The use of copulas for directional dependence modeling

In this chapter, we will discuss modeling of directional dependence by using two- and higher-dimensional copulas and introduce copula-based directional dependence measures. Generating and using various classes of copulas with directional dependence properties, introducing operator-based directional dependence, and using regression to model directional dependence will be some of the topics covered. We will also look at directional association in cross-tables. The copula-based directional dependence approach is rapidly developing, with many new approaches to the concept emerging in various applications. In our approach, we consider two types of directional dependence: one originating from marginals, and the other originating from the joint behavior of variables. Since the dependence structure between variables is not related with the marginal, but rather, the joint behavior, we will use the concept of copulas. A copula approach to directional dependence eliminates the influence of marginals and provides the required tools for decisions concerning the direction of dependence. To be able to explain this approach, we need to define copulas, explain the reasons why they are useful, and define directional dependence.