Asymptotic efficiency of the order selection of a nongaussian AR process

Abstract

Motivated by Shibata's (1980) asymptotic efficiency results for the order selected for a zero mean Gaussian AR process this paper establishes the asymptotic efficiency of AIC-like model selection criteria for infinite order autoregressive processes with zero mean and unobservable errors that constitute a sequence of nongaussian random variables. Furthermore, from the spectral density point of view, the asympotic efficiency of AIC-like information criteria is established when the underlying process is an infinite order nonzero mean nongaussian AR process.