  This article proposes a novel Bayesian multivariate quantile regression to
forecast the tail behavior of energy commodities, where the homoskedasticity
assumption is relaxed to allow for time-varying volatility. In particular, we
exploit the mixture representation of the multivariate asymmetric Laplace
likelihood and the Cholesky-type decomposition of the scale matrix to introduce
stochastic volatility and GARCH processes and then provide an efficient MCMC to
estimate them. The proposed models outperform the homoskedastic benchmark
mainly when predicting the distribution's tails. We provide a model combination
using a quantile score-based weighting scheme, which leads to improved
performances, notably when no single model uniformly outperforms the other
across quantiles, time, or variables.
