Use the data in INTQRT.RAW for this exercise.
(i) Using the data from all but the last four years (16 quarters), estimate an AR(1) model for Δr6t. (We use the difference because it appears that r6t has a unit root.) Find the RMSE of the one-step-ahead forecasts for Δr6, using the last 16 quarters.
(ii) Now, add the error correction term sprt-1 = r6t-1 - r3t-1 to the equation from part (i). (This assumes that the co integrating 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 co integrating 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 Δr6? Explain.