A Robust Method for Shift Detection in Time Series

TL;DR

This paper introduces a new robust change-point detection method for time series using the Hodges-Lehmann estimator, supported by new limit theory and extensive simulation comparisons.

Contribution

It develops a novel change-point test based on U-quantile processes with proven asymptotic properties for dependent data, advancing robustness in time series analysis.

Findings

The proposed test performs well in finite samples.

It is more robust than classical methods like CUSUM.

The test has favorable asymptotic properties under dependence.

Abstract

We present a robust test for change-points in time series which is based on the two-sample Hodges-Lehmann estimator. We develop new limit theory for a class of statistics based on the two-sample U-quantile processes, in the case of short range dependent observations. Using this theory we can derive the asymptotic distribution of our test statistic under the null hypothesis. We study the finite sample properties of our test via a simulation study and compare the test with the classical CUSUM test and a test based on the Wilcoxon-Mann-Whitney statistic.