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PREDICTION ERRORS IN NONSTATIONARYAUTOREGRESSIONS OF INFINITE ORDER

Published online by Cambridge University Press:  26 October 2009

Ching-Kang Ing ,
Chor-yiu Sin  and
Shu-Hui Yu
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Abstract

Assume that observations are generated fromnonstationary autoregressive (AR) processes ofinfinite order. We adopt a finite-orderapproximation model to predict future observationsand obtain an asymptotic expression for themean-squared prediction error (MSPE) of the leastsquares predictor. This expression provides thefirst exact assessment of the impacts ofnonstationarity, model complexity, and modelmisspecification on the corresponding MSPE. It notonly provides a deeper understanding of the leastsquares predictors in nonstationary time series, butalso forms the theoretical foundation for acompanion paper by the same authors, which obtainsasymptotically efficient order selection innonstationary AR processes of possibly infiniteorder.

Information

Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 3 , June 2010 , pp. 774 - 803
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

The authors are deeply grateful to a co-editorand two referees for their helpful suggestions andcomments. The research of the first and thirdauthors as partially supported by the NationalScience Council of Taiwan under grants NSC94-2118-M-001-013 and NSC 94-2416-H-260-019,respectively.

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