Empirical and sequential empirical copula processes under serial dependence
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Date
2011-11-21
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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.
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Keywords
bootstrap, weak dependency, weak convergence, serial dependence, sequential empirical copula process, functional delta method, empirical copula process