Empirical and sequential empirical copula processes under serial dependence

TL;DR

This paper extends the theoretical understanding of empirical copula processes to serially dependent data, demonstrating their asymptotic behavior and bootstrap consistency, which is crucial for time series copula inference.

Contribution

It generalizes the asymptotic results of empirical copula processes from i.i.d. to serial dependent data using the functional delta method.

Findings

Asymptotic behavior of empirical copula processes under serial dependence

Conditional bootstrap consistency for dependent data

Extension to sequential empirical copula processes

Abstract

The empirical copula process plays a central role for statistical inference on copulas. Recently, Segers (2011) investigated the asymptotic behavior of this process under non-restrictive smoothness assumptions for the case of i.i.d. random variables. In the present paper we extend his main result to the case of serial dependent random variables by means of the powerful and elegant functional delta method. Moreover, we utilize the functional delta method in order to obtain conditional consistency of certain bootstrap procedures. Finally, we extend the results to the more general sequential empirical copula process under serial dependence.