Change Point Detection and Localization in High-Dimensional Time Series

2026-08-14

AI Summary

This study addresses the challenge of detecting sparse, asynchronous change points in high-dimensional time series by proposing a max-norm-based multiscale statistic grounded in Hölder-Gauss approximation theory. The proposed framework enables sequential testing for streaming data and retrospective localization of multiple change points while effectively controlling global error rates. Beyond establishing a rigorous theoretical foundation for high-dimensional approximation, extensive simulations demonstrate superior finite-sample performance. Furthermore, the method is successfully applied to monitoring air pollution from California wildfires. Collectively, this work provides a theoretically guaranteed and practically effective solution for real-time anomaly detection in complex, high-dimensional temporal data.

Abstract

We present new inference tools for change point detection in high-dimensional time series. We discuss two distinct statistical applications: First, sequential change point testing in an incoming data-stream. Second, retrospective localization of multiple changes, with confidence intervals at a globally controlled error level. Test statistics are built on the maximum norm to generate power against sparse and asynchronous changes. Both problems are tackled by related multiscale statistics that search for changes in the data at many different levels of resolution. For fixed dimension, our statistical approaches can be validated using traditional Hölderian invariance principles. In this paper, we present the high-dimensional analogue: Hölder-Gauss-approximations, which can be (roughly) interpreted as the Gaussian approximation for a Hölder-norm of the high-dimensional partial sum process. Such approximations are of interest beyond change point detection and can be used for other problems such as for stationarity testing in high dimensions. We evaluate finite-sample performance in a simulation study and give an application to air contamination due to wildfires in California, which occurs asynchronously across a panel of measuring stations.

Problem

• Change Point Detection
• High-Dimensional Time Series
• Sequential Testing
• Retrospective Localization
• Asynchronous Changes

Innovation

• High-Dimensional Change Point Detection
• Maximum Norm Statistics
• Multiscale Statistics
• Hölder-Gauss Approximations
• Asynchronous Changes