About Conditional Copulas and the Simplifying Assumption

Jean-David Fermanian

In a general framework, we give an overview of the so-called ``simplifying assumption'' for conditional copulas. The usual approaches and challenges will be discussed, particularly their links with pair-copula constructions. Several tests of the latter assumption for non- and semiparametric copula models will be proposed, most of them relying on empirical copula processes. Some related test procedures based on conditioning subsets instead of point-wise events will be introduced. The limiting distributions of these test statistics under the null will be approximated by several bootstrap schemes, whose validity is discussed too. Some simulations illustrate the relevance of our approach.