High-Dimensional Change Point Analysis for Temporally Dependent Data

2026-07-22

AI Summary

This study addresses the challenge of detecting and localizing mean change points in high-dimensional dependent time series, particularly under non-Gaussian distributions and temporal dependence. The authors propose an adaptive method that integrates a quadratic-form CUSUM statistic with a coordinate-wise maximum statistic to effectively capture dense and sparse changes, respectively, while employing a weighting scheme to distinguish interior from boundary change points. A key theoretical contribution lies in establishing the limiting distributions and asymptotic independence of these two statistics under non-Gaussian dependence, thereby providing rigorous justification for a Cauchy combination test. Coupled with wild binary segmentation, the approach achieves consistent estimation of multiple change points. Theoretical analysis confirms the validity of centering and scaling procedures, and extensive numerical experiments demonstrate superior detection accuracy and localization efficiency across diverse scenarios.

Abstract

This paper develops adaptive procedures for detecting and locating mean changes in high-dimensional time series. Quadratic CUSUM statistics target dense changes, whereas coordinatewise maximum statistics target sparse changes. Two weighting schemes are considered to accommodate both interior and boundary changes. Under general non-Gaussian vector dependence, we establish the limiting distributions, validate the required centering and scaling estimators, and prove asymptotic independence between matched quadratic and maximum statistics. These results justify Cauchy combination tests. We further establish single-change localization and consistent multiple-change recovery using wild binary segmentation. Numerical results illustrate the effectiveness of the proposed methods.

Problem

• high-dimensional
• change point
• time series
• temporal dependence
• mean change

Innovation

• high-dimensional change point
• temporal dependence
• adaptive testing
• Cauchy combination test
• wild binary segmentation