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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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    1. 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.
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    3. Yaozhong Hu & David Nualart & Hongjuan Zhou, 2019. "Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter," Statistical Inference for Stochastic Processes, Springer, vol. 22(1), pages 111-142, April.
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    6. 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.
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    Cited by:

    1. Héctor Araya & Soledad Torres & Ciprian A. Tudor, 2024. "Least squares estimation for the Ornstein–Uhlenbeck process with small Hermite noise," Statistical Papers, Springer, vol. 65(7), pages 4745-4766, September.

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