Consistent Estimation of Multiple Breakpoints in Dependence Measures

TL;DR

This paper develops and compares methods for detecting multiple change points in dependence measures like Spearman's rho, demonstrating their consistency and effectiveness through simulations and real data analysis.

Contribution

It introduces and proves the consistency of various procedures, including binary segmentation, wild binary segmentation, and an information criterion-based method, for multiple break detection in dependence measures.

Findings

Wild binary segmentation performs best in many scenarios.

All methods are consistent in estimating breakpoints and number of breaks.

Real data application confirms practical usefulness.

Abstract

This paper proposes different methods to consistently detect multiple breaks in copula-based dependence measures, mainly focusing on Spearman's $\rho$. The leading model is a factor copula model due to its usefulness for analyzing data in high dimensions. Starting with the classical binary segmentation, also the more recent wild binary segmentation (WBS) and a procedure based on an information criterion are considered. For all procedures, consistency of the estimators for the location of the breakpoints as well as the number of breaks is proved. Monte Carlo simulations indicate that WBS performs best in many, but not in all, situations. A real data application on recent Euro Stoxx 50 data reveals the usefulness of the procedures.