# STA 437/1005, Assignment #2, Question #1.

# Define functions for multivariate tests and confidence intervals.

source("mvn.r")

# Read the data into the data frame "ret".

ret <- read.table("ret.txt",head=T)

# Put plots in a PDF file (one per page).

pdf("ass2-Q1-plots.pdf",pointsize=9,horizontal=F)

# Plot each variable against year (which is the first variable).

par(mfrow=c(ncol(ret)-1,1))  # Seven plots on one page
par(mar=c(3,4,1,1))          # Small margins

for (i in 2:ncol(ret))
{ plot (ret$year, ret[,i], xlab="", ylab=colnames(ret)[i])
  abline(h=1)
}

# Histograms of returns and log returns.

par(mfrow=c(ncol(ret)-1,2))  # Seven plots on one page
par(mar=c(3,4,1,1))          # Small margins

for (i in 2:ncol(ret))
{ hist (ret[,i], main=colnames(ret)[i])
  abline(v=1,lwd=4)
  hist (log(ret[,i]), main=paste("log",colnames(ret)[i]))
  abline(v=0,lwd=4)
}

# Done with plotting.

dev.off()

# 90% confidence intervals for returns.

cat("\n90% T-square confidence intervals for returns\n\n")

print(round(Tsq.conf.int(ret[,-1],level=0.9),4))

cat("\n90% univariate t confidence intervals for returns\n\n")

for (i in 2:ncol(ret)) 
{ print(round(t.test(ret[,i],conf.level=0.9)$conf.int[1:2],4))
}

cat("\n90% Bonferroni confidence intervals for returns\n\n")

for (i in 2:ncol(ret)) 
{ print(round(t.test(ret[,i],conf.level=1-0.1/(ncol(ret)-1))$conf.int[1:2],4))
}

# 95% confidence intervals for returns.

cat("\n95% T-square confidence intervals for returns\n\n")

print(round(Tsq.conf.int(ret[,-1],level=0.95),4))

cat("\n95% univariate t confidence intervals for returns\n\n")

for (i in 2:ncol(ret)) 
{ print(round(t.test(ret[,i],conf.level=0.95)$conf.int[1:2],4))
}

cat("\n95% Bonferroni confidence intervals for returns\n\n")

for (i in 2:ncol(ret)) 
{ print(round(t.test(ret[,i],conf.level=1-0.05/(ncol(ret)-1))$conf.int[1:2],4))
}

# Standard deviations of returns.

cat("\nStandard deviations of returns\n\n")

print(round(sd(ret[,-1]),4))

# 90% confidence intervals for log returns.

cat("\n90% T-square confidence intervals for log returns\n\n")

print(round(Tsq.conf.int(log(ret[,-1]),level=0.9),4))

cat("\n90% univariate t confidence intervals for log returns\n\n")

for (i in 2:ncol(ret)) 
{ print(round(t.test(log(ret[,i]),conf.level=0.9)$conf.int[1:2],4))
}

cat("\n90% Bonferroni confidence intervals for log returns\n\n")

for (i in 2:ncol(ret)) 
{ print(round(t.test(log(ret[,i]),conf.level=1-0.1/(ncol(ret)-1))$conf.int[1:2],4))
}

# 95% confidence intervals for log returns.

cat("\n95% T-square confidence intervals for log returns\n\n")

print(round(Tsq.conf.int(log(ret[,-1]),level=0.95),4))

cat("\n95% univariate t confidence intervals for log returns\n\n")

for (i in 2:ncol(ret)) 
{ print(round(t.test(log(ret[,i]),conf.level=0.95)$conf.int[1:2],4))
}

cat("\n95% Bonferroni confidence intervals for log returns\n\n")

for (i in 2:ncol(ret)) 
{ print(round(t.test(log(ret[,i]),conf.level=1-0.05/(ncol(ret)-1))$conf.int[1:2],4))
}

# Standard deviations of log returns.

cat("\nStandard deviations of log returns\n\n")

print(round(sd(log(ret[,-1])),4))