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M-estimators in linear models with long range dependent errors

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  • Koul, Hira L.

Abstract

This paper discusses the asymptotic behavior of a class of M-estimators in linear models when errors are Gaussian, or a function of Gaussian random variables, that are long range dependent. The asymptotics are discussed when the design variables are either i.i.d. or long range dependent, independent of the errors, or known constants. It is observed that in the latter two cases, the leading r.v.'s in the approximation of the class M-estimators of the regression parameter vector corresponding to the skew symmetric scores and symmetric errors is proportional to the least squares estimator in the Gaussian errors case. Moreover, if the design variables are either i.i.d. or the known constants then the limiting distributions are normal. But if the design variables are long range dependent then the limiting distributions are nonnormal.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:14:y:1992:i:2:p:153-164
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    Citations

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    Cited by:

    1. Leonenko, Nikolai N. & Sharapov, Michail M. & El-Bassiouny, Ahmed H., 2000. "On the exactness of normal approximation of LSE of regression coefficient of long-memory random fields," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 121-130, June.
    2. Beran, Jan, 2006. "On location estimation for LARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1766-1782, September.
    3. 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.
    4. Koul, Hira L. & Surgailis, Donatas, 2001. "Asymptotics of empirical processes of long memory moving averages with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 309-336, February.
    5. Zhibiao Zhao & Yiyun Zhang & Runze Li, 2014. "Non-Parametric Estimation Under Strong Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 4-15, January.
    6. Masry, Elias & Mielniczuk, Jan, 1999. "Local linear regression estimation for time series with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 173-193, August.
    7. Giraitis, Liudas & Koul, Hira, 1997. "Estimation of the dependence parameter in linear regression with long-range-dependent errors," Stochastic Processes and their Applications, Elsevier, vol. 71(2), pages 207-224, November.
    8. Liudas Giraitis & Peter M Robinson, 2001. "Parametric Estimation under Long-Range Dependence," STICERD - Econometrics Paper Series 416, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    9. Giraitis, Liudas & Robinson, Peter M., 2001. "Parametric estimation under long-range dependence," LSE Research Online Documents on Economics 2227, London School of Economics and Political Science, LSE Library.
    10. Yaeji Lim & Hee-Seok Oh, 2022. "Quantile spectral analysis of long-memory processes," Empirical Economics, Springer, vol. 62(3), pages 1245-1266, March.
    11. 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.
    12. Koul, Hira L. & Baillie, Richard T., 2003. "Asymptotics of M-estimators in non-linear regression with long memory designs," Statistics & Probability Letters, Elsevier, vol. 61(3), pages 237-252, February.

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