Multivariate sparse clustering for extremes

TL;DR

This paper introduces MUSCLE, a scalable algorithm leveraging sparse regular variation to identify extremal directions and clusters in multivariate data, demonstrated on financial returns.

Contribution

It presents a novel sparse regular variation-based method for multivariate extreme value analysis, including an efficient algorithm for clustering extremal coordinates.

Findings

MUSCLE effectively identifies extremal clusters in simulated data.

The method accurately determines thresholds for extreme events.

Application to financial data reveals meaningful extremal dependence patterns.

Abstract

Identifying directions where extreme events occur is a major challenge in multivariate extreme value analysis. In this paper, we use the concept of sparse regular variation introduced by Meyer and Wintenberger (2021)} to infer the tail dependence of a random vector X. This approach relies on the Euclidean projection onto the simplex which better exhibits the sparsity structure of the tail of X than the standard methods. Our procedure based on a rigorous methodology aims at capturing clusters of extremal coordinates of X. It also includes the identification of the threshold above which the values taken by X are considered as extreme. We provide an efficient and scalable algorithm called MUSCLE and apply it on numerical examples to highlight the relevance of our findings. Finally we illustrate our approach with financial return data.