Multiple change-points detection based on U-Statistics under weak dependence

TL;DR

This paper develops a statistical method for detecting multiple change-points in time series data using U-statistics, extending previous work on single change-point detection, with proven asymptotic properties and simulation validation.

Contribution

It introduces a new multi-sample testing approach based on U-statistics for weakly dependent data, extending prior single change-point methods with explicit asymptotic distributions and consistency results.

Findings

Tests are consistent in detecting multiple changes.

Explicit asymptotic distributions under null and alternatives.

Simulations show effective detection of mean, variance, and autocorrelation changes.

Abstract

We study multiple change-points detection using multi-samples tests based on U-statistics for absolutely regular observations. Our results extend those of Ngatchou-Wandji et al. (2022) concerned with the study of one single changepoint. The asymptotic distributions of the test statistics under the null hypothesis and under a sequence of local alternatives are given explicitly, and the tests are shown to be consistent. A small set of simulations is done for evaluating the performance of the tests in detecting multiple changes in the mean, variance and autocorrelation of some simple times series models.