Extending one-factor copulas

TL;DR

This paper extends one-factor copulas to include conditional dependence, introducing new representations, estimation methods, and a statistical test to distinguish dependence structures, supported by examples and real data analysis.

Contribution

It introduces a novel extension of one-factor copulas to model conditional dependence, along with estimation techniques and a test to identify dependence structures.

Findings

New parametric factor copulas with varying dependence

A statistical test for conditional independence vs dependence

Empirical validation through examples and real data

Abstract

So far, one-factor copulas induce conditional independence with respect to a latent factor. In this paper, we extend one-factor copulas to conditionally dependent models. This is achieved through new representations which allow to build new parametric factor copulas with a varying conditional dependence structure. We discuss estimation and properties of these representations. In order to distinguish between conditionally independent and conditionally dependent factor copulas, we provide a novel statistical test which does not assume any parametric form for the conditional dependence structure. Illustrations of our framework are provided through examples, numerical experiments, as well as a real data analysis.