This paper compares alternative models of time-varying volatility on the basis of the accuracy of real-time point and density forecasts of key macroeconomic time series for the USA. We consider Bayesian autoregressive and vector autoregressive models that incorporate some form of time-varying volatility, precisely random walk stochastic volatility, stochastic volatility following a stationary AR process, stochastic volatility coupled with fat tails, GARCH and mixture of innovation models. The results show that the AR and VAR specifications with conventional stochastic volatility dominate other volatility specifications, in terms of point forecasting to some degree and density forecasting to a greater degree. Copyright © 2014 John Wiley & Sons, Ltd.