Vine constructions of Lévy copulas

Lévy copulas are the most general concept to capture jump dependence in multivariate Lévy processes. They translate the intuition and many features of the copula concept into a time series setting. A challenge faced by both, distributional and Lévy copulas, is to find flexible but still applicable models for higher dimensions. To overcome this problem, the concept of pair-copula constructions has been successfully applied to distributional copulas. In this paper, we develop the pair Lévy copula construction (PLCC). Similar to pair constructions of distributional copulas, the pair construction of a d-dimensional Lévy copula consists of d(d−1)/2 bivariate dependence functions. We show that only d−1 of these bivariate functions are Lévy copulas, whereas the remaining functions are distributional copulas. Since there are no restrictions concerning the choice of the copulas, the proposed pair construction adds the desired flexibility to Lévy copula models. We discuss estimation and simulation in detail and apply the pair construction in a simulation study. To reduce the complexity of the notation, we restrict the presentation to Lévy subordinators, i.e., increasing Lévy processes.