High-Dimensional Change Point Analysis for Temporally Dependent Data

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.