Hierarchical Kendall copulas: Properties and inference

Abstract

AbstractWhile there is substantial need for dependence models in higher dimensions, most existing models quickly become rather restrictive and barely balance parsimony and flexibility. Hierarchical constructions may improve on that by grouping variables in different levels. In this paper, the new class of hierarchical Kendall copulas is proposed and discussed. Hierarchical Kendall copulas are built up by flexible copulas specified for groups of variables, where aggregation is facilitated by the Kendall distribution function, the multivariate analog to the probability integral transform for univariate random variables. After deriving properties of the general model formulation, particular focus is given to inference techniques of hierarchical Kendall copulas with Archimedean components, for which closed‐form analytical expressions can be derived. A substantive application to German stock returns finally shows that hierarchical Kendall copulas perform very well for real data, out‐of‐ as well as in‐sample. The Canadian Journal of Statistics 42: 78–108; 2014 © 2014 Statistical Society of Canada