Dependent Lindeberg CLT - Finite Dimensional for Empirical Processes of Cluster Functionals

Drees and Rootzén [2010] have proven central limit theorems (CLT) for empirical processes of extreme values cluster functionals built from $β$-mixing processes. The problem with this family of $β$-mixing processes is that it is quite restrictive, as has been shown by Andrews [1984]. We expand this result to a more general dependent processes family, known as weakly dependent processes in the sense of Doukhan and Louhichi [1999], but in finite-dimensional convergence (fidis). We show an example where the application of the CLT-fidis is sufficient in several cases, including a small simulation of the extremogram introduced by Davis and Mikosch [2009] to confirm the efficacy of our result.

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