Statistics and Data Science seminar: Dr. Callum Murphy-Barltrop (TU Dresden)

In many environmental and financial datasets, the relationships between extreme values of multiple variables change over time — a phenomenon known as non-stationary extremal dependence. Most multivariate extreme value models (MEVMs) fail to account for such trends, motivating the need for novel developments. Furthermore, many recent MEVMs utilise a geometric approach, whereby extremal dependence features are inferred from the limiting shapes of scaled sample clouds. Such approaches possess many attractive features; for example, they can capture a wide range of dependence structures and can be used to estimate various practically relevant quantities.

In this work, we propose a novel geometric approach for modelling extremal dependence in the non-stationary setting. Our framework is more flexible compared to many existing approaches and can be applied for a wide variety of use cases. Through rigorous simulation studies, we demonstrate that our proposed framework is both robust and accurate. To conclude, we apply our framework to stock data from 'The Magnificent 7,' a group consisting of the world's largest tech companies. Our results illustrate that the relationships between extreme stock prices are constantly evolving, suggesting many traditional wealth management approaches are outdated.