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Title: Extremal dependence properties of vine copulas Authors:  Emma Simpson - Lancaster University (United Kingdom) [presenting]
Jenny Wadsworth - Lancaster University (United Kingdom)
Jonathan Tawn - Lancaster University (United Kingdom)
Ingrid Hobaek Haff - University of Oslo (Norway)
Abstract: Vine copulas form a class of multivariate dependence model, and are composed of a series of bivariate copulas with certain underlying dependence structures. These models are flexible, and the use of pair copulas in their construction means that they extend well to moderate or high dimensions. We investigate the tail dependence properties of such models. In particular, we examine some of the extremal dependence structures that can be achieved in vine copula modelling, and demonstrate how to calculate the coefficients of tail dependence, denoted by $\eta$, for this class of models. We present examples in the trivariate case, with pair copulas being either logistic (asymptotically dependent) or inverted logistic (asymptotically independent), and use geometric approaches to find the corresponding bivariate and trivariate $\eta$ values. We also explain how the same approaches can be extended for studying vine copulas in higher dimensions.