Selections of vine structures and their applications

Abstract

Copulas are important models that allow to capture the dependence among variables. There are many types of bivariate parametric copula families, which allow to model data sets with different properties: symmetric and asymmetric dependence, upper (lower) tail dependence. In higher dimensions popular families of copulas, e.g., Gaussian, Student-t and canonical Archimedean are not sufficiently flexible in representing different types of dependence that they can realize. By decomposing the multivariate copula into a sequence of bivariate (conditional) copulas, based on a graph called vine (which is a nested set of trees), one is able to construct a n dimensional copula with the bivariate copulas that can have different types of dependence (e.g., tail behavior and asymmetries). The model constructed this way is called the vine copulamodel...