#####################################################################
### R code for lake.tsm example from Chapter 1 of Brockwell & Davis (2002)
# Read in data. These are resids from fitting line to lake.tsm
x <- scan("lak.tsm")
par(mfrow=c(2,2))
ts.plot(x,main="Series X(t)")
x1 <- x[1:97]
x2 <- x[2:98]
plot(x1,x2,ylab="X(t)",xlab="X(t-1)")
#
# Regress x1 against x2
myfit <- lm(x2~x1-1)
abline(myfit)
summary(myfit)
z <- myfit$residuals
ts.plot(z,main="Series Z(t)")
acf(z,main="Series Z(t)",ylim=c(-1,1))


#####################################################################
### Trivariate time series plot to illustrate cointegration ### 
# replace "postscript" with "pdf" to save plot, "coint.pdf", as pdf
postscript(file="coint.eps",horizontal=FALSE,width=6,height=5,pointsize=9)
# Simulate data: Z and W are independent Gaussian white noise sequences
Z <- rnorm(100); W <- rnorm(length(Z)); X <- Z; Y <- Z;
# X is a random walk, Y is random walk plus noise
for (t in 1:length(Z)){
  X[t] <- sum(Z[1:t])
  Y[t] <- X[t]+W[t]
}
# form a ts structure (myts) for plotting with ts.plot
myts <- ts(matrix(c(X,Y,Y-X), length(X), 3), start=c(1,1,1))
ts.plot(myts, gpars=list(main="Cointegration Example", xlab="time", ylab="", lty=c(2,3,1)))
# draw a line along x-axis for reference
lines(c(1,length(X)),c(0,0))
# add a legend, with math expressions (subscripts)
legend(0,10,legend=c(expression(X[t]),expression(Y[t]),expression(Y[t]-X[t])),lty=c(2,3,1))
# this is needed if saving plot to a file, generates the actual plot file
dev.off()