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

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Listed:
  • Herold Dehling
  • Brice Franke
  • Thomas Kott
  • Reg Kulperger

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 $$\begin{aligned} dX_t=(L(t)-\alpha X_t) dt + \sigma dB_t \end{aligned}$$ d X t = ( L ( t ) - α X t ) d t + σ d B t 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 $$L(t)$$ 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. Copyright Springer Science+Business Media Dordrecht 2014

Suggested Citation

  • Herold Dehling & Brice Franke & Thomas Kott & Reg Kulperger, 2014. "Change point testing for the drift parameters of a periodic mean reversion process," Statistical Inference for Stochastic Processes, Springer, vol. 17(1), pages 1-18, April.
    • Handle: RePEc:spr:sistpr:v:17:y:2014:i:1:p:1-18
    DOI: 10.1007/s11203-014-9092-7
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    References listed on IDEAS

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    1. Reinhard Höpfner & Yury Kutoyants, 2010. "Estimating discontinuous periodic signals in a time inhomogeneous diffusion," Statistical Inference for Stochastic Processes, Springer, vol. 13(3), pages 193-230, October.
    2. Ilia Negri & Yoichi Nishiyama, 2012. "Asymptotically distribution free test for parameter change in a diffusion process model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 911-918, October.
    3. Sangyeol Lee & Yoichi Nishiyama & Nakahiro Yoshida, 2006. "Test for Parameter Change in Diffusion Processes by Cusum Statistics Based on One-step Estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 211-222, June.
    4. 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.
    5. Mihalache, Stefan, 2012. "Strong approximations and sequential change-point analysis for diffusion processes," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 464-472.
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    Cited by:

    1. Sévérien Nkurunziza, 2023. "Estimation and Testing in Multivariate Generalized Ornstein-Uhlenbeck Processes with Change-Points," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 351-400, February.
    2. Koji Tsukuda, 2017. "A change detection procedure for an ergodic diffusion process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 833-864, August.
    3. Sévérien Nkurunziza & Pei Patrick Zhang, 2018. "Estimation and testing in generalized mean-reverting processes with change-point," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 191-215, April.
    4. Sévérien Nkurunziza & Lei Shen, 2020. "Inference in a multivariate generalized mean-reverting process with a change-point," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 199-226, April.
    5. Fuqi Chen & Rogemar Mamon & Sévérien Nkurunziza, 2018. "Inference for a change-point problem under a generalised Ornstein–Uhlenbeck setting," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 807-853, August.

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