# https://finance.yahoo.com/quote/PBR/

library("stochvol")

data = read.csv("https://hedibert.org/wp-content/uploads/2024/06/PBR.csv")

names(data)

attach(data)

n    = nrow(data)

days = seq(1,n,length=5)
date = data[days,1]



y    = Adj.Close[2:n]/Adj.Close[1:(n-1)]-1

par(mfrow=c(1,1))
plot(Adj.Close,axes=FALSE,xlab="Day",ylab="Price (US dollars)",type="l")
axis(2);box()
axis(1,at=days,lab=date)

hist(y,breaks=seq(min(y),max(y),length=100),prob=TRUE,main="",
     xlab="Return")

plot(y,xlab="Week",ylab="Return",type="l",axes=FALSE)
axis(2);box()
axis(1,at=days,lab=date)


fit.svtl = svtlsample(y,draws=5000,burnin=1000,thin=1)
q.svtl   = t(apply(exp(fit.svtl$latent[[1]]/2),2,quantile,c(0.1,0.5,0.9)))
volvol   = sqrt(fit.svtl$para[[1]][,3]^2/(1-fit.svtl$para[[1]][,2]^2))

par(mfrow=c(2,3))
plot(density(fit.svtl$para[[1]][,1]),xlab=expression(mu),main="",lwd=2)
plot(density(fit.svtl$para[[1]][,2]),xlab=expression(phi),main="",lwd=2)
plot(density(fit.svtl$para[[1]][,3]),xlab=expression(sigma),main="",lwd=2)
plot(density(volvol),xlab=expression(sigma/sqrt(1-phi^2)),main="",lwd=2)
plot(density(fit.svtl$para[[1]][,4]),xlab=expression(nu),main="",lwd=2)
plot(density(fit.svtl$para[[1]][,5]),xlab=expression(rho),main="",lwd=2)


par(mfrow=c(1,1))
plot(q.svtl[,2],xlab="Day",main="SV-tl",lwd=2,type="l",ylab="Standard deviation",
ylim=c(-0.04,max(q.svtl)),col=2,axes=FALSE)
lines(q.svtl[,1],col=3)
lines(q.svtl[,3],col=3)
lines(0.2*y,type="h")
axis(2);box()
axis(1,at=days,lab=date)



days = seq(1500,2500,length=5)
date = data[days,1]
par(mfrow=c(1,1))
plot(q.svtl[1500:2500,2],xlab="Day",main="SV-tl",lwd=2,type="l",
     ylab="Standard deviation",col=2,axes=FALSE,ylim=c(0,0.12))
axis(2);box()
axis(1,at=days-1499,lab=date)
lines(0.2*abs(y[1500:2500]),type="h")