Least-squares forecast averaging

This paper proposes forecast combination based on the method of Mallows Model Averaging (MMA). The method selects forecast weights by minimizing a Mallows criterion. This criterion is an asymptotically unbiased estimate of both the in-sample mean-squared error (MSE) and the out-of-sample one-step-ahead mean-squared forecast error (MSFE). Furthermore, the MMA weights are asymptotically mean-square optimal in the absence of time-series dependence. We show how to compute MMA weights in forecasting settings, and investigate the performance of the method in simple but illustrative simulation environments. We find that the MMA forecasts have low MSFE and have much lower maximum regret than other feasible forecasting methods, including equal weighting, BIC selection, weighted BIC, AIC selection, weighted AIC, Bates–Granger combination, predictive least squares, and Granger–Ramanathan combination.