Clustered Archimax Copulas

TL;DR

This paper introduces clustered Archimax copulas, extending their ability to model complex multivariate extremal dependence with flexible dependence structures within and between clusters.

Contribution

The paper proposes a novel clustered construction of Archimax copulas, allowing for both asymptotic dependence and independence across clusters, enhancing modeling flexibility.

Findings

Characterization of clustered Archimax copulas via radial copulas

Ability to model both asymptotic dependence and independence

Derivation of the asymptotic behavior and stable tail dependence functions

Abstract

When modeling multivariate phenomena, properly capturing the joint extremal behavior is often one of the many concerns. Archimax copulas appear as successful candidates in case of asymptotic dependence. In this paper, the class of Archimax copulas is extended via their stochastic representation to a clustered construction. These clustered Archimax copulas are characterized by a partition of the random variables into groups linked by a radial copula; each cluster is Archimax and therefore defined by its own Archimedean generator and stable tail dependence function. The proposed extension allows for both asymptotic dependence and independence between the clusters, a property which is sought, for example, in applications in environmental sciences and finance. The model also inherits from the ability of Archimax copulas to capture dependence between variables at pre-extreme levels. The asymptotic behavior of the model is established, leading to a rich class of stable tail dependence functions.