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Estimation and testing in generalized mean-reverting processes with change-point

Author

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  • Sévérien Nkurunziza

    (University of Windsor)

  • Pei Patrick Zhang

    (University of Windsor)

Abstract

In this paper, we study an inference problem in generalized Ornstein–Uhlenbeck processes with an unknown change-point when the drift parameter is suspected to satisfy a linear restriction. The testing problem studied generalizes a very recent problem about testing the existence of a change-point. To this end, we derive the asymptotic properties of the unrestricted estimator (UE) and the restricted estimator for the drift parameters, and we construct some shrinkage estimators (SEs). Further, we derive a test for testing the uncertain restriction and establish its asymptotic power. Moreover, we derive the asymptotic distributional risk of the proposed estimators and we prove that SEs dominate the UE. Finally, we present some numerical results which confirm the consistency of the proposed test as well as the superiority of the SEs over UE.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:21:y:2018:i:1:d:10.1007_s11203-016-9151-3
    DOI: 10.1007/s11203-016-9151-3
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    References listed on IDEAS

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    9. Robbins, Michael W. & Lund, Robert B. & Gallagher, Colin M. & Lu, QiQi, 2011. "Changepoints in the North Atlantic Tropical Cyclone Record," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 89-99.
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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. Yunhong Lyu & Sévérien Nkurunziza, 2023. "Inference in generalized exponential O–U processes," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 581-618, October.
    3. 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.

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