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Asymptotic theory for certain regression models with long memory errors

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  • R. S. Deo

Abstract

The asymptotic distribution of a weighted linear combination of a linear long memory series is shown to be normal for certain weights. This result can be used to derive the limiting distribution of the least squares estimators for polynomial trends and of the periodogram at fixed Fourier frequencies. A closed form expression for the asymptotic relative bias of the tapered periodogram at fixed Fourier frequencies is also obtained. A weighted least squares estimator, which is asymptotically efficient for polynomial trend regressors, is shown to be asymptotically normal.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:18:y:1997:i:4:p:385-393
    DOI: 10.1111/1467-9892.00057
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    Cited by:

    1. Hualde, Javier & Iacone, Fabrizio, 2017. "Fixed bandwidth asymptotics for the studentized mean of fractionally integrated processes," Economics Letters, Elsevier, vol. 150(C), pages 39-43.
    2. Chen, Willa W. & Deo, Rohit S., 2006. "Estimation of mis-specified long memory models," Journal of Econometrics, Elsevier, vol. 134(1), pages 257-281, September.
    3. Gennadi Gromykov & Mohamedou Ould Haye & Anne Philippe, 2018. "A frequency-domain test for long range dependence," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 513-526, October.
    4. Deo, Rohit S. & Chen, Willa W., 2003. "Estimation of Mis-Specified Long Memory Models," Papers 2004,03, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    5. 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.
    6. N. N. Leonenko & Emanuele Taufer, 2001. "Asymptotic properties of LSE in multivariate continuous regression with long memory stationary errors," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1-2), pages 54-71.
    7. Nikolai Leonenko & Emanuele Taufer, 2001. "On the rate of convergence to the Normal approximation of LSE in multiple regression with long memory random fields," Quaderni DISA 044, Department of Computer and Management Sciences, University of Trento, Italy, revised 12 Sep 2003.

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