Bayesian nonparametric mixtures of Archimedean copulas

TL;DR

This paper introduces a Bayesian nonparametric mixture model using the Poisson-Dirichlet process to enhance the flexibility of dependence modeling with Archimedean copulas, addressing limitations of parametric approaches.

Contribution

It proposes a novel Bayesian nonparametric framework for Archimedean copulas, allowing for more adaptable dependence modeling beyond traditional parametric methods.

Findings

Model effectively captures complex dependence structures.

Numerical experiments demonstrate improved flexibility and fit.

Applicable to both simulated and real datasets.

Abstract

Copula-based dependence modeling often relies on parametric formulations. This is mathematically convenient, but can be statistically inefficient when the parametric families are not suitable for the data and model in focus. A Bayesian nonparametric mixture of Archimedean copulas is introduced to increase the flexibility of copula-based dependence modeling. Specifically, the Poisson-Dirichlet process is used as a mixing distribution over the Archimedean copulas' parameter. Properties of the mixture model are studied for the main Archimedean families, and posterior distributions are sampled via their full conditional distributions. The performance of the model is illustrated via numerical experiments involving simulated and real data.