testing the constancy of spearman s rho in multivariate time series

• DOI: 10.48550/arxiv.1407.1624
• Publication Date: 2015-05-01
• Authors: Kojadinovic, Ivan; Quessy, J.-F.; Rohmer, T.
• Keywords: FOS: Computer and information sciences; Ranks; Empirical copula; Multiplier central limit theorems; Partial-sum processes; 05 social sciences; Change-point detection; [MATH.MATH-PR]Mathematics [math]/Probability [math.PR]; Methodology (stat.ME); [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]; Strong mixing; 0502 economics and business; [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]; Spearman's rho; [MATH]Mathematics [math]; HAC kernel variance estimator; [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]; Statistics - Methodology

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.<br/>42 pages, 5 tables<br/>