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Change point detection in high dimensional covariance matrix using Pillai’s statistics

Author

Listed:
  • Seonghun Cho

    (Inha University)

  • Minsup Shin

    (Seoul National University)

  • Young Hyun Cho

    (Purdue University)

  • Johan Lim

    (Seoul National University)

Abstract

This research proposes a method to test and estimate change points in the covariance structure of high-dimensional multivariate series data. Our method uses the trace of the beta matrix, known as Pillai’s statistics, to test the change in covariance matrix at each time point. We study the asymptotic normality of Pillai’s statistics for testing the equality of two covariance matrices when both sample size and dimension increase at the same rate. We test the existence of a single change point in a given time period using Cauchy combination test, the test using an weighted sum of Cauchy transformed p-values, and estimate the change point as the point whose statistic is the greatest. To test and estimate multiple change points, we use the idea of the wild binary segmentation and repeatedly apply the procedure for a single change point to each segmented period until no significant change point exists. We numerically provide the size and power of our method. We finally apply our procedure to finding abnormal behavior in the investment of a private equity fund.

Suggested Citation

  • Seonghun Cho & Minsup Shin & Young Hyun Cho & Johan Lim, 2025. "Change point detection in high dimensional covariance matrix using Pillai’s statistics," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 109(1), pages 53-84, March.
    • Handle: RePEc:spr:alstar:v:109:y:2025:i:1:d:10.1007_s10182-024-00516-z
    DOI: 10.1007/s10182-024-00516-z
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    References listed on IDEAS

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    1. Bai, Jushan, 1997. "Estimating Multiple Breaks One at a Time," Econometric Theory, Cambridge University Press, vol. 13(3), pages 315-352, June.
    2. Cho, Haeran & Fryzlewicz, Piotr, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," LSE Research Online Documents on Economics 57147, London School of Economics and Political Science, LSE Library.
    3. Luger, Richard, 2006. "Exact permutation tests for non-nested non-linear regression models," Journal of Econometrics, Elsevier, vol. 133(2), pages 513-529, August.
    4. Fryzlewicz, Piotr, 2014. "Wild binary segmentation for multiple change-point detection," LSE Research Online Documents on Economics 57146, London School of Economics and Political Science, LSE Library.
    5. Chen, Kuo-mei & Cohen, Arthur & Sackrowitz, Harold, 2011. "Consistent multiple testing for change points," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1339-1343, November.
    6. Paul Glasserman & Wanmo Kang, 2014. "OR Forum—Design of Risk Weights," Operations Research, INFORMS, vol. 62(6), pages 1204-1220, December.
    7. Yaowu Liu & Jun Xie, 2020. "Cauchy Combination Test: A Powerful Test With Analytic p-Value Calculation Under Arbitrary Dependency Structures," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 393-402, January.
    8. Haeran Cho & Piotr Fryzlewicz, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 475-507, March.
    9. Bodnar, Taras & Dette, Holger & Parolya, Nestor, 2019. "Testing for independence of large dimensional vectors," MPRA Paper 97997, University Library of Munich, Germany, revised May 2019.
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