Tail Forecasting with Multivariate Bayesian Additive Regression Trees

Abstract

We develop novel multivariate time series models using Bayesian additive regression trees that 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 nonparametric specification. Estimation is carried out using 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 nonparametric models generally leads to improved forecast accuracy. In particular, 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 nonlinearities in the conditional mean, allowing for heteroskedasticity becomes less important. A scenario analysis reveals highly nonlinear relations between the predictive distribution and financial conditions.

Tail Forecasting With Multivariate Bayesian Additive Regression Trees

“…which provides shrinkage by quantile. A similar prior structure for quantile regression has been proposed in Clark et al (2021). For the scale parameter of the AL distribution, we use a weakly informative inverse Gamma prior:…”

Can Machine Learning Catch the Covid-19 Recession?

“…Another relevant related paper is Goulet Coulombe et al (2019), which however does not include an analysis of the Covid-19 period and focuses on the United States. A third related paper, again with a focus on the United States, is Clark et al (2021), who consider alternative specifications of BART-VARs, possibly with also a non-parametric specification for the time-varying volatility, and compare their point, density and tail forecast performance with that of large Bayesian VARs with stochastic volatility, finding often gains, though of limited size.…”