Just the first attempt to modelling time-varying copulas. So far, only for observation driven models (GAS of Creal et al., 2013, and ACM, in the parlance of Koopman et al., 2016). And only for eliptical copulas (Gaussian and Student's t).
Creal, D., S. J. Koopman and A. Lucas (2013), "Generalized Autoregressive Score Models with Applications", Journal of Applied Econometrics, 28(5), 777-795.
Koopman, S. J., A. Lucas and M. Scharth (2016), "Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models", Review of Economics and Statistics, 98, 97-110.