Beyond dimension two: A test for higher-order tail risk - Carsten Bormann; Julia Schaumburg; Melanie Schienle (Karlsruher Institut für Technologie (KIT), Institut für Volkswirtschaftslehre (ECON), 2016)
In practice, multivariate dependencies between extreme risks are often only assessed in a pairwise way. We propose a test for detecting situations when such pairwise measures are inadequate and give incomplete 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 describing multivariate tail dependence. The asymptotic properties of the test are provided and a bootstrap based finite sample version of the test is proposed. A simulation study documents good size and power properties of the test including settings with time-series components and factor models. In an application to stock indices for non-crisis times, pairwise tail models seem appropriate for global markets while the test finds them not admissible for the tightly interconnected European market. From 2007/08 on, however, higher order dependencies generally increase and require a multivariate tail model in all cases.
urn:nbn:de:swb:90-518143
Keywords: C01; C46; C58; 330; decomposition of multivariate tail dependence; multivariate extreme values; stable tail dependence function; extreme dependence modeling