Title: Search of a vine structure in vine copula model based on sampling order proximity
Authors: Dorota Kurowicka - Delft University of Technology (Netherlands) [presenting]
Abstract: Vine copulas become recently very popular in modelling continuous distributions with complicated dependence structures. In this model, a joint density of random vector $(X_1,...,X_d)$ is specified by the product of marginal distributions and $(d-1)d/2$ (un)conditional bivariate copulas. There are exponentially many decompositions of a density into these bivariate building blocks, and theoretically all these vine structures are equivalent. In practice, however, when copulas are fitted to data sequentially level by level of the vine structure and conditional copulas are assumed not to depend directly on the conditioning variables some vine structures constitute a better model of the data than the others. A heuristic search of the best vine structure has been briefly introduced recently. It has been observed that for two vine structures, common sampling orders consistent with these vine structures, give an indication of how similar (how many repeated bivariate copulas they have in the decomposition) these vines are. We present a thorough evaluation of the heuristic based on sampling order proximity. We present an algorithm to find all vine structures with the given number of sampling orders in common and show results of an extensive simulation study of a heuristic search based on sampling order proximity.