Consider the monthly unemployment rates of the State of California and United States from January 1976 to September 2011. The data are in the file m-CAUS7611 . txt (year, mon, CA, US).

(a) Build a pure time series model for the monthly unemployment rates of California. Perform model checking and write down the fitted model.

(b) Build a time series model for the monthly unemployment rates of California using the lag-1 US monthly unemployment rate as an explanatory variable. Perform model checking and write down the fitted model.

(c) Let the forecasting period be from January 2008 to September 2011. Compare the two models using out-of-sample forecasts.