Multivariate Kendall's tau for change-point detection in copulas

Abstract

Statistical procedures for the detection of a change in the dependence structure of a series of multivariate observations are studied in this work. The test statistics that are proposed are L1, L2, and L∞ distances computed from vectors of differences of Kendall's tau; two multivariate extensions of Kendall's measure of association are used. Since the distributions of these statistics under the null hypothesis of no change depend on the unknown underlying copula of the vectors, a procedure based on the multiplier central limit theorem is used for the computation of p-values; the method is shown to be valid both asymptotically and for moderate sample sizes. Alternative versions of the tests that take into account possible breakpoints in the marginal distributions are also investigated. Monte Carlo simulations show that the tests are powerful under many scenarios of change-point. In addition, two estimators of the time of change are proposed and their efficiency is carefully studied. The methodologies are illustrated on simulated series from the Canadian Regional Climate Model. © 2012 Statistical Society of Canada.