Hierarchical Archimedean Copulas for MATLAB and Octave: The HACopula Toolbox

Abstract

To extend the current implementation of copulas in MATLAB to non-elliptical distributions in arbitrary dimensions enabling for asymmetries in the tails, the toolbox HACopula provides functionality for modeling with hierarchical (or nested) Archimedean copulas. This includes their representation as MATLAB objects, evaluation, sampling, estimation and goodness-of-fit testing, as well as tools for their visual representation or computation of corresponding matrices of Kendall's tau and tail dependence coefficients. These are first presented in a quick-and-simple manner and then elaborated in more detail to show the full capability of HACopula. As an example, sampling, estimation and goodness-of-fit of a 100-dimensional hierarchical Archimedean copula is presented, including a speed up of its computationally most demanding part. The toolbox is also compatible with Octave, where no support for copulas in more than two dimensions is currently provided.