Real-time density forecasts from VARs with stochastic volatility

Central banks and other forecasters have become increasingly interested in various aspects of density forecasts. However, recent sharp changes in macroeconomic volatility such as the Great Moderation and the more recent sharp rise in volatility associated with greater variation in energy prices and the deep global recession pose significant challenges to density forecasting. Accordingly, this paper examines, with real-time data, density forecasts of U.S. GDP growth, unemployment, inflation, and the federal funds rate from VAR models with stochastic volatility. The model of interest extends the steady state prior BVAR of Villani (2009) to include stochastic volatility, because, as found in some prior work and this paper, incorporating informative priors on the steady states of the model variables often improves the accuracy of point forecasts. The evidence presented in the paper shows that adding stochastic volatility to the BVAR with a steady state prior materially improves the real-time accuracy of point and density forecasts.