Some results on change-point detection in cross-sectional dependence of multivariate data with changes in marginal distributions

TL;DR

This paper introduces a new statistical test to detect changes in the dependence structure of multivariate data, specifically in the copula, even when marginal distributions change at a known point, addressing limitations of existing methods.

Contribution

It proposes a novel test for change-point detection in copulas that accounts for changes in marginal distributions, improving upon prior methods that require constant margins.

Findings

The test performs well in Monte Carlo simulations.

It effectively detects dependence changes despite marginal distribution shifts.

The method is applicable when the change point is known.

Abstract

Tests for break points detection in the law of random vectors have been proposed in several papers. Nevertheless, they have often little powers for alternatives involving a change in the dependence between components of vectors. Specific tests for detection of a change in the copula of random vectors have been proposed in recent papers, but they do not allow to conclude of a change in the dependence structure without condition that the margins are constant. The goal of this article is to propose a test for detection of a break in the copula when a change in marginal distribution occurs at a known instant. The performances of this test are illustrated by Monte Carlo simulations.