Small sample properties of forecasts from autoregressive models under structural breaks

This paper develops a theoretical framework for the analysis of small-sample properties of forecasts from general autoregressive models under structural breaks. Finite-sample results for the mean squared forecast error of one-step ahead forecasts are derived, both conditionally and unconditionally, and numerical results for different types of break specifications are presented. It is established that forecast errors are unconditionally unbiased even in the presence of breaks in the autoregressive coefficients and/or error variances so long as the unconditional mean of the process remains unchanged. Insights from the theoretical analysis are demonstrated in Monte Carlo simulations and on a range of macroeconomic time series from G7 countries. The results are used to draw practical recommendations for the choice of estimation window when forecasting from autoregressive models subject to breaks.