B0961
Title: Long range dependence in extreme value analysis
Authors: Ioan Scheffel - University of Stuttgart (Germany) [presenting]
Marco Oesting - University of Stuttgart (Germany)
Abstract: Long- and short-range dependence (LRD/SRD) are commonly defined by properties of the bulk of the distribution. In extreme value analysis, where one considers the tail of the distribution, common notions of mixing are too restrictive. Therefore, the study of LRD in extreme value analysis is still in its infancy. A promising approach has recently been made by finding a notion of LRD/SRD that uses indicators of excursion sets. It relies on tail properties only and thus befits time series with heavy tails. For max-stable time series, the transition from SRD to LRD can be characterized by so-called tail-dependence coefficients. This equivalence has been used to study simple peaks-over-threshold-type estimators. It has been shown that convergence rates in the max-stable case start to slow down at the transition from SRD to LRD. We introduce the existing theory for max-stable time series and discuss the first extensions to max-domains of attraction.
