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

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