B0654
Title: $l_2$ inference for change points in high-dimensional time series via a two-way MOSUM
Authors: Jiaqi Li - University of Chicago (United States) [presenting]
Likai Chen - Washington University in Saint Louis (United States)
Weining Wang - Humboldt-Universitat zu Berlin (Germany)
Wei Biao Wu - University of Chicago (United States)
Abstract: A new inference method is proposed for multiple change-point detection in high-dimensional time series, targeting dense or spatially clustered signals. Specifically, we aggregate MOSUM (moving sum) statistics cross-sectionally by an l2-norm and maximize them over time. To account for breaks only occurring in a few clusters, we also introduce a novel Two-Way MOSUM statistic, aggregated within each cluster and maximized over clusters and time. Such an aggregation scheme substantially improves the performance of change-point inference. We contribute to both theory and methodology. Theoretically, we develop an asymptotic theory concerning the limit distribution of an $l_2$-aggregated statistic to test the existence of breaks. The core of our theory is to extend a high-dimensional Gaussian approximation theorem fitting to non-stationary, spatial-temporally dependent data-generating processes. We provide consistency results of estimated break numbers, time stamps and sizes of breaks. Furthermore, our theory facilitates novel change-point detection algorithms involving newly proposed Two-Way MOSUM statistics. We show that our test enjoys power enhancement in the presence of spatially clustered breaks. A simulation study presents favorable performance of our testing method for non-sparse signals. Two applications concerning equity returns and COVID-19 cases in the United States demonstrate the applicability of our proposed algorithms.
