About tests of the "simplifying" assumption for conditional copulas

TL;DR

This paper develops new tests for the simplifying assumption in conditional copulas, introducing bootstrap methods and demonstrating their effectiveness through simulations.

Contribution

It proposes several novel tests for the simplifying assumption in conditional copulas, including bootstrap schemes and theoretical validation.

Findings

New bootstrap schemes for testing the assumption

Validation of bootstrap methods through simulations

Enhanced understanding of conditional copula models

Abstract

We discuss the so-called "simplifying assumption" of conditional copulas in a general framework. We introduce several tests of the latter assumption for non- and semiparametric copula models. Some related test procedures based on conditioning subsets instead of point-wise events are proposed. The limiting distribution of such test statistics under the null are approximated by several bootstrap schemes, most of them being new. We prove the validity of a particular semiparametric bootstrap scheme. Some simulations illustrate the relevance of our results.