Composite likelihood methods for large Bayesian VARs with stochastic volatility

Adding multivariate stochastic volatility of a flexible form to large Vector Autoregressions (VARs) involving over a hundred variables has proved challenging due to computational considerations and over‐parameterization concerns. The existing literature either works with homoskedastic models or smaller models with restrictive forms for the stochastic volatility. In this paper, we develop composite likelihood methods for large VARs with multivariate stochastic volatility. These involve estimating large numbers of parsimonious models and then taking a weighted average across these models. We discuss various schemes for choosing the weights. In our empirical work involving VARs of up to 196 variables, we show that composite likelihood methods forecast much better than the most popular large VAR approach which is computationally practical in very high dimensions: the homoskedastic VAR with Minnesota prior. We also compare our methods to various popular approaches which allow for stochastic volatility using medium and small VARs involving up to 20 variables. We find our methods to forecast appreciably better than these as well.