Assessing Data Support for the Simplifying Assumption in Bivariate Conditional Copulas

The paper considers the problem of establishing data support for the simplifying assumption (SA) in a bivariate conditional copula model. It is known that SA greatly simplifies the inference for a conditional copula model, but standard tools and methods for testing SA tend to not provide reliable results. After splitting the observed data into training and test sets, the method proposed will use a flexible training data Bayesian fit to define tests based on randomization and standard asymptotic theory. Theoretical justification for the method is provided and its performance is studied using simulated data. The paper also discusses implementations in alternative models of interest, e.g. Gaussian, Logistic and Quantile regressions.