Assessing Data Support for the Simplifying Assumption in Bivariate Conditional Copulas

TL;DR

This paper develops a Bayesian-based testing method to assess the validity of the simplifying assumption in bivariate conditional copula models, addressing limitations of existing tools and providing theoretical justification and simulation validation.

Contribution

It introduces a novel Bayesian approach for testing the simplifying assumption in conditional copulas, with theoretical support and applicability to various models.

Findings

Method performs well in simulated data

Provides reliable tests for the simplifying assumption

Applicable to Gaussian, Logistic, and Quantile regression models

Abstract

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.