Simplified vine copula models: state of science and affairs

Thomas Nagler

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.