nyse = ts(scan("http://www.stat.ualberta.ca/~wiens/stat479/S&Sdatasets/nyse.dat"))
nyse = ts(scan("nyse.dat"))

plot(nyse)  # Compare with Figure 1.4

## Set the CRAN mirror to Canada (BC) (Menu:  Packages -> Set CRAN mirror)
## Install package tseries (Packages -> Install package)
## Load it: 
library(tseries)
nyse.g = garch(nyse, order=c(1,1))
summary(nyse.g)

win.graph()
plot(nyse.g)

names(nyse.g)
resids = nyse.g$resid
shapiro.test(resids)

# Verification that "residuals" refers to w_t^hat, not eta_t^hat:
win.graph()
sigma = nyse.g$fitted.values[,1]
eta = sigma*resids
plot(nyse, eta, type = "l")


win.graph()
par(mfrow=c(2,1))

u = predict(nyse.g)
	## See help(predict.garch): u contains predictions +/- one 
	## conditional standard deviation 
v = nyse.g$fitted.values #  gives +/- one s.d., so w = u+v gives predictions +/- two s.d.

plot(800:1000, nyse[800:1000], ylim = c(-.16,.06), type = "l", xlab = "Time", ylab = "Returns +/- one s.d.")
lines(u[,1], col = "blue", lty="dashed")
lines(u[,2], col = "blue", lty="dashed")

w = u+v

plot(800:1000, nyse[800:1000], ylim = c(-.16,.06), type = "l", xlab = "Time", ylab = "Returns +/- 2 s.d.")
lines(w[,1], col = "blue", lty="dashed")
lines(w[,2], col = "blue", lty="dashed")