Rolling window selection for out-of-sample forecasting with time-varying parameters

There is strong evidence of structural changes in macroeconomic time series, and the forecasting performance is often sensitive to the choice of estimation window size. This paper develops a method for selecting the window size for forecasting. Our proposed method is to choose the optimal size that minimizes the forecaster's quadratic loss function, and we prove the asymptotic validity of our approach. Our Monte Carlo experiments show that our method performs well under various types of structural changes. When applied to forecasting US real output growth and inflation, the proposed method tends to improve upon conventional methods, especially for output growth.