Most existing empirical studies on affine term structure models have primarily focused on in-sample Þt of historical bond yields and ignored out-of-sample forecast of future bond yields. Using an omnibus nonparametric procedure for density forecast evaluation developed in this paper, we provide probably the first comprehensive empirical analysis of the out-of-sample performance of affine term structure models in forecasting the joint conditional probability density of bond yields. We show that although it is difficult to forecast the conditional mean of bond yields, some affine models have good forecasts of the joint conditional density of bond yields and they significantly outperform simple random walk models in density forecast. Our analysis demonstrates the great potential of affine models for financial risk management in fixed-income markets.

We develop a nonparametric specification test for continuous-time models using the transition density. Using a data transform and correcting for boundary bias of kernel estimators, our test is robust to serial dependence in data and provides excellent finite sample performance. Besides univariate diffusion models, our test is applicable to a wide variety of continuous-time and discretetime dynamic models, including time-inhomogeneous diffusion, GARCH, stochastic volatility, regimeswitching,jump-diffusion, and multivariate diffusion models. A class of separate inference procedures is also proposed to help gauge possible sources of model misspecification. We strongly reject a variety of univariate diffusion models for daily Eurodollar spot rates and some popular multivariate affine term structure models for monthly U.S. Treasury yields.