Forecasting autoregressive time series in the presence of deterministic components

Abstract

This paper studies the error in forecasting an autoregressive process with a deterministic component. We show that when the data are strongly serially correlated, forecasts based on a model that detrends the data using OLS before estimating the autoregressive parameters are much less precise than those based on an autoregression that includes the deterministic components, and the asymptotic distribution of the forecast errors under the two-step procedure exhibits bimodality. We explore the conditions under which feasible GLS trend estimation can lead to forecast error reduction. The finite sample properties of OLS and feasible GLS forecasts are compared with forecasts based on unit root pretesting. The procedures are applied to 15 macroeconomic time series to obtain real time forecasts. Forecasts based on feasible GLS trend estimation tend to be more efficient than forecasts based on OLS trend estimation. A new finding is when a unit root pretest rejects non-stationarity, use of GLS yields smaller forecast errors than OLS. When the series to be forecasted is highly persistent, GLS trend estimation in conjunction with unit root pretests can lead to sharp reduction in forecast errors.