  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.
