l² inference for change points in high-dimensional time series via a two-way mosum

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 l2
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.