Testing for equality between conditional copulas given discretized conditioning events
This work addresses the need for more flexible testing of conditional dependence structures in statistics, particularly for applications in finance and insurance, though it is incremental as it builds on existing methods for the simplifying assumption.
The paper tackles the problem of testing whether conditional copulas remain constant across different conditioning subsets, rather than pointwise events, by introducing test statistics based on conditional Kendall's tau and deriving their asymptotic distributions. The results are validated through simulations and applied to financial stock returns and insurance data, showing practical utility in these domains.
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.