,3],lty=2,col=3)

dev.off()