Trunc-Opt vine building algorithms

TL;DR

This paper introduces a novel approach for constructing truncated vine copulas that exploits conditional independences, improving upon existing methods by using a new scoring criterion and demonstrating better performance on real datasets.

Contribution

It proposes a new methodology for truncated vine construction based on the first tree after truncation, utilizing a novel score called the Weight of the truncated vine, and incorporates conditional independences into the algorithms.

Findings

The new algorithms outperform existing methods on real datasets.

Exploiting conditional independences improves the efficiency of vine construction.

The proposed score effectively guides the fitting of truncated vines.

Abstract

Vine copula models have become highly popular and practical tools for modelling multivariate probability distributions due to their flexibility in modelling different kinds of dependences between the random variables involved. However, their flexibility comes with the drawback of a high-dimensional parameter space. To tackle this problem, truncated vine copulas were introduced by Kurowicka (2010) (Gaussian case) and Brechmann and Czado (2013) (general case). Truncated vine copulas contain conditionally independent pair copulas after the truncation level. So far, in the general case, truncated vine constructing algorithms started from the lowest tree in order to encode the largest dependences in the lower trees. The novelty of this paper starts from the observation that a truncated vine is determined by the first tree after the truncation level (see Kov\'acs and Sz\'antai (2017)). This paper introduces a new score for fitting truncated vines to given data, called the Weight of the truncated vine. Then we propose a completely new methodology for constructing truncated vines. We prove theorems which motivate this new approach. While earlier algorithms did not use conditional independences, we give algorithms for constructing and encoding truncated vines which do exploit them. Finally, we illustrate the algorithms on real datasets and compare the results with well-known methods included in R packages. Our method generally compare favorably to previously known methods.