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

Seonghun Cho, Minsup Shin, Young Hyun Cho and Johan Lim ()
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Seonghun Cho: Inha University
Minsup Shin: Seoul National University
Young Hyun Cho: Purdue University
Johan Lim: Seoul National University

AStA Advances in Statistical Analysis, 2025, vol. 109, issue 1, No 3, 53-84

Abstract: 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.

Keywords: Change point detection; Covariance matrix; Linear spectral statistics; Pillai’s trace statistic; Private equity fund (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10182-024-00516-z

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