Selection of Sparse Vine Copulas in High Dimensions with the Lasso

TL;DR

This paper introduces a fast, Lasso-based method for selecting sparse vine copula structures in high-dimensional settings, improving efficiency and accuracy over traditional greedy algorithms.

Contribution

It presents a novel connection between vine copulas and structural equation models, enabling high-dimensional structure selection independent of pair copula fitting.

Findings

Outperforms existing methods in high-dimensional simulations

Efficient structure estimation using Lasso in vine copulas

Demonstrates effectiveness on real high-dimensional data

Abstract

We propose a novel structure selection method for high dimensional (d > 100) sparse vine copulas. Current sequential greedy approaches for structure selection require calculating spanning trees in hundreds of dimensions and fitting the pair copulas and their parameters iteratively throughout the structure selection process. Our method uses a connection between the vine and structural equation models (SEMs). The later can be estimated very fast using the Lasso, also in very high dimensions, to obtain sparse models. Thus, we obtain a structure estimate independently of the chosen pair copulas and parameters. Additionally, we define the novel concept of regularization paths for R-vine matrices. It relates sparsity of the vine copula model in terms of independence copulas to a penalization coefficient in the structural equation models. We illustrate our approach and provide many numerical examples. These include simulations and data applications in high dimensions, showing the superiority of our approach to other existing methods.