data(EuStockMarkets)

mode(EuStockMarkets)

## [1] "numeric"

class(EuStockMarkets)

## [1] "mts"    "ts"     "matrix"

plot(EuStockMarkets)

pdf("EuStocks.pdf", width = 6, height = 5)

plot(EuStockMarkets)

graphics.off()

Problem 1 Write a brief description of the time series plots of the four indices.

logR = diff(log(EuStockMarkets))

plot(logR)

Ploblem 2 Write brief decsription of the time series plots of the four series of log returns.

plot(as.data.frame(logR))

par(mfrow = c(2,2))

for(i in colnames(logR)) 
  {
  qqnorm(logR[ ,i], datax = T, main = i)

qqline(logR[ ,i], datax = T)

print(shapiro.test(logR[ ,i]))
}

## 
##  Shapiro-Wilk normality test
## 
## data:  logR[, i]
## W = 0.95384, p-value < 2.2e-16

## 
##  Shapiro-Wilk normality test
## 
## data:  logR[, i]
## W = 0.95537, p-value < 2.2e-16

## 
##  Shapiro-Wilk normality test
## 
## data:  logR[, i]
## W = 0.98203, p-value = 1.574e-14

## 
##  Shapiro-Wilk normality test
## 
## data:  logR[, i]
## W = 0.97994, p-value = 1.754e-15

Problem 3 Briefly describe the shape of each of the four normal plots

n=dim(logR)[1] 

q_grid = (1:n) / (n + 1)

df_grid = c(1, 4, 6, 10, 20, 30) 

index.names = dimnames(logR)[[2]] 

for(i in 1:4) 
{
  # dev.new() 
  par(mfrow = c(3, 2)) 
  for(df in df_grid) 
  { 
    qqplot(logR[,i], qt(q_grid,df), 
  main = paste(index.names[i], ", df = ", df) )
    abline(lm(qt(c(0.25, 0.75), df = df) ~
              quantile(logR[,i], c(0.25, 0.75)))) 
  }
}