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
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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