Forecasting using the 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 possible unit root (UR). Time series of this sort play an important role in economics, particularly macroeconomics. We consider a variety of estimators of the model and use simulation methods to compare the forecast errors that result from applying each of these estimators. Our main conclusion is that no single estimation procedure emerges as a dominant procedure, but we are able to provide some potentially useful results regarding the circumstances under which certain estimation procedures work better than the alternatives. We then apply the estimators to produce real time, out-of-sample forecasts of six macroeconomic time series. In these applications, the Roy-Fuller bias-corrected Prais-Winsten (PW) estimator emerges as the best procedure in five of the six cases.