Use CONSUMP for this exercise.

(i) Let yt be real per capita disposable income. Use the data through 1989 to estimate the model yt 5 a 1 bt 1 ryt21 1 ut and report the results in the usual form.

(ii) Use the estimated equation from part (i) to forecast y in 1990. What is the forecast error?

(iii) Compute the mean absolute error of the one-step-ahead forecasts for the 1990s, using the parameters estimated in part (i).

(iv) Now, compute the MAE over the same period, but drop yt21 from the equation. Is it better to include yt21 in the model or not?

C10 Use the data in INTQRT for this exercise.

(i) Using the data from all but the last four years (16 quarters), estimate an AR(1) model for Dr6t

.

(We use the difference because it appears that r6t has a unit root.) Find the RMSE of the onestep-ahead forecasts for Dr6, using the last 16 quarters.

(ii) Now, add the error correction term sprt21 5 r6t21 2 r3t21 to the equation from part (i). (This assumes that the cointegrating parameter is one.) Compute the RMSE for the last 16 quarters.

Does the error correction term help with out-of-sample forecasting in this case?

(iii) Now, estimate the cointegrating parameter, rather than setting it to one. Use the last 16 quarters again to produce the out-of-sample RMSE. How does this compare with the forecasts from parts

(i) and (ii)?

(iv) Would your conclusions change if you wanted to predict r6 rather than Dr6? Explain.