Vine constructions of Levy copulas

Levy copulas are the most general concept to capture jump dependence in multivariate Levy processes. They translate the intuition and many features of the copula concept into a time series setting. A challenge faced by both, distributional and Levy 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 Levy copula construction (PLCC). Similar to pair constructions of distributional copulas, the pair construction of a d-dimensional Levy copula consists of d(d 1)/2 bivariate dependence functions. We show that only d 1 of these bivariate functions are Levy 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 Levy 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 Levy subordinators, i.e., increasing Levy processes. (C) 2013 Elsevier Inc. All rights reserved.