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PREDICTION ERRORS IN NONSTATIONARY AUTOREGRESSIONS 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 from nonstationary autoregressive (AR) processes of infinite order. We adopt a finite-order approximation model to predict future observations and obtain an asymptotic expression for the mean-squared prediction error (MSPE) of the least squares predictor. This expression provides the first exact assessment of the impacts of nonstationarity, model complexity, and model misspecification on the corresponding MSPE. It not only provides a deeper understanding of the least squares predictors in nonstationary time series, but also forms the theoretical foundation for a companion paper by the same authors, which obtains asymptotically efficient order selection in nonstationary AR processes of possibly infinite order.

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-editor and two referees for their helpful suggestions and comments. The research of the first and third authors as partially supported by the National Science Council of Taiwan under grants NSC 94-2118-M-001-013 and NSC 94-2416-H-260-019, respectively.

References

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