  Copulas provide an attractive approach for constructing multivariate
distributions with flexible marginal distributions and different forms of
dependences. Of particular importance in many areas is the possibility of
explicitly forecasting the tail-dependences. Most of the available approaches
are only able to estimate tail-dependences and correlations via nuisance
parameters, but can neither be used for interpretation, nor for forecasting.
Aiming to improve copula forecasting performance, we propose a general Bayesian
approach for modeling and forecasting tail-dependences and correlations as
explicit functions of covariates. The proposed covariate-dependent copula model
also allows for Bayesian variable selection among covariates from the marginal
models as well as the copula density. The copulas we study include Joe-Clayton
copula, Clayton copula, Gumbel copula and Student's \emph{t}-copula. Posterior
inference is carried out using an efficient MCMC simulation method. Our
approach is applied to both simulated data and the S\&P 100 and S\&P 600 stock
indices. The forecasting performance of the proposed approach is compared with
other modeling strategies based on log predictive scores. Value-at-Risk
evaluation is also preformed for model comparisons.
