Testing for equality between conditional copulas given discretized conditioning events

TL;DR

This paper introduces new statistical tests for assessing the constancy of conditional dependence structures in copulas over general conditioning sets, using decision trees and asymptotic analysis, with applications in finance and insurance.

Contribution

It proposes novel test procedures based on conditional Kendall's tau for general Borelian sets and a data-driven recursive method using decision trees to identify relevant subsets.

Findings

Tests perform well in simulations

Effective in financial dependence analysis

Applicable to insurance coverage data

Abstract

Several procedures have been recently proposed to test the simplifying assumption for conditional copulas. Instead of considering pointwise conditioning events, we study the constancy of the conditional dependence structure when some covariates belong to general borelian conditioning subsets. Several test statistics based on the equality of conditional Kendall's tau are introduced, and we derive their asymptotic distributions under the null. When such conditioning events are not fixed ex ante, we propose a data-driven procedure to recursively build such relevant subsets. It is based on decision trees that maximize the differences between the conditional Kendall's taus corresponding to the leaves of the trees. The performances of such tests are illustrated in a simulation experiment. Moreover, a study of the conditional dependence between financial stock returns is managed, given some clustering of their past values. The last application deals with the conditional dependence between coverage amounts in an insurance dataset.