Asymptotics and multiplier bootstrap of the sequential empirical copula process with applications to change-point detection

The weak limit of the sequential empirical copula process is obtained and the asymptotic validity of a resampling scheme based on multipliers is established under the nonrestrictive smoothness conditions considered by Segers. The empirical process under consideration differs from the sequential process initially studied by R\"uschendorf which cannot be expressed in terms of the empirical copula. The obtained theoretical results are used to derive tests for detecting a change in the copula of a sequence of independent continuous marginally identically distributed observations. The finite-sample performance of the proposed tests is studied through large-scale Monte Carlo experiments. The derived tests appear to be substantially more powerful than similar tests recently considered in the literature based on the sequential process initially studied by R\"uschendorf. The sensitivity of the tests to a violation of some of the underlying hypotheses is also investigated empirically.