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Estimation and Testing in Multivariate Generalized Ornstein-Uhlenbeck Processes with Change-Points

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  • Sévérien Nkurunziza

    (University of Windsor)

Abstract

In this paper, we consider an inference problem about the drift parameter matrix of multivariate generalized Ornstein-Uhlenbeck processes with multiple unknown change-points in the case where the drift parameter matrix is suspected to satisfy some restrictions. The established results generalize in six ways some recent findings about univariate generalized Ornstein-Uhlenbeck processes. First, we consider a multivariate process with multiple change-points. Second, we weaken the assumptions underlying some recent findings and we derive the unrestricted estimator (UE) and the restricted estimator (RE). Third, we derive the asymptotic property of the UE and the RE. Fourth, we construct a test for testing the hypothesized constraint. Fifth, we establish the asymptotic power of the derived test and we prove that it is consistent. Sixth, we derive a class of shrinkage estimators (SEs) and its asymptotic distributional risk.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-021-00251-6
    DOI: 10.1007/s13171-021-00251-6
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    References listed on IDEAS

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    1. 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.
    2. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
    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. 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.
    5. 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.
    6. Sévérien Nkurunziza, 2013. "Extension of some important identities in shrinkage-pretest strategies," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(7), pages 937-947, October.
    7. Fuqi Chen & Sévérien Nkurunziza, 2016. "A class of Stein-rules in multivariate regression model with structural changes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 83-102, March.
    8. 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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