Generalized Forecast Averaging in Autoregressions with a Near Unit Root

Abstract

Summary This paper develops a new approach to forecasting a highly persistent time series that employs feasible generalized least squares (FGLS) estimation of the deterministic components in conjunction with Mallows model averaging. Within a local-to-unity asymptotic framework, we derive analytical expressions for the asymptotic mean squared error and one-step-ahead mean squared forecast risk of the proposed estimator and show that the optimal FGLS weights are different from their ordinary least squares (OLS) counterparts. We also provide theoretical justification for a generalized Mallows averaging estimator that incorporates lag order uncertainty in the construction of the forecast. Monte Carlo simulations demonstrate that the proposed procedure yields a considerably lower finite-sample forecast risk relative to OLS averaging. An application to U.S. macroeconomic time series illustrates the efficacy of the advocated method in practice and finds that both persistence and lag order uncertainty have important implications for the accuracy of forecasts.