Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series A, Pt. 1, pp.93--106

AN ASYMPTOTICALLY OPTIMAL SELECTION OF THE ORDER OF A LINEAR PROCESS

By

SANGYEOL LEE, Seoul National University, Korea

and

ALEX KARAGRIGORIOU, University of Cyprus, Cyprus

SUMMARY. A linear zero mean infinite order not necesssarily Gaussian autoregressive process with unobservable errors that constitute a sequence of i.i.d random variables with mean zero and variance $\sigma^2$ is assumed and the issue of asymptotic optimality of the order selected by a selection procedure is discussed. The paper greatly improves upon previous results since it only requires the existence of the fourth moments of the error distribution for the evaluation of the lower bound of the mean squared error of prediction and consequently provides the mildest possible conditions required for the asymptotic optimality for AIC-type selection criteria to be established. In addition, certain extensions regarding the asymptotic optimality for the order selected of nonzero mean AR processes as well as the asymptotic optimality from the spectral density point of view are discussed.

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

Key words and phrases. AIC, AR process, asymptotic optimality, mean squared error of prediction.

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