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Regression Model Fitting With A Long Memory Covariate Process

Author

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  • Koul, Hira L.
  • Baillie, Richard T.
  • Surgailis, Donatas

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.

Suggested Citation

  • Koul, Hira L. & Baillie, Richard T. & Surgailis, Donatas, 2004. "Regression Model Fitting With A Long Memory Covariate Process," Econometric Theory, Cambridge University Press, vol. 20(3), pages 485-512, June.
    • Handle: RePEc:cup:etheor:v:20:y:2004:i:03:p:485-512_20
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    Cited by:

    1. Toshio Honda, 2010. "Nonparametric estimation of conditional medians for linear and related processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(6), pages 995-1021, December.
    2. Hira Koul & Donatas Surgailis & Nao Mimoto, 2015. "Minimum distance lack-of-fit tests under long memory errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(2), pages 119-143, February.
    3. Hira L. Koul & Fang Li, 2020. "Comparing two nonparametric regression curves in the presence of long memory in covariates and errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 499-517, May.
    4. Lihong Wang, 2020. "Lack of fit test for long memory regression models," Statistical Papers, Springer, vol. 61(3), pages 1043-1067, June.

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