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

  • Herold Dehling
  • Brice Franke
  • Thomas Kott
  • Reg Kulperger
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.

Keywords

Time-inhomogeneous diffusion process Change point Generalized likelihood ratio test 

Notes

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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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Herold Dehling
    • 1
  • Brice Franke
    • 2
  • Thomas Kott
    • 1
  • Reg Kulperger
    • 3
  1. 1.Fakultät für MathematikRuhr-Universität BochumBochumGermany
  2. 2.Département de Mathématique, UFR Sciences et TechniquesUniversité de Bretagne OccidentaleBrestFrance
  3. 3.Department of Statistical & Actuarial SciencesUniversity of Western OntarioLondonCanada

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