April 2024 2 inference for change points in high-dimensional time series via a Two-Way MOSUM
Jiaqi Li, Likai Chen, Weining Wang, Wei Biao Wu
Author Affiliations +
Ann. Statist. 52(2): 602-627 (April 2024). DOI: 10.1214/24-AOS2360


We propose an inference method for detecting multiple change points in high-dimensional time series, targeting dense or spatially clustered signals. Our method aggregates moving sum (MOSUM) statistics cross-sectionally by an 2-norm and maximizes them over time. We further introduce a novel Two-Way MOSUM, which utilizes spatial-temporal moving regions to search for breaks, with the added advantage of enhancing testing power when breaks occur in only a few groups. The limiting distribution of an 2-aggregated statistic is established for testing break existence by extending a high-dimensional Gaussian approximation theorem to spatial-temporal nonstationary processes. Simulation studies exhibit promising performance of our test in detecting nonsparse weak signals. Two applications on equity returns and COVID-19 cases in the United States show the real-world relevance of our algorithms. The R package “L2hdchange” is available on CRAN.

Funding Statement

Likai Chen’s research is partially supported by the NSF (Grant NSF-2222403). Weining Wang’s research is partially supported by the ESRC (Grant ES/T01573X/1).


We express our gratitude to the Co-Editor, the Associate Editor and the reviewers for their insightful comments, which enhanced the quality of this paper.


Download Citation

Jiaqi Li. Likai Chen. Weining Wang. Wei Biao Wu. "2 inference for change points in high-dimensional time series via a Two-Way MOSUM." Ann. Statist. 52 (2) 602 - 627, April 2024. https://doi.org/10.1214/24-AOS2360


Received: 1 October 2023; Revised: 1 February 2024; Published: April 2024
First available in Project Euclid: 9 May 2024

Digital Object Identifier: 10.1214/24-AOS2360

Primary: 62E20 , 62M10
Secondary: 62G20

Keywords: Gaussian approximation , ℓ2 inference , multiple change-point detection , nonlinear time series , temporal and spatial dependence , Two-Way MOSUM

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.52 • No. 2 • April 2024
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