Subsampling and model selection in time series analysis

Research Report SRR98-004

Subsampling and model selection in time series analysis

Jun-ichiro Fukuchi

Abstract: In this article, the subsampling method of Carlstein (1986) is used to estimate the risk of prediction for time series data. First, we extend Carlstein's result by proving strong consistency of the subsampling estimator. Second, we propose a procedure of selecting a time series model empirically from a set of possibly nonnested and misspecified models by using estimated risk of prediction as a sel ection criterion. Specifically, when this procedure is applied to the selection of the order of an autoregressive model, it is shown to be a consistent order se lector if an appropriate subsample size is chosen. We propose a practical model selection procedure with a common subsample size chosen by Hall and Jing (1996)' s procedure.

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