Vine Constructions of Levy Copulas

TL;DR

This paper introduces a new pair construction method for Levy copulas, enhancing flexibility in modeling multivariate jump dependence by combining Levy and distributional copulas, with detailed estimation and simulation procedures.

Contribution

It develops the pair construction for Levy copulas (PLCC), allowing flexible modeling of high-dimensional jump dependence by combining Levy and distributional copulas.

Findings

The PLCC framework effectively models high-dimensional Levy processes.

Simulation studies demonstrate the flexibility and applicability of the proposed method.

The approach simplifies estimation and simulation of complex Levy copulas.

Abstract

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 construction for Levy copulas (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.