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Polynomial Trend Regression With Long‐memory Errors

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  • Hwai‐Chung Ho
  • Nan‐Jung Hsu

Abstract

. For a time series generated by polynomial trend with stationary long‐memory errors, the ordinary least squares estimator (OLSE) of the trend coefficients is asymptotically normal, provided the error process is linear. The asymptotic distribution may no longer be normal, if the error is in the form of a long‐memory linear process passing through certain nonlinear transformations. However, one hardly has sufficient information about the transformation to determine which type of limiting distribution the OLSE converges to and to apply the correct distribution so as to construct valid confidence intervals for the coefficients based on the OLSE. The present paper proposes a modified least squares estimator to bypass this drawback. It is shown that the asymptotic normality can be assured for the modified estimator with mild trade‐off of efficiency even when the error is nonlinear and the original limit for the OLSE is non‐normal. The estimator performs fairly well when applied to various simulated series and two temperature data sets concerning global warming.

Suggested Citation

  • Hwai‐Chung Ho & Nan‐Jung Hsu, 2005. "Polynomial Trend Regression With Long‐memory Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 323-354, May.
    • Handle: RePEc:bla:jtsera:v:26:y:2005:i:3:p:323-354
    DOI: 10.1111/j.1467-9892.2005.00405.x
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    References listed on IDEAS

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    1. R. S. Deo, 1997. "Asymptotic theory for certain regression models with long memory errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(4), pages 385-393, July.
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    3. Hidalgo, Javier & Robinson, Peter, 2001. "Adapting to unknown disturbance autocorrelation in regression with long memory," LSE Research Online Documents on Economics 2078, London School of Economics and Political Science, LSE Library.
    4. Giraitis, Liudas & Koul, Hira L. & Surgailis, Donatas, 1996. "Asymptotic normality of regression estimators with long memory errors," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 317-335, September.
    5. Javier Hidalgo & Peter M Robinson, 2001. "Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory," STICERD - Econometrics Paper Series 427, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    6. Koul, Hira L., 1992. "M-estimators in linear models with long range dependent errors," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 153-164, May.
    7. Rohit S. Deo & Clifford M. Hurvich, 1998. "Linear Trend with Fractionally Integrated Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(4), pages 379-397, July.
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    Cited by:

    1. 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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