Consider the US monthly 30-year conventional mortgage rates from April 1971 to November 2011. The data are available from FRED and are in the file m-morgfed-7111.txt (year, mon, day, morg, fed).

(a) Build a pure time series model for the monthly mortgage rate. Perform model checking and write down the fitted model.

(b) Mortgage rate is known to depend on the Federal Funds rate. Build a time series model for the mortgage rate using the lag-1 effective Federal Funds rate as an explanatory variable. Perform model checking and write down the fitted model. On the basis of the fitted model, does mortgage rate depend on the Federal Funds rate at the 5\% significance level?

(c) Let the forecasting period be from January 2007 to November 2011. Use out-of-sample predictions to compare the two models.