Forecast Combination across Estimation Windows∗

This paper considers the problem of forecast combination when forecasts are generated from the same model but use different estimation windows. It develops theoretical results for random walks when their drift and/or volatility are subject to one or more structural breaks. The analysis is then extended to a linear regression model with an exogenous regressor. It is shown that compared to forecasts based on a single estimation window, averaging of forecasts over different estimation windows leads to a lower bias and to a lower root mean square forecast error for all but the smallest of breaks. Similar results are also obtained when observations are exponentially down-weighted, although in this case the forecast performance critically depends on the choice of the weighting coefficient. An application to weekly returns on 20 equity index futures shows that averaging forecasts over estimation windows generally leads to a smaller RMSFE compared to a range of competing methods.