Three-Pass Regression Filter Model with Time-Varying Coefficients: A Rolling Window Selection Approach

In this study, we introduce smooth time-varying coefficients to the three-pass regression filter (3PRF) forecasting method. We employ a rolling window selection procedure to estimate the parameters and to generate forecasts. The rolling window selection uses only the most recent observations, which resolves the trade-off between forecast bias and variance. We establish the optimal rate for selecting the most recent observations. Monte Carlo simulations demonstrate that, in general, the rolling window selection method for 3PRF forecasting with time-varying coefficients produces relatively smaller forecasting mean squared errors compared to the original 3PRF forecasting method or the method that uses the full sample. Empirical applications of our proposed method are considered to forecast eight macroeconomic variables and market returns, which highlight the necessity of using our approach.