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

While forecasting is a common practice in academia, government and business alike, practitioners are often left wondering how to choose the sample for estimating forecasting models. When we forecast inflation in 2018, for example, should we use the last 30 years of data or the last 10 years of data? There is strong evidence of structural changes in economic time series, and the forecasting performance is often quite sensitive to the choice of such window size. In this paper, we develop a novel method for selecting the estimation window size for forecasting. Specifically, we propose to choose the optimal window 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 quite 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.