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A change detection procedure for an ergodic diffusion process

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  • Koji Tsukuda

    (Waseda University
    The University of Tokyo)

Abstract

A test procedure based on continuous observation to detect a change in drift parameters of an ergodic diffusion process is proposed. The asymptotic behavior of a random field relating to an estimating equation under the null hypothesis is established using weak convergence theory in separable Hilbert spaces. This result is applied to a change point detection test.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:4:d:10.1007_s10463-016-0564-y
    DOI: 10.1007/s10463-016-0564-y
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Junmo Song & Sangyeol Lee, 2009. "Test for parameter change in discretely observed diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 12(2), pages 165-183, June.
    4. Mihalache, Stefan, 2012. "Strong approximations and sequential change-point analysis for diffusion processes," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 464-472.
    5. 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.
    6. Harry Van Zanten, 2003. "On Uniform Laws of Large Numbers for Ergodic Diffusions and Consistency of Estimators," Statistical Inference for Stochastic Processes, Springer, vol. 6(2), pages 199-213, May.
    7. LaRiccia, Vincent & Mason, David M., 1986. "Cramér-von Mises statistics based on the sample quantile function and estimated parameters," Journal of Multivariate Analysis, Elsevier, vol. 18(1), pages 93-106, February.
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    Cited by:

    1. Yozo Tonaki & Yusuke Kaino & Masayuki Uchida, 2022. "Adaptive tests for parameter changes in ergodic diffusion processes from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 397-430, July.

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