Model averaging prediction for possibly nonstationary autoregressions

Abstract

As an alternative to model selection (MS), this paper considers model averaging (MA) for integrated autoregressive processes of infinite order (AR($\infty$)). We derive a uniformly asymptotic expression for the mean squared prediction error (MSPE) of the averaging prediction with fixed weights and then propose a Mallows-type criterion to select the data-driven weights that minimize the MSPE asymptotically. We show that the proposed MA estimator and its variants, Shibata and Akaike MA estimators, are asymptotically optimal in the sense of achieving the lowest possible MSPE. We further demonstrate that MA can provide significant MSPE reduction over MS in the algebraic-decay case. These theoretical findings are extended to integrated AR($\infty$) models with deterministic time trends and are supported by Monte Carlo simulations and real data analysis.