# read data (may need to include full path)
y1<-scan("d:/r/My Documents/itsm2000/lake.tsm")
plot(y1,type='l',xlab='Year',ylab='Level of Lake')

# Fit and display linear trend
x1<-1:length(y1)
reg1<-lm(y1~x1)
lines(x1,reg1$fitted)
summary(reg1)

# calculate residuals, display acf and pacf
y2<-reg1$resid
acf(y2)

# fit AR(2) and AR(3) models with regressor
reg2<-arima(y1,order=c(2,0,0),xreg=x1)
reg3<-arima(y1,order=c(3,0,0),xreg=x1)

# Time series diagnostics
tsdiag(reg2)

# Predict next 10 values
pred1<-predict(reg2,n.ahead=10,newxreg=99:108,se.fit=T)
pred1$pred
pred1$se

# Redraw time series with predictions
plot(x1,y1,xlab='Year',ylab='Lake Level',type='l',xlim=c(1,108),
ylim=range(c(y1,pred1$pred-2*pred1$se,pred1$pred+2*pred1$se)))
lines(99:108,pred1$pred,col='blue')
lines(99:108,pred1$pred-2*pred1$se,col='red')
lines(99:108,pred1$pred+2*pred1$se,col='red')