Consider usmelec , the total net generation of electricity (in billion kilowatt hours) by the U.S. electric industry (monthly for the period January 1973 – June 2013). In general there are two peaks per year: in mid-summer and mid-winter.
a. Examine the 12-month moving average of this series to see what kind of trend is involved.
b. Do the data need transforming? If so, nd a suitable transformation.
c. Are the data stationary? If not, nd an appropriate dierencing which yields stationary data.
d. Identify a couple of ARIMA models that might be useful in describing the time series. Which of your models is the best according to their AIC values?
e. Estimate the parameters of your best model and do diagnostic testing on the residuals. Do the residuals resemble white noise? If not, try to nd another ARIMA model which ts better.
f. Forecast the next 15 years of electricity generation by the U.S. electric industry. Get the latest gures from the EIA to check the accuracy of your forecasts.
g. Eventually, the prediction intervals are so wide that the forecasts are not particularly useful. How many years of forecasts do you think are suciently accurate to be usable?