Asymptotically efficient autoregressive model selection for multistep prediction. (English) Zbl 0926.62086
Summary: A direct method for multistep prediction of a stationary time series involves fitting, by linear regression, a different autoregression for each lead time, \(h\), and to select the order to be fitted, \(\widetilde{k}_h\), from the data. By contrast, a more usual ‘plug-in’ method involves the least-squares fitting of an initial \(k\)-th order autoregression, with \(k\) itself selected by an order selection criterion. A bound for the mean squared error of prediction of the direct method is derived and employed for defining an asymptotically efficient order selection for \(h\)-step prediction, \(h\geq 1\); the \(S_h(k)\) criterion of R. Shibata [Ann. Statist. 8, 147-164 (1980; Zbl 0425.62069)] is asymptotically efficient according to this definition. A bound for the mean squared error of prediction of the plug-in method is also derived used for a comparison of these two alternative methods of multistep prediction. Examples illustrating the results are given.
MSC:
| 62M20 | Inference from stochastic processes and prediction |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
Citations:
Zbl 0425.62069References:
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