Forecast Combination for VARs in Large N and T Panels

Abstract

We propose a new forecast combination method for panel data vector autoregressions that permit limited forms of parameterized heterogeneity (including fixed effects or incidental trends). Models are fitted using bias-corrected least squares in order to attenuate the effects of small sample bias of forecast loss. We begin by constructing a general estimator of the quadratic forecast risk of the averaged model that is asymptotically unbiased as both (cross sections) and (time series) grow large. Armed with this result, we propose a specific weighting mechanism, in which weights are chosen to minimize the estimated quadratic risk of the averaged forecast error. The objective function in this minimization problem is a version of the Mallows C criterion modified for application to the panel data setting. The forecast combination method performs well in Monte Carlo simulations and pseudo-out-of-sample forecasting applications. Full paper available at http://doi.org/10.1016/j.ijforecast.2021.04.006

Keywords: Forecast combination, Model averaging, Panel data, Mallows criterion, Bias correction