Model Averaging Multistep Prediction in an Infinite Order Autoregressive Process

The key issue in the frequentist model averaging is the choice of weights. In this paper, the authors advocate an asymptotic framework of mean-squared prediction error (MSPE) and develop a model averaging criterion for multistep prediction in an infinite order autoregressive (AR(∞)) process. Under the assumption that the order of the candidate model is bounded, this criterion is proved to be asymptotically optimal, in the sense of achieving the lowest out of sample MSPE for the same-realization prediction. Simulations and real data analysis further demonstrate the effectiveness and the efficiency of the theoretical results.