Vector autoregressive (VAR) models are the main work-horse models for macroeconomic forecasting, and provide a framework for the analysis of complex dynamics that are present between macroeconomic variables. Whether a classical or a Bayesian approach is adopted, most VAR models are linear with Gaussian innovations. This can limit the model's ability to explain the relationships in macroeconomic series. We propose a nonparametric VAR model that allows for nonlinearity in the conditional mean, heteroscedasticity in the conditional variance, and non-Gaussian innovations. Our approach differs from that of previous studies by modelling the stationary and transition densities using Bayesian nonparametric methods. Our Bayesian nonparametric VAR (BayesNP-VAR) model is applied to US and UK macroeconomic time series, and compared to other Bayesian VAR models. We show that BayesNP-VAR is a flexible model that is able to account for nonlinear relationships as well as heteroscedasticity in the data. In terms of short-run out-of-sample forecasts, we show that BayesNP-VAR predictively outperforms competing models.
Kalli, M., & Griffin, J. E. (2018). Bayesian nonparametric vector autoregressive models. Journal of Econometrics, 203(2), 267–282. https://doi.org/10.1016/j.jeconom.2017.11.009