Time-dependent copulas

For the study of dynamic dependence structures, the authors introduce the concept of a pseudo-copula, which extends Patton’s definition of a conditional copula. They state the equivalent of Sklar’s theorem for pseudo-copulas. They establish the asymptotic normality of nonparametric estimators of pseudo-copulas under strong mixing assumptions, and discuss applications to specification tests. They complement the theory with a small simulation study on the power of the proposed tests.