Abstract
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 -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 -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).
Wei Wu’s research is partially supported by the NSF (Grants NSF/DMS-1916351, NSF/DMS-2311249, NSF/DMS-2027723).
Version Information
The current online version of this article, posted on 12 August 2024, supersedes the previous version posted on 9 May 2024 and the version appearing in print copies of volume 52, number 2. The change is as follows: The Funding Section has been updated to include Wei Wu’s research grant information.
Acknowledgments
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.
Citation
Jiaqi Li. Likai Chen. Weining Wang. Wei Biao Wu. " 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
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