Adaptive Change Point Detection with Matrix Time Series: Leveraging Structured Mean Shifts

Xinyu Zhang; Kung-Sik Chan

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arXiv · 2401.17473

Adaptive Change Point Detection with Matrix Time Series: Leveraging Structured Mean Shifts

Xinyu Zhang·Kung-Sik Chan

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Abstract

In high-dimensional time series, the component processes are often assembled into a matrix to display their interrelationship. We focus on detecting mean shifts with unknown change point locations in these matrix time series. Series that are activated by a change may cluster along certain rows (columns), which forms mode-specific change point alignment. Leveraging mode-specific change point alignments may substantially enhance the power for change point detection. Yet, there may be no mode-specific alignments in the change point structure. We propose a powerful test to detect mode-specific change points, yet robust to non-mode-specific changes. We show the validity of using the multiplier bootstrap to compute the p-value of the proposed methods, and derive non-asymptotic bounds on the size and power of the tests. We also propose a parallel bootstrap, a computationally efficient approach for computing the p-value of the proposed adaptive test. In particular, we show the consistency of the proposed test, under mild regularity conditions. To obtain the theoretical results, we derive new, sharp bounds on Gaussian approximation and multiplier bootstrap approximation, which are of independent interest for high dimensional problems with diverging sparsity.

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BibTeX RIS

Xinyu Zhang, Kung-Sik Chan. 2024-01-30. Adaptive Change Point Detection with Matrix Time Series: Leveraging Structured Mean Shifts. https://arxiv.org/abs/2401.17473

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