IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v109y2025i1d10.1007_s10182-024-00516-z.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-024-00516-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10182-024-00516-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:alstar:v:109:y:2025:i:1:d:10.1007_s10182-024-00516-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.