Nonparametric estimation of pair-copula constructions with the empirical pair-copula

TL;DR

This paper introduces an empirical, nonparametric method for estimating pair-copula constructions that maintains parametric convergence rates, reducing model risk and enabling robust inference on dependence structures.

Contribution

It proposes a nonparametric estimator for pair-copulas within vine structures, offering a flexible alternative to parametric models with reliable convergence properties.

Findings

Achieves parametric convergence rate with nonparametric estimation.

Enables inference on dependence measures and hypothesis testing.

Supports model selection and pruning in vine copula structures.

Abstract

A pair-copula construction is a decomposition of a multivariate copula into a structured system, called regular vine, of bivariate copulae or pair-copulae. The standard practice is to model these pair-copulae parametrically, which comes at the cost of a large model risk, with errors propagating throughout the vine structure. The empirical pair-copula proposed in the paper provides a nonparametric alternative still achieving the parametric convergence rate. It can be used as a basis for inference on dependence measures, for selecting and pruning the vine structure, and for hypothesis tests concerning the form of the pair-copulae.