Simplified vine copula models: state of science and affairs

TL;DR

This paper reviews the current state, limitations, and debates surrounding simplified vine copula models, emphasizing their practical use in modeling multivariate dependencies and discussing the implications of the simplifying assumption.

Contribution

It provides a comprehensive review of simplified vine copula models, analyzing their flexibility, limitations, and the ongoing debate within the copula community.

Findings

Simplified vine copula models are widely used for multivariate dependency modeling.

The simplifying assumption has both practical benefits and theoretical limitations.

The paper offers a perspective aiming to reconcile differing views on the simplifying assumption.

Abstract

Vine copula models have become highly popular practical tools for modeling multivariate dependencies. To maintain tractability, a commonly employed simplifying assumption is that conditional copulas remain unchanged by the conditioning variables. This assumption has sparked a somewhat polarizing debate within the copula community. The fact that much of this dispute occurs outside the public record has placed the field in an unfortunate position, impeding scientific progress. In this article, I will review what we know about the flexibility and limitations of simplified vine copula models, explore the broader implications, and offer my own, hopefully reconciling, perspective on the issue.