Testing exchangeability of copulas in arbitrary dimension

A test for exchangeability of copulas for arbitrary dimensions is proposed, generalising and extending a result by Genest et al. (2012), ‘Tests of Symmetry for Bivariate Copulas’, Annals of the Institute of Statistical Mathematics, 64, 811–834]. Three test statistics together with some modifications are presented and their asymptotical behaviour is analysed. Empirical p-values are computed by using a bootstrap-procedure proposed by Rémillard and Scaillet (2009), ‘Testing for Equality between Two Copulas’, Journal of Multivariate Analysis, 100, 377–386] and suggested by Bücher and Dette (2010), ‘A Note on Bootstrap Approximations for the Empirical Copula Process’, Statistics & Probability Letters, 80, 1925–1932], based on a multiplier central limit theorem by van der Vaart and Wellner (1996), Weak Convergence and Empirical Processes, Springer Series in Statistics, New York: Springer]. Finally a simulation study compares various versions of the proposed tests.