Elliptical Regularized Hotelling Tests for High-Dimensional Change-Point Detection

2026-07-24

AI Summary

This study addresses the problem of mean change-point detection in high-dimensional, heavy-tailed time series exhibiting cross-sectional dependence. The authors propose a novel approach based on an elliptically regularized Hotelling statistic, which integrates the spatial median with a ridge-regularized inverse of the centered spatial sign covariance matrix. This construction effectively captures complex dependence structures among variables while maintaining robustness against radial heavy-tailed noise. Innovatively incorporating spatial sign covariance and elliptical regularization into high-dimensional change-point analysis, the work establishes a joint Gaussian process limit theory under multiple regularization parameters, enabling asymptotically exact calibration of an adaptive Cauchy combination test and consistent change-point localization. Embedded within a wild binary segmentation framework, the method handles multiple change points efficiently. Empirical results demonstrate superior calibration and high testing power under strong cross-sectional dependence and heavy tails, successfully identifying four structural breaks in the Fama–French 49-industry portfolio returns.

Abstract

We propose an elliptical regularized Hotelling (ERHT) procedure for detecting location changes in high-dimensional sequences with heavy-tailed, cross-sectionally dependent observations. ERHT contrasts spatial medians on adjacent segments using a ridge-regularized inverse of the pooled centered spatial-sign covariance matrix, thereby combining robustness to radial variation with dependence-aware weighting. We establish Gaussian-process limits for the single- and multiple-change scans and joint convergence over a finite set of regularization parameters. These results provide asymptotically exact calibration of a Cauchy-aggregated adaptive test through the joint Gaussian limit, together with guarantees for local power and single-change localization. We further embed the ERHT score in wild binary segmentation and prove consistency for estimating the number and locations of multiple changes. Simulations show that ERHT is generally well calibrated and delivers competitive power under heavy-tailed distributions, particularly when cross-sectional dependence is substantial. An analysis of the Fama--French 49 industry portfolios reveals persistent evidence of location instability and identifies four structural breaks.

Problem

• change-point detection
• high-dimensional data
• heavy-tailed distributions
• cross-sectional dependence
• location shifts

Innovation

• elliptical regularized Hotelling test
• high-dimensional change-point detection
• spatial median
• ridge regularization
• cross-sectional dependence