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Change point testing for the drift parameters of a periodic mean reversion process

Statistical Inference for Stochastic Processes volume 17, pages 1–18 (2014)Cite this article

Abstract

In this paper we investigate the problem of detecting a change in the drift parameters of a generalized Ornstein–Uhlenbeck process which is defined as the solution of

$$\begin{aligned} dX_t=(L(t)-\alpha X_t) dt + \sigma dB_t \end{aligned}$$

and which is observed in continuous time. We derive an explicit representation of the generalized likelihood ratio test statistic assuming that the mean reversion function \(L(t)\) is a finite linear combination of known basis functions. In the case of a periodic mean reversion function, we determine the asymptotic distribution of the test statistic under the null hypothesis.

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Acknowledgments

This work was partly supported by the Collaborative Research Project SFB 823 (Statistical modelling of nonlinear dynamic processes) of the German Research Foundation DFG. Thomas Kott was supported by the E.ON Ruhrgas AG. The authors wish to thank Martin Wendler for his help with the proof of Propostion 4.2, and two anonymous referees for their careful reading of the manuscript and for their comments that helped to improve the paper.

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Authors and Affiliations

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

    Herold Dehling & Thomas Kott

  2. Département de Mathématique, UFR Sciences et Techniques, Université de Bretagne Occidentale, 29200, Brest, France

    Brice Franke

  3. Department of Statistical & Actuarial Sciences, University of Western Ontario, London, ON, N6A 5B7, Canada

    Reg Kulperger

Authors
  1. Herold Dehling
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  2. Brice Franke
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  3. Thomas Kott
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  4. Reg Kulperger
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Correspondence to Herold Dehling.

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Dehling, H., Franke, B., Kott, T. et al. Change point testing for the drift parameters of a periodic mean reversion process. Stat Inference Stoch Process 17, 1–18 (2014). https://doi.org/10.1007/s11203-014-9092-7

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  • DOI: https://doi.org/10.1007/s11203-014-9092-7

Keywords

  • Time-inhomogeneous diffusion process
  • Change point
  • Generalized likelihood ratio test