Forecasting issues for the linear regression model with MA(1) error process

This paper investigated a range of issues which concerned the forecasting from the linear regression model with MA(1) errors. These include (i) a comparison of one-step ahead forecasts (OSAF) and two-step-ahead forecasts (TSAF) (ii) investigating an improved method of estimating the lagged part of the moving average term, (iii) a comparison of the use of maximum likelihood estimator (MLE) with the maximum marginal likelihood estimator (MMLE) and (iv) investigating the effect of accepting a possible local maxima on forecast accuracy. A simulation study has been conducted to compare the performance of the techniques (TSAF OSAF) as well estimators (MLE MMLE). It is observed that the forecasting performance of TSAF is much more accurate than OSAF for small and moderate sample sizes, different values of Y and for all design matrices. It appears that for larger sample sizes, OSAF outperforms TSAF in the case of stationary design matrices, but the opposite scenario is observed for non-stationary design matrices. It is also noted that the forecasting based on the MML estimator is much better than that based on ML estimates. We have found that the second best forecasting performance result is based on the MML estimator with further searching for the global maximum.