Use the data in BARIUM.RAW for this exercise.
(i) Estimate the linear trend model chnimp, = a + fit + ur using the first 119 observations (this excludes the last 12 months of observations for 1988). What is the standard error of the regression?
(ii) Now, estimate an AR(1) model for chnimp, again using all data but the last 12 months. Compare the standard error of the regression with that from part (i). Which model provides a better in-sample fit?
(iii) Use the models from parts (i) and (ii) to compute the one-step-ahead forecast errors for the 12 months in 1988. (You should obtain 12 forecast errors for each method.) Compute and compare the RMSEs and the MAEs for the two methods. Which forecasting method works better out-of-sample for one-step-ahead forecasts?
(iv) Add monthly dummy variables to the regression from part (i). Are these jointly significant? (Do not worry about the slight serial correlation in the errors from this regression when doing the joint test.)