Statistica Sinica 7(1997), 407-423

ASYMPTOTIC EFFICIENCY OF THE ORDER

SELECTION OF A NONGAUSSIAN AR PROCESS

Alexandros Karagrigoriou

University of Cyprus

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.

Key words and phrases: AR processes, asymptotic efficiency, Brillinger's mixing condition, model selection criteria, spectral density.