Long-Range Dependence in Extreme Value Analysis

Oesting Marco, University of Stuttgart

Long- and short-range dependence (LRD/SRD) in time series 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 taken by [1] who propose a notion of LRD/SRD that uses indicators of excursion sets 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 extremal coefficients [2]. In this talk, we will make use of this equivalence to study simple peaks-over-threshold-type estimators for the tail dependence coefficient showing that convergence rates in the max-stable case start to slow down at the transition from SRD to LRD (see [3]). Furthermore, we will discuss first extensions from max-stable time series to their max-domains of attraction. This is joint work with Albert Rapp and Ioan Scheffel.

Area: CS60 - Extreme value theory (Evgeny Spodarev)

Keywords: long-range dependence, extreme value theory, time series

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