When modelling multivariate phenomena, accounting for joint extremal behaviour is often an important concern. Archimax copula models have emerged recently as flexible constructions that can reproduce any type of asymptotic dependence between extremes and at the same time capture joint risks at medium levels. These properties have rendered them particularly useful, e.g., for the modelling of extreme rainfall at neighbouring weather stations. However, the relatively strong dependence these models impose is too stringent for stations that are further apart. In this talk, I will extend the class of Archimax copulas via their stochastic representation to a hierarchical model. The resulting clustered Archimax copulas are characterized by a partition of the random variables into groups linked by a radial copula; each cluster is Archimax and allowed to have its own Archimedean generator and stable tail dependence function. I will show that clustered Archimax copulas allow for asymptotic dependence as well as independence between clusters and characterize their extremal limit. The model will be further shown to maintain the ability of Archimax copulas to capture dependence between variables at pre-extreme levels. I will propose rank-based inference tools for these models and illustrate their applicability on rainfall data from southern France.
This talk is based on joint work with Simon Chatelain, Samuel Perreault, and Anne-Laure Fougères.

Underlying paper: https://arxiv.org/abs/2210.15622

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