Nonparametric estimation of simplified vine copula models: comparison of methods

TL;DR

This paper compares various nonparametric methods for estimating simplified vine copula models, highlighting the influence of dependence strength on their performance through simulations and real data analysis.

Contribution

It extends existing nonparametric estimation approaches for vine copulas and provides a comprehensive comparison of their effectiveness under different dependence conditions.

Findings

Kernel estimators generally perform best.

No single method outperforms others in all scenarios.

Performance depends heavily on the strength of dependence.

Abstract

In the last decade, simplified vine copula models have been an active area of research. They build a high dimensional probability density from the product of marginals densities and bivariate copula densities. Besides parametric models, several approaches to nonparametric estimation of vine copulas have been proposed. In this article, we extend these approaches and compare them in an extensive simulation study and a real data application. We identify several factors driving the relative performance of the estimators. The most important one is the strength of dependence. No method was found to be uniformly better than all others. Overall, the kernel estimators performed best, but do worse than penalized B-spline estimators when there is weak dependence and no tail dependence.