Extremal behavior of pMAX processes

TL;DR

This paper introduces a comprehensive multivariate model that captures both asymptotic dependence and independence, extending existing models like M4, and analyzes its extremal properties such as tail dependence and extremal coefficients.

Contribution

The paper develops a new general multivariate model encompassing both dependence types, extending the extended M4 class, and provides theoretical analysis of its extremal behavior.

Findings

Computed multivariate extremal index for the new model

Derived tail dependence and extremal coefficients

Demonstrated the model's flexibility in capturing various extremal behaviors

Abstract

The well-known M4 processes of Smith and Weissman are very flexible models for asymptotically dependent multivariate data. Extended M4 of Heffernan \emph{et al.} allows to also account for asymptotic independence. In this paper we introduce a more general multivariate model comprising asymptotic dependence and independence, which has the extended M4 class as a particular case. We study properties of the proposed model. In particular, we compute the multivariate extremal index, tail dependence and extremal coefficients.