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 multi-information, 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 S&P 250 index.
