Change-Point Detection under Dependence Based on Two-Sample U-Statistics

TL;DR

This paper introduces a robust change-point detection method for dependent time series using Wilcoxon two-sample U-statistics, extending existing theorems to dependent data for improved sensitivity and robustness.

Contribution

It proposes a new robust change-point detection test based on Wilcoxon two-sample U-statistics for dependent data, extending theoretical results to dependent time series.

Findings

The proposed test is robust to outliers.

Asymptotic distribution derived from a functional CLT for dependent data.

Extension of Csorgo and Horvath's theorem to dependent sequences.

Abstract

We study the detection of change-points in time series. The classical CUSUM statistic for detection of jumps in the mean is known to be sensitive to outliers. We thus propose a robust test based on the Wilcoxon two-sample test statistic. The asymptotic distribution of this test can be derived from a functional central limit theorem for two-sample U-statistics. We extend a theorem of Csorgo and Horvath to the case of dependent data.