Tail forecasting with multivariate Bayesian additive regression trees

We develop novel multivariate time series models using Bayesian additive regression trees which posit nonlinear relationships among macroeconomic variables, their lags, and possibly the lags of the errors. The variance of the errors can be stable, driven by stochastic volatility (SV), or follow a novel non-parametric specification. We develop scalable Markov Chain Monte Carlo estimation algorithms for each specification. We evaluate the real-time density and tail forecasting performance of the various models for a set of US macroeconomic and financial indicators. Our results suggest that using non-parametric models generally leads to improved forecast accuracy. Especially when interest centers on the tails of the posterior predictive, flexible models improve upon standard VAR models with SV. Another key finding is that if we allow for non-linearities in the conditional mean, allowing for heteroscedasticity becomes less important.