Statistical Testing for Conditional Copulas

TL;DR

This paper develops a likelihood ratio test for assessing parametric forms of the calibration function in conditional copula models, improving inference efficiency and computational cost.

Contribution

It introduces a generalized likelihood ratio test for parametric calibration functions in conditional copulas, with theoretical and simulation validation.

Findings

The test has correct asymptotic null distribution.

Simulation studies show good finite sample performance.

Application to real data demonstrates practical utility.

Abstract

In conditional copula models, the copula parameter is deterministically linked to a covariate via the calibration function. The latter is of central interest for inference and is usually estimated nonparametrically. However, when a parametric model for the calibration function is appropriate, the resulting estimator exhibits significant gains in statistical efficiency and requires smaller computational costs. We develop methodology for testing a parametric formulation of the calibration function against a general alternative and propose a generalized likelihood ratio-type test that enables conditional copula model diagnostics. We derive the asymptotic null distribution of the proposed test and study its finite sample performance using simulations. The method is applied to two data examples.