Robust change point tests by bounded transformations

TL;DR

This paper introduces a flexible, robust change point testing framework using bounded transformations, significantly improving detection in heavy-tailed and contaminated data compared to classical methods.

Contribution

It proposes a new class of change point tests based on robust transformations of observations, enhancing detection of various structural changes in complex time series.

Findings

Effective in detecting changes in mean, scale, and dependence.

Outperforms existing methods in heavy-tailed multivariate series.

Shows high power in identifying variance shifts in ARCH processes.

Abstract

Classical moment based change point tests like the cusum test are very powerful in case of Gaussian time series with one change point but behave poorly under heavy tailed distributions and corrupted data. A new class of robust change point tests based on cusum statistics of robustly transformed observations is proposed. This framework is quite flexible, depending on the used transformation one can detect for instance changes in the mean, scale or dependence of a possibly multivariate time series. Simulations indicate that this approach is very powerful in detecting changes in the marginal variance of ARCH processes and outperforms existing proposals for detecting structural breaks in the dependence structure of heavy tailed multivariate time series.