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Estimation of the dependence parameter in linear regression with long-range-dependent errors

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  • Giraitis, Liudas
  • Koul, Hira

Abstract

This paper establishes the consistency and the root-n asymptotic normality of the exact maximum likelihood estimator of the dependence parameter in linear regression models where the errors are a nondecreasing function of a long-range-dependent stationary Gaussian process. The spectral density of the Gaussian process is assumed to be unbounded at the origin. The paper thus generalizes some of the results of Dahlhaus (1989) to linear regression models with non-Gaussian long-range-dependent errors.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:71:y:1997:i:2:p:207-224
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Fleming, Jeff & Kirby, Chris, 2011. "Long memory in volatility and trading volume," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1714-1726, July.
    2. 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.
    3. Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
    4. 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.
    5. 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.
    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.

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