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

Carsten Bormann, Melanie Schienle and Julia Schaumburg

No 2014-042, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

Abstract: 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 simpli cations would produce misleading results. This occurs when a signi cant 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 nite 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.

Keywords: decomposition of tail dependence; multivariate extreme values; stable tail dependence function; subsample bootstrap; tail correlation (search for similar items in EconPapers)
JEL-codes: C01 C46 C58 (search for similar items in EconPapers)
Date: 2014
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Related works:
Journal Article: Beyond Dimension two: A Test for Higher-Order Tail Risk (2016)
Working Paper: Beyond dimension two: A test for higher-order tail risk (2016)
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