# 14-024/III (2014-02-25; 2014-06-23)

Author(s)
Carsten Bormann; Melanie Schienle, Leibniz Universität Hannover, Germany; Julia Schaumburg, VU University Amsterdam
Keywords:
decomposition of tail dependence, multivariate extreme values, stable tail dependence function, subsample bootstrap, tail correlation
JEL codes:
C12, C19

In practice, multivariate dependencies between extreme risks are often only assessed in a pairwise way. We propose a test to detect when tail dependence is truly high-dimensional and bivariate simplifications would
produce misleading results. This occurs when a significant portion of the multivariate dependence structure in the tails is of higher dimension than two. Our test statistic is based on a decomposition of the stable tail dependence function, which is standard in extreme value theory for describing multivariate tail dependence.
The asymptotic properties of the test are provided and a bootstrap based finite sample version of the test is suggested. A simulation study documents the good performance of the test for standard sample sizes. In an application to international government bonds, we detect a high tail{risk and low return situation during the last decade which can essentially be attributed to increased higher{order tail risk. We also illustrate the empirical consequences from ignoring higher-dimensional tail risk.