Hypergraphs in the characterization of regular vine copula structures

TL;DR

This paper introduces a novel hypergraph-based representation of regular vine copula structures, enabling better understanding and management of complex dependence models in high-dimensional settings.

Contribution

It presents a new hypergraph framework for regular vine copulas, capturing conditional independences and simplifying the analysis of high-dimensional dependence structures.

Findings

Hypergraph representation encodes conditional independences.

Simplifies analysis of high-dimensional vine copulas.

Facilitates understanding of complex dependence structures.

Abstract

Vine copulas constitute a flexible way for modeling of dependences using only pair copulas as building blocks. The pair-copula constructions introduced by Joe (1997) are able to encode more types of dependences in the same time since they can be expressed as a product of different types of bi-variate copulas. The Regular-vine structures (R-vines), as pair copulas corresponding to a sequence of trees, have been introduced by Bedford and Cooke (2001, 2002) and further explored by Kurowicka and Cooke (2006). The complexity of these models strongly increases in larger dimensions. Therefore the so called truncated R-vines were introduced in Brechmann et al. (2012). In this paper we express the Regular-vines using a special type of hypergraphs, which encodes the conditional independences.