A model for U.S. macroeconomic time series that has been used for forecasting for several years is described in some detail. The model is a multivariate Bayesian autoregression, with allowance for conditional heteroskedasticity, stochastic time-variation in parameters, and non-normality of disturbances. It specifies the prior distribution in ways that improve on previous Bayesian vector autoregression specifications in realism and forecasting performance. The model's record of forecasting in recent years is displayed and discussed.