Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series A, Pt. 3, 381--397

ASYMPTOTICALLY EFFICIENT ORDER SELECTION OF A NONZERO MEAN AR PROCESS FOR h-STEP PREDICTION

By

ALEX KARAGRIGORIOU,

and

FILIA VONTA, University of Cyprus, Nicosia, Cyprus

SUMMARY. Following Shibata (1980), Karagrigoriou (1995), and Bhansali (1996) this paper with the use of the direct method for h-step prediction, discusses the concept of asymptotically efficient order selection for h-step prediction by AIC-type selection procedures for an infinite order autoregressive process with nonzero mean and unobservable errors that constitute a sequence of iid random variables with mean zero and variance s2. A bound for the mean squared error of prediction is obtained and 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.

AMS (1991) subject classification. Primary 62M10, secondary 62M20.

Key words and phrases. AIC-type criteria; asymptotic efficiency; AR process; MSE.

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