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Beyond dimension two: A test for higher-order tail risk

Bormann, Carsten; Schaumburg, Julia; Schienle, Melanie ORCID iD icon


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.

Volltext §
DOI: 10.5445/IR/1000051814
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Volkswirtschaftslehre (ECON)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2016
Sprache Englisch
Identifikator ISSN: 2190-9806
KITopen-ID: 1000051814
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 36 S.
Serie Working paper series in economics ; 80
Schlagwörter decomposition of multivariate tail dependence, multivariate extreme values, stable tail dependence function, extreme dependence modeling
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