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

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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 \(n^{1-H}\).

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Acknowledgments

The financial support of the DFG (German Science Foundation) SFB 823: Statistical modeling of nonlinear dynamic processes (Projects C3 and C5) is gratefully acknowledged. Furthermore, we would like to thank the anonymous referees and the associate editor for their helpful comments and suggestions.

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Authors and Affiliations

  1. Fakultät für Mathematik, Ruhr-Universität Bochum, 44780, Bochum, Germany

    Herold Dehling

  2. Département de Mathématique, Université de Bretagne Occidentale, 29200, Brest, France

    Brice Franke

  3. Fakultät für Mathematik, Technische Universität Dortmund, 44221, Dortmund, Germany

    Jeannette H. C. Woerner

Authors
  1. Herold Dehling
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  2. Brice Franke
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  3. Jeannette H. C. Woerner
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Correspondence to Jeannette H. C. Woerner.

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Dehling, H., Franke, B. & Woerner, J.H.C. Estimating drift parameters in a fractional Ornstein Uhlenbeck process with periodic mean. Stat Inference Stoch Process 20, 1–14 (2017). https://doi.org/10.1007/s11203-016-9136-2

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  • DOI: https://doi.org/10.1007/s11203-016-9136-2

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