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April 2004 Selecting optimal multistep predictors for autoregressive processes of unknown order
Ching-Kang Ing
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Ann. Statist. 32(2): 693-722 (April 2004). DOI: 10.1214/009053604000000148


We consider the problem of choosing the optimal (in the sense of mean-squared prediction error) multistep predictor for an autoregressive (AR) process of finite but unknown order. If a working AR model (which is possibly misspecified) is adopted for multistep predictions, then two competing types of multistep predictors (i.e., plug-in and direct predictors) can be obtained from this model. We provide some interesting examples to show that when both plug-in and direct predictors are considered, the optimal multistep prediction results cannot be guaranteed by correctly identifying the underlying model”s order. This finding challenges the traditional model (order) selection criteria, which usually aim to choose the order of the true model. A new prediction selection criterion, which attempts to seek the best combination of the prediction order and the prediction method, is proposed to rectify this difficulty. When the underlying model is stationary, the validity of the proposed criterion is justified theoretically. To obtain this result, asymptotic properties of accumulated squares of multistep prediction errors are investigated. In addition to overcoming the above difficulty, some other advantages of the proposed criterion are also mentioned.


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Ching-Kang Ing. "Selecting optimal multistep predictors for autoregressive processes of unknown order." Ann. Statist. 32 (2) 693 - 722, April 2004.


Published: April 2004
First available in Project Euclid: 28 April 2004

zbMATH: 1048.62088
MathSciNet: MR2060174
Digital Object Identifier: 10.1214/009053604000000148

Primary: 62M20
Secondary: 60F15 , 62M10

Keywords: Accumulated prediction error , autoregressive process , Model selection , optimal multistep predictor

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 2 • April 2004
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