$\ell^2$ Inference for Change Points in High-Dimensional Time Series via a Two-Way MOSUM

TL;DR

This paper introduces an $$-norm based inference method for detecting multiple change points in high-dimensional time series, utilizing a novel Two-Way MOSUM approach that improves detection power for sparse or clustered signals.

Contribution

It develops a new $$-norm based testing procedure with a Two-Way MOSUM that enhances change point detection in high-dimensional, non-stationary time series.

Findings

Effective detection of non-sparse weak signals demonstrated in simulations

Theoretical distribution derived for high-dimensional Gaussian approximation

Successful application to financial and epidemiological data

Abstract

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.