At Tilburg University

## Umut Can (University of Amsterdam)

**Title**: Two-Sample Testing for Tail Copulas with an Application to Equity Indices

**Abstract**: A novel, general two-sample hypothesis testing procedure is established for testing the equality of tail copulas associated with bivariate data. More precisely, using a martingale transformation of a natural two-sample tail copula process, a test process is constructed, which is shown to converge in distribution to a standard Wiener process. Hence, from this test process a myriad of asymptotically distribution-free two-sample tests can be obtained. The good finite-sample behavior of our procedure is demonstrated through Monte Carlo simulations. Using the new testing procedure, no evidence of a difference in the respective tail copulas is found for pairs of negative daily log-returns of equity indices during and after the global financial crisis. This is joint work with Roger Laeven and John Einmahl.

## Johan Segers (Université catholique de Louvain)

**Title**: Modelling Multivariate Extreme Value Distributions via Markov Trees

**Abstract**:

Multivariate extreme value distributions are a common choice for modelling multivariate extremes. In high dimensions, however, the construction of flexible and parsimonious models is challenging. We propose to combine bivariate extreme value distributions into a Markov random field with respect to a tree. Although in general not an extreme value distribution itself, this Markov tree is attracted by a multivariate extreme value distribution. The latter serves as a tree-based approximation to an unknown extreme value distribution with the given bivariate distributions as margins. Given data, we learn an appropriate tree structure by Prim’s algorithm with estimated pairwise upper tail dependence coefficients or Kendall’s tau values as edge weights. The distributions of pairs of connected variables can be fitted in various ways. The resulting tree-structured extreme value distribution allows for inference on rare event probabilities, as illustrated on river discharge data from the upper Danube basin. This is joint work with Shuang Hu and Zuoxiang Peng.