Empirical copula processes under serial dependence and weak smooth - ness conditions

The empirical copula process plays a central role for statistical inference on copulas. Recently, Segers (2012) investigated the asymptotic behavior of this process under non-restrictive smoothness assumptions for the case of i.i.d. random variables. In the first part of the talk, we extend his main result to the case of serial dependent random variables by means of the powerful and elegant functional delta method, and provide new ways to prove bootstrap consistency in this setting. We also show how these findings can be extended to the more general sequential empirical copula process under serial dependence. In the second part of the talk, we focus on the asymptotic properties of copula processes in settings where the copula does not have continuous partial derivatives and process convergence with respect to the supremum norm is known to fail [Fermanian, D. Radulović, M.Wegkamp (2004)]. In particular, we introduce a weaker metric that allows to obtain process convergence and discuss some applications.