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REGRESSION MODEL FITTING WITH A LONG MEMORY COVARIATE PROCESS

Published online by Cambridge University Press:  08 June 2004

Hira L. Koul ,
Richard T. Baillie  and
Donatas Surgailis
Hira L. Koul
Affiliation:
Michigan State University
Richard T. Baillie
Affiliation:
Michigan State University and Queen Mary University of London
Donatas Surgailis
Affiliation:
Institute of Mathematics and Informatics, Vilnius
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Abstract

This paper proposes some tests for fitting a regression model with a long memory covariate process and with errors that form either a martingale difference sequence or a long memory moving average process, independent of the covariate. The tests are based on a partial sum process of the residuals from the fitted regression. The asymptotic null distribution of this process is discussed in some detail under each set of these assumptions. The proposed tests are shown to have known asymptotic null distributions in the case of martingale difference errors and also in the case of fitting a polynomial of a known degree through the origin when the errors have long memory. The theory is then illustrated with some examples based on the forward premium anomaly where a squared interest rate differential proxies a time dependent risk premium. The paper also shows that the proposed test statistic converges weakly to nonstandard distributions in some cases.The authors gratefully acknowledge the helpful comments of the co-editor Don Andrews and two anonymous referees. The research of the first two authors was partly supported by NSF grant DMS 00-71619.

Type
Research Article
Information
Econometric Theory , Volume 20 , Issue 3 , June 2004 , pp. 485 - 512
Copyright
© 2004 Cambridge University Press

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