Is there significant time-variation in multivariate copulas?

Abstract: We demonstrate how the uncertainty of parameter point estimates can be assessed in a maximum likelihood framework in order to prevent overfitting and erroneous detection of time-inhomogeneity. The class of models we consider are regular vine (R-vine) copula models, for which we describe a new algorithm for the exact computation of the score function and observed information. R-vine copulas constitute a flexible class of dependence models which are constructed hierarchically from bivariate copulas as building blocks only, and our algorithm exploits the hierarchical nature for subsequent computation of log-likelihood derivatives. Results obtained using the proposed methods are discussed in the context of the asymptotic efficiency of different estimation methods for R-vine based models. In a substantial application to a dataset of exchange rates, we obtain clear indications for time-inhomogeneous dependence between some currency pairs.