Systematic co-occurrence of tail correlation functions among max-stable processes

TL;DR

This paper investigates the ability of the tail correlation function (TCF) to differentiate between classes of max-stable processes and identifies cases where different processes share identical TCFs, highlighting limitations in using TCF alone.

Contribution

It provides a systematic analysis of the TCF's discriminative power among max-stable processes and reveals instances of non-uniqueness in TCF representations.

Findings

TCF can distinguish many max-stable process classes

Some different processes share the same TCF

Limitations of TCF as a sole identifier

Abstract

The tail correlation function (TCF) is one of the most popular bivariate extremal dependence measures that has entered the literature under various names. We study to what extent the TCF can distinguish between different classes of well-known max-stable processes and identify essentially different processes sharing the same TCF.