  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.
