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Biometrika 1999 86(3):591-604; doi:10.1093/biomet/86.3.591
© 1999 by Biometrika Trust
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Subsampling and model selection in time series analysis

J-I Fukuchi

Faculty of Economics, Hiroshima University, Higashi-hiroshima, 739 Japan E-mail: jfukuch@ipc.hiroshima-u.ac.jp

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

Key Words: Autoregressive model; Mean squared error of prediction; Model selection; Subsampling; Threshold autoregressive model


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