Parsimonious Factor Models for Asymmetric Dependence in Multivariate Extremes

Authors

Pavel Krupskii, Boris Berangér

Categories

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 Hüsler-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 Hüsler-Reiss model.