Tail dependence functions and vine copulas

Tail dependence and conditional tail dependence functions describe, respectively, the tail probabilities and conditional tail probabilities of a copula at various relative scales. The properties as well as the interplay of these two functions are established based upon their homogeneous structures. The extremal dependence of a copula, as described by its extreme value copulas, is shown to be completely determined by its tail dependence functions. For a vine copula built from a set of bivariate copulas, its tail dependence function can be expressed recursively by the tail dependence and conditional tail dependence functions of lower-dimensional margins. The effect of tail dependence of bivariate linking copulas on that of a vine copula is also investigated. Mathematics Subject Classification: 62H20

• Type: Journal
• Year: 2010
• Where: MA
• Authors: Harry Joe, Haijun Li, Aristidis K. Nikoloulopoulos
• Keywords: Communications, Conditional Tail Dependence, MA 2010, Tail Dependence, Tail Dependence Functions