  Modeling and predicting extreme movements in GDP is notoriously difficult and
the selection of appropriate covariates and/or possible forms of nonlinearities
are key in obtaining precise forecasts. In this paper, our focus is on using
large datasets in quantile regression models to forecast the conditional
distribution of US GDP growth. To capture possible non-linearities, we include
several nonlinear specifications. The resulting models will be huge dimensional
and we thus rely on a set of shrinkage priors. Since Markov Chain Monte Carlo
estimation becomes slow in these dimensions, we rely on fast variational Bayes
approximations to the posterior distribution of the coefficients and the latent
states. We find that our proposed set of models produces precise forecasts.
These gains are especially pronounced in the tails. Using Gaussian processes to
approximate the nonlinear component of the model further improves the good
performance, in particular in the right tail.
