Tree-based conditional copula estimation

Abstract: This paper proposes a regression tree procedure to estimate conditional copulas. The associated algorithm determines classes of observations based on covariate values and fits a simple parametric copula model on each class. The association parameter changes from one class to another, allowing for non-linearity in the dependence structure modeling. It also allows the definition of classes of observations on which the so-called "simplifying assumption" [see Derumigny and Fermanian, 2017] holds reasonably well. When considering observations belonging to a given class separately, the association parameter no longer depends on the covariates according to our model. In this paper, we derive asymptotic consistency results for the regression tree procedure and show that the proposed pruning methodology, that is the model selection techniques selecting the appropriate number of classes, is optimal in some sense. Simulations provide finite sample results and an analysis of data of cases of human influenza presents the practical behavior of the procedure.