Model Averaging in Predictive Regressions

This paper considers forecast combination in a predictive regression. We construct the point forecast by combining predictions from all possible linear regression models given a set of potentially relevant predictors. We propose a frequentist model averaging criterion, an asymptotically unbiased estimator of the mean squared forecast error (MSFE), to select forecast weights. In contrast to the existing literature, we derive the MSFE in a local asymptotic framework without the i.i.d. normal assumption. This result allows us to decompose the MSFE into the bias and variance components and also to account for the correlations between candidate models. Monte Carlo simulations show that our averaging estimator has much lower MSFE than alternative methods such as weighted AIC, weighted BIC, Mallows model averaging, and jackknife model averaging. We apply the proposed method to stock return predictions.