Large Bayesian vector autoregressions with stochastic volatility and non-conjugate priors

Recent research has shown that a reliable vector autoregression (VAR) for forecasting and structural analysis of macroeconomic data requires a large set of variables and modeling time variation in their volatilities. Yet, there are no papers that provide a general solution for combining these features, due to computational complexity. Moreover, homoskedastic Bayesian VARs for large data sets so far restrict substantially the allowed prior distributions on the parameters. In this paper we propose a new Bayesian estimation procedure for (possibly very large) VARs featuring time-varying volatilities and general priors. We show that indeed empirically the new estimation procedure performs well in applications to both structural analysis and out-of-sample forecasting.