Testing the constancy of Spearman's rho in multivariate time series

TL;DR

This paper introduces new change-point detection tests for multivariate time series that are sensitive to shifts in Spearman's rho, utilizing resampling and asymptotic methods, validated through simulations and financial data analysis.

Contribution

It develops two novel, parameter-free tests for detecting changes in Spearman's rho in multivariate time series, with proven asymptotic validity and practical implementation guidance.

Findings

Tests effectively detect change points in simulated data.

Resampling and asymptotic approaches show comparable performance.

Application to financial data demonstrates practical utility.

Abstract

A class of tests for change-point detection designed to be particularly sensitive to changes in the cross-sectional rank correlation of multivariate time series is proposed. The derived procedures are based on several multivariate extensions of Spearman's rho. Two approaches to carry out the tests are studied: the first one is based on resampling, the second one consists of estimating the asymptotic null distribution. The asymptotic validity of both techniques is proved under the null for strongly mixing observations. A procedure for estimating a key bandwidth parameter involved in both approaches is proposed, making the derived tests parameter-free. Their finite-sample behavior is investigated through Monte Carlo experiments. Practical recommendations are made and an illustration on trivariate financial data is finally presented.