Modelling non-stationary extremal dependence through a geometric approach

Non-stationary extremal dependence, whereby the relationship between the extremes of multiple variables evolves over time, is commonly observed in many environmental and financial data sets. However, most multivariate extreme value models are only suited to stationary data. A recent approach to multivariate extreme value modelling uses a geometric framework, whereby extremal dependence features are inferred through the limiting shapes of scaled sample clouds. This framework can capture a wide range of dependence structures, and a variety of inference procedures have been proposed in the stationary setting. In this work, we first extend the geometric framework to the non-stationary setting and outline assumptions to ensure the necessary convergence conditions hold. We then introduce a flexible, semi-parametric modelling framework for obtaining estimates of limit sets in the non-stationary setting. Through rigorous simulation studies, we demonstrate that our proposed framework can capture a wide range of dependence forms and is robust to different model formulations. We illustrate the proposed methods on financial returns data and present several practical uses.