We propose a method to produce density forecasts of the term structure of government bond yields that accounts for (i) the possible mispecification of an underlying Gaussian Affine Term Structure Model (GATSM) and (ii) the time varying volatility of interest rates. For this, we derive a Bayesian prior from a GATSM and use it to estimate the coefficients of a BVAR for the term structure, specifying a common, multiplicative, time varying volatility for the VAR disturbances. Results based on U.S. data show that this method significantly improves the precision of point and density forecasts of the term structure. While this paper focuses on term structure modelling, the proposed method can be applied for a wide range of alternative models, including DSGE models, and is a generalization of the method of Del Negro and Schorfheide (2004) to VARs featuring drifting volatilities. Our results show that both time variation in volatilities, and a hierarchical specification for the prior means, improve model fit and forecasting performance. (Coauthors: Todd E. Clark (Federal Reserve Bank of Cleveland), Massimiliano Marcellino (Bocconi University.)