#Fitting ARIMA Models to US Savings Rate 1955-1980 (as % of disposable income)

sr <- scan("https://edoras.sdsu.edu/~babailey/stat496/savings_rate.txt", skip=1)

sr <- ts(sr, start=1955)

# Graph the data.
par(mfrow=c(3,2))
plot(sr)
title("US Saving Rate Data")
plot(diff(sr))
title("Differenced")
acf(sr)
acf(diff(sr))
acf(sr, type="partial")
acf(diff(sr), type="partial")


#Fit Some models

fit1 <- arima(sr, order=c(1,0,2))
fit2 <- arima(sr, order=c(0,1,1))
fit3 <- arima(sr, order=c(0,1,2))

# forecast 
pred <- predict(fit1,n.ahead=16)

# graph the forecasts 
par(mfrow=c(1,1))
plot(c(sr,pred$pred), ylim=c(0,10), type="n")
lines(1:104, sr, lty=1)
lines(105:120, pred$pred + 2*pred$se, lty=2)
lines(105:120, pred$pred - 2*pred$se, lty=2)
points(105:120, pred$pred, pch=3)
title("95% Forecast intervals")