Recent work has analyzed the forecasting performance of standard dynamic
stochastic general equilibrium (DSGE) models, but little attention has been given to DSGE models that incorporate nonlinearities in exogenous driving processes. Against that background, we explore whether incorporating stochastic volatility improves DSGE forecasts (point, interval, and density). We examine real-time forecast accuracy for key macroeconomic variables including output growth, inflation, and the policy rate. We find that incorporating stochastic volatility in DSGE models of macroeconomic fundamentals markedly improves their density forecasts, just as incorporating stochastic volatility in models of financial asset returns improves their density forecasts.