Copulae in High Dimensions: An Introduction

Abstract

This paper reviews the latest proceeding of research in high dimensional copulas. At the beginning the bivariate copulas are given as a fundamental followed with the multivariate copulas which are the concentration of the paper. In multivariate copula sections, the hierarchical Archimedean copula, the factor copula and vine copula are introduced. In the following section the estimation methods for multivariate copulas including parametric and nonparametric routines, are presented. Also the introduction of the goodness of fit tests in copula context is given. An empirical study of multivariate copulas in risk management is performed thereafter.