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 $\ell^2$-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 $\ell^2$-aggregated statistic is established for testing break existence by extending a high-dimensional Gaussian approximation theorem to spatial-temporal non-stationary processes. Simulation studies exhibit promising performance of our test in detecting non-sparse weak signals. Two applications, analyzing equity returns and COVID-19 cases in the United States, showcase the real-world relevance of our proposed algorithms.

翻译：本文提出一种适用于高维时间序列中多个变点检测的推断方法，特别针对密集或空间聚集信号而设计。该方法通过$\ell^2$范数对移动和统计量进行截面聚合，并在时间维度上最大化该聚合量。我们进一步引入新颖的两向MOSUM方法，利用时空移动区域搜索断点，其附加优势在于当断点仅出现在少数分组时增强检验效能。通过将高维高斯逼近定理推广至时空非平稳过程，我们建立了$\ell^2$聚合统计量的极限分布以检验断点存在性。模拟研究显示，该检验在检测非稀疏弱信号方面性能优异。两项应用——分析美国股票收益与COVID-19病例数据——展示了所提算法的实际应用价值。