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.

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 US. A third related paper, again with a focus on the US, 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.…”

Impulse response estimation via flexible local projections

“…Huber et al (2020) extend the BART-VAR to a mixed frequency setting and evaluate the forecasting performance of the model. Clark et al (2021) show that multivariate BART regression models perform well in terms of tail forecasting. To the best of our knowledge, our paper is the first one to use BART in an LP framework.…”

“…Intuitive descriptions of this MCMC algorithm can be found inClark et al (2021) andHill et al (2020).…”

Nonlinearities in Macroeconomic Tail Risk through the Lens of Big Data Quantile Regressions

“…2 Times of economic stress such as the global financial crisis (GFC) or the Covid-19 pandemic have highlighted that exploiting information contained in many time series and allowing for nonlinearities improves predictive performance in turbulent periods (see, e.g., Huber et al, 2023). Since economic dynamics change in volatile economic regimes, models that control for structural breaks allow for different effects of economic shocks over time or imply nonlinear relations between GDP growth and its predictors often excel in forecasting applications (see D 'Agostino et al, 2013;Carriero et al, 2016;Adrian et al, 2021;Clark et al, 2022b;Pfarrhofer, 2022;Huber et al, 2023). Moreover, another important empirical regularity is that the set of predictors might change over time.…”