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, in many applications it is scientifically important to test whether the calibration function is constant or not. Moreover, a correct model of a constant relationship results in significant gains of statistical efficiency. 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.
"Statistical testing of covariate effects in conditional copula models." Electron. J. Statist. 7 2822 - 2850, 2013. https://doi.org/10.1214/13-EJS866