Parsimonious Factor Models for Asymmetric Dependence in Multivariate Extremes

TL;DR

This paper introduces a flexible, parsimonious class of additive factor models for multivariate extremes that capture asymmetric dependence and non-stationarity, with demonstrated improved fit over existing models in real-world data.

Contribution

The authors develop a new family of additive factor models for multivariate extremes that are both flexible and computationally scalable, addressing limitations of existing symmetric models.

Findings

Models effectively capture asymmetric tail dependence.

Simulation studies confirm parameter identifiability.

Application shows improved fit over Hüsler-Reiss model.

Abstract

Modelling multivariate extreme events is essential when extrapolating beyond the range of observed data. Parametric models that are suitable for real-world extremes must be flexible -- particularly in their ability to capture asymmetric dependence structures -- while also remaining parsimonious for interpretability and computationally scalable in high dimensions. Although many models have been proposed, it is rare for any single construction to satisfy all of these requirements. For instance, the popular H\"usler-Reiss model is limited to symmetric dependence structures. In this manuscript, we introduce a class of additive factor models and derive their extreme-value limits. This leads to a broad and tractable family of models characterised by a manageable number of parameters. These models naturally accommodate asymmetric tail dependence and allow for non-stationary behaviour. We present the limiting models from both the componentwise-maxima and Peaks-over-Thresholds perspectives, via the multivariate extreme value and multivariate generalized Pareto distributions, respectively. Simulation studies illustrate identifiability properties based on existing inference methodologies. Finally, applications to summer temperature maxima in Melbourne, Australia, and to weekly negative returns from four major UK banks demonstrate improved fit compared with the H\"usler-Reiss model.