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Forecast Combination for Panel Data Vectorautoregressions

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 n (cross sections) and T (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_{p} 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.