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On the Whittle estimator for linear random noise spectral density parameter in continuous-time nonlinear regression models

Author

Listed:
  • A. V. Ivanov

    (National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”)

  • N. N. Leonenko

    (Cardiff University)

  • I. V. Orlovskyi

    (National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”)

Abstract

A continuous-time nonlinear regression model with Lévy-driven linear noise process is considered. Sufficient conditions of consistency and asymptotic normality of the Whittle estimator for the parameter of spectral density of the noise are obtained in the paper.

Suggested Citation

  • A. V. Ivanov & N. N. Leonenko & I. V. Orlovskyi, 2020. "On the Whittle estimator for linear random noise spectral density parameter in continuous-time nonlinear regression models," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 129-169, April.
    • Handle: RePEc:spr:sistpr:v:23:y:2020:i:1:d:10.1007_s11203-019-09206-z
    DOI: 10.1007/s11203-019-09206-z
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    References listed on IDEAS

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    1. Bai, Shuyang & Ginovyan, Mamikon S. & Taqqu, Murad S., 2016. "Limit theorems for quadratic forms of Lévy-driven continuous-time linear processes," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1036-1065.
    2. Jiti Gao & Vo Anh & Chris Heyde & Quang Tieng, 2001. "Parameter Estimation of Stochastic Processes with Long‐range Dependence and Intermittency," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(5), pages 517-535, September.
    3. Hira Koul & Donatas Surgailis, 2000. "Asymptotic Normality of the Whittle Estimator in Linear Regression Models with Long Memory Errors," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 129-147, January.
    4. Heyde, C. C. & Gay, R., 1993. "Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 169-182, March.
    5. Leonenko, N.N. & Sakhno, L.M., 2006. "On the Whittle estimators for some classes of continuous-parameter random processes and fields," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 781-795, April.
    6. Liudas Giraitis & Masanobu Taniguchi & Murad S. Taqqu, 2017. "Asymptotic normality of quadratic forms of martingale differences," Statistical Inference for Stochastic Processes, Springer, vol. 20(3), pages 315-327, October.
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