Bayesian nonparametric time varying vector autoregressive models

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. However, 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 time-dependent nonparametric VAR model that allows for nonlinearity in the conditional mean, heteroscedasticity in the conditional variance, non-Gaussian innovations, and time-dependent transion density. The novel construction of the transion density allows for the identification of regime changes, informed by the lagged values of the variables in the systems and the time dependence. Our approach differs from that of previous studies by modelling the stationary and transition densities using Bayesian nonparametric methods. Our Bayesian nonparametric time varying VAR (BayesNP-TV-VAR) model is applied to US and UK macroeconomic time series, and compared to the gold standard TVP-SV-VAR. We show that BayesNP-TV-VAR is a flexible model that is able to account for nonlinear relationships, time-varying parameters, as well as heteroscedasticity in the data. In terms of both short-term and long term out-of-sample forecasts, we show that BayesNP-TV-VAR predictively outperforms the TVP-SV-VAR.