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 \cite{Seg12}. The empirical process under consideration differs from the sequential process initially studied by \cite{Rus76} which cannot be expressed in terms of the empirical copula. The obtained theoretical results are used to derive tests for detecting distributional changes in a sequence of independent continuous observations. The tests are based on the comparison of the empirical copula of the $k$ first and the $n-k$ last observations for all possible values of $k$. The finite-sample performance of the resulting testing procedures is studied through large-scale Monte Carlo experiments. In the case of distributional changes due to a change in the copula only, 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.