Forecasting Using the Linear Trend Model with Autoregressive Errors

This paper is concerned with forecasting time series generated by the linear trend model with autoregressive errors, allowing for a unit root in the autoregressive component. Time series of this sort play an important role in economics, particularly in macroeconomics. We produce simulation results for the linear trend models, comparing forecasts generated by Ordinary Least Squares, Generalized Least Squares, bias-corrected GLS estimators and estimators that include unit root pretests. Our most general conclusion is that no single procedure emerges as a dominant procedure. However, we are able to provide some potentially useful results regarding the circumstances under which certain of these procedures work best relative to the alternatives. We apply these estimators to produce real time out-of-sample forecasts of seven major macroeconomic time series. In these applications, the Roy-Fuller bias-corrected Prais-Winsten estimator emerges as the best procedure in five of the seven cases.