Multiple Change Point Detection in the Mean and Covariance of High-Dimensional Matrix Time Series

2026-10-05

AI Summary

This study addresses the challenge of detecting multiple change points that simultaneously occur in both the mean and covariance structures of high-dimensional matrix-valued time series. To this end, it proposes a unified detection framework based on a principal effect factor model and moving-sum statistics. Under general regularity conditions, the proposed method achieves simultaneous localization and separate identification of two types of non-aligned change points, effectively resolving the issues of row-column attribution and mutual masking between change points. Rigorous theoretical guarantees for detection consistency are established. Furthermore, the practical utility and interpretability of the approach are demonstrated through an empirical application to New York City taxi data.

Abstract

This paper studies simultaneous change point detection in the first- and second-order structures of high-dimensional matrix-valued time series. Specifically, we extend the framework of main effect factor models to accommodate multiple change points so that shifts in the mean and covariance structures are characterized by changes in the trend-stationary main effects main effects and in the factor-driven common components, respectively. Under this framework, the two types of changes are not necessarily aligned and can be arbitrarily large without masking the effects of each other, and each of the detected change points is identified either with the row or column categorizations which improves their interpretability. We propose a unified procedure based on moving-sum statistics to detect and localize both types of changes. Under general regularity conditions that allow for temporal and cross-sectional dependence, we derive detection and localization guarantees for the proposed method. The finite-sample performance of the method is demonstrated through extensive experiments, and its practical usefulness is illustrated by a real data application to New York City Yellow Taxi trip records.

Problem

• Change Point Detection
• High-Dimensional Matrix Time Series
• Mean and Covariance
• Multiple Change Points

Innovation

• High-dimensional matrix time series
• Multiple change point detection
• Main effect factor model
• Moving-sum statistics
• Mean and covariance structures