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 ℓ2-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 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.