Multivariate tail dependence: further insights with an application to the Spanish banking sector

Abstract

Extending bivariate dependence concepts to higher dimensions is a challenging but essential task for a comprehensive understanding of multivariate dependence. Moreover, measuring overall dependence based on averages across the full domain of the joint distribution may fail to discern changes in dependence across different segments of the distribution, especially in the tails. In order to incorporate these features, we present the multivariate tail concentration function (TCF) as a graphical tool to assess both global and tail dependence. We show that this tool allows to represent multivariate dependence in a 2D plot regardless of the number of dimensions, it quantifies both lower and upper tail dependence at a finite scale, and it relates to multivariate Blomqvist’s beta. We propose to estimate the TCF non-parametrically using two methods and we compare their finite sample performance through a simulation study. To illustrate its practical application, we use the TCF to evaluate co-movements among the six Spanish banks included in the IBEX 35 stock index.