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Parameter estimation for the Rosenblatt Ornstein–Uhlenbeck process with periodic mean

Author

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  • Radomyra Shevchenko

    (TU Dortmund)

  • Ciprian A. Tudor

    (CNRS, Université de Lille
    Romanian Academy)

Abstract

We study the least squares estimator for the drift parameter of the Langevin stochastic equation driven by the Rosenblatt process. Using the techniques of the Malliavin calculus and the stochastic integration with respect to the Rosenblatt process, we analyze the consistency and the asymptotic distribution of this estimator. We also introduce alternative estimators, which can be simulated, and we study their asymptotic properties.

Suggested Citation

  • Radomyra Shevchenko & Ciprian A. Tudor, 2020. "Parameter estimation for the Rosenblatt Ornstein–Uhlenbeck process with periodic mean," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 227-247, April.
    • Handle: RePEc:spr:sistpr:v:23:y:2020:i:1:d:10.1007_s11203-019-09200-5
    DOI: 10.1007/s11203-019-09200-5
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    References listed on IDEAS

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    4. Herold Dehling & Brice Franke & Jeannette H. C. Woerner, 2017. "Estimating drift parameters in a fractional Ornstein Uhlenbeck process with periodic mean," Statistical Inference for Stochastic Processes, Springer, vol. 20(1), pages 1-14, April.
    5. Brice Franke & Thomas Kott, 2013. "Parameter estimation for the drift of a time inhomogeneous jump diffusion process," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(2), pages 145-168, May.
    6. Hu, Yaozhong & Nualart, David, 2010. "Parameter estimation for fractional Ornstein-Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 1030-1038, June.
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