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Estimating drift parameters in a fractional Ornstein Uhlenbeck process with periodic mean

Author

Listed:
  • Herold Dehling

    (Ruhr-Universität Bochum)

  • Brice Franke

    (Université de Bretagne Occidentale)

  • Jeannette H. C. Woerner

    (Technische Universität Dortmund)

Abstract

We construct a least squares estimator for the drift parameters of a fractional Ornstein Uhlenbeck process with periodic mean function and long range dependence. For this estimator we prove consistency and asymptotic normality. In contrast to the classical fractional Ornstein Uhlenbeck process without periodic mean function the rate of convergence is slower depending on the Hurst parameter H, namely $$n^{1-H}$$ n 1 - H .

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:20:y:2017:i:1:d:10.1007_s11203-016-9136-2
    DOI: 10.1007/s11203-016-9136-2
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    References listed on IDEAS

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    1. Alexandre Brouste & Marina Kleptsyna, 2010. "Asymptotic properties of MLE for partially observed fractional diffusion system," Statistical Inference for Stochastic Processes, Springer, vol. 13(1), pages 1-13, April.
    2. 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.
    3. Herold Dehling & Brice Franke & Thomas Kott, 2010. "Drift estimation for a periodic mean reversion process," Statistical Inference for Stochastic Processes, Springer, vol. 13(3), pages 175-192, October.
    4. Hu, Yaozhong & Nualart, David, 2010. "Parameter estimation for fractional Ornstein-Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 1030-1038, June.
    5. Michael Diether, 2012. "Wavelet estimation in diffusions with periodicity," Statistical Inference for Stochastic Processes, Springer, vol. 15(3), pages 257-284, October.
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    Cited by:

    1. Reinhard Höpfner, 2021. "Polynomials under Ornstein–Uhlenbeck noise and an application to inference in stochastic Hodgkin–Huxley systems," Statistical Inference for Stochastic Processes, Springer, vol. 24(1), pages 35-59, April.
    2. Giacomo Ascione & Yuliya Mishura & Enrica Pirozzi, 2021. "Fractional Ornstein-Uhlenbeck Process with Stochastic Forcing, and its Applications," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 53-84, March.
    3. Selim Amrouni & Aymeric Moulin & Tucker Balch, 2022. "CTMSTOU driven markets: simulated environment for regime-awareness in trading policies," Papers 2202.00941, arXiv.org, revised Feb 2022.
    4. Qian Yu, 2021. "Least squares estimator of fractional Ornstein–Uhlenbeck processes with periodic mean for general Hurst parameter," Statistical Papers, Springer, vol. 62(2), pages 795-815, April.
    5. 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.

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