Huron<-scan("huron.txt")
Huron<-Huron+570
n.H<-length(Huron); t.H<-c(1:n.H); x<-c(1875:1972)

plot(t.H,Huron,type="l",
     xlab="Years since 1872",ylab=expression(X[t]))
points(t.H,Huron,pch=19)
abline(lm(Huron~t.H))
a0<-lm(Huron~t.H)$coeff[1]; a1<-lm(Huron~t.H)$coeff[2]

mt.H<-a0+a1*t.H; et.H<-Huron-mt.H
plot(t.H,et.H,type="l",xlab="Years since 1872",
                       ylab=expression(hat(e)[t]))
points(t.H,et.H,pch=19); abline(h=0,lty=2)

y1<-et.H[2:98];y2<-et.H[1:97];cor(y1,y2)
par(pty="s")
plot(y1,y2,xlab=expression(hat(e)[t-1]),
           ylab=expression(hat(e)[t]),pch=19)