Telling tales from the tails: high-dimensional tail interdependence

We propose a simple and flexible framework that allows for a comprehensive analysis of tail interdependence in high dimensions. We use co-exceedances to capture the structure of the dependence in the tails and, relying on the concept of multiinformation, define the coefficient of tail interdependence. Within this framework, we develop statistical tests of (i) independence in the tails, (ii) goodness-of-fit of the tail interdependence structure of a hypothesized model with the one observed in the data, and (iii) dependence symmetry between any two tails. We present an analysis of tail interdependence among 250 constituents of the SP250 index.