In light of widespread evidence of parameter instability in macroeconomic models, many time-varying parameter (TVP) models have been proposed. This paper proposes a nonparametric TVP-VAR model using Bayesian additive regression trees (BART). The novelty of this model stems from the fact that the law of motion driving the parameters is treated nonparametrically. This leads to great flexibility in the nature and extent of parameter change, both in the conditional mean and in the conditional variance. In contrast to other nonparametric and machine learning methods that are black box, inference using our model is straightforward because, in treating the parameters rather than the variables nonparametrically, the model remains conditionally linear in the mean. Parsimony is achieved through adopting nonparametric factor structures and use of shrinkage priors. In an application to US macroeconomic data, we illustrate the use of our model in tracking both the evolving nature of the Phillips curve and how the effects of business cycle shocks on inflationary measures vary nonlinearly with movements in uncertainty.
We develop multivariate time series models using Bayesian additive regression trees that posit nonlinearities among macroeconomic variables, their lags, and possibly their lagged errors. The error variances can be stable, feature stochastic volatility, or follow a nonparametric specification. We evaluate density and tail forecast performance for a set of US macroeconomic and financial indicators. Our results suggest that the proposed models improve forecast accuracy both overall and in the tails. Another finding is that when allowing for nonlinearities in the conditional mean, heteroskedasticity becomes less important. A scenario analysis reveals nonlinear relations between predictive distributions and financial conditions.
The relationship between inflation and predictors such as unemployment is potentially nonlinear with a strength that varies over time, and prediction errors may be subject to large, asymmetric shocks. Inspired by these concerns, we develop a model for inflation forecasting that is nonparametric both in the conditional mean and in the error using Gaussian and Dirichlet processes, respectively. We discuss how both these features may be important in producing accurate forecasts of inflation. In a forecasting exercise involving CPI inflation, we find that our approach has substantial benefits, both overall and in the left tail, with nonparametric modeling of the conditional mean being of particular importance.
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.