Asymptotic efficiency of model selection criteria: The nonzero mean Gaussian AR(∞) case

Abstract

Motivated by Shibata's (1980) asymptotic efficiency results this paper discusses the asymptotic efficiency of the order selected by a selection procedure for an infinite order autoregressive process with nonzero mean and unobservable errors that constitute a sequence of independent Gaussian random variables with mean zero and variance σ2. The asymptotic efficiency is established for AIC—type selection criteria such as AIC, FPE, and Sn(k). In addition, some asymptotic results about the estimators of the parameters of the process and the error—sequence are presented. © 1995, Taylor & Francis Group, LLC. All rights reserved.