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 propose two nonparametric transition density-based speciÞcation tests for continuous-time models. Unlike the marginal density used in the literature, the transition density can capture the full dynamics of a continuous-time process. To address the concerns of the Þnite sample perfor- mance of nonparametric methods in the literature, we introduce an appropriate data transfor- mation and correct the boundary bias of kernel estimators. As a result, our tests are robust to persistent dependence in data and provide reliable inferences for sample sizes often encountered in empirical Þnance. Simulation studies show that even for data with highly persistent depen- dence, our tests have reasonable size and good power against a variety of alternatives in Þnite samples. Besides one-factor diffusion models, our tests can be applied to a broad class of dynamic models, including discrete-time dynamic models, time-inhomogeneous diffusion models, stochas- tic volatility models, jump-diffusion models, and multi-factor diffusion models. When applied to Eurodollar interest rates, our tests overwhelmingly reject a variety of popular one-factor diffusion models. We Þnd that introducing nonlinear drift does not signiÞcantly improve the goodness of Þt, and the main reason for the rejection of one-factor diffusion models is the violation of the Markov assumption. Some popular non-Markovian models with GARCH, regime switching and jumps perform signiÞcantly better than one-factor diffusion models, but they are still far from being adequate to fully capture the interest rate dynamics. Our study shows that, contrary to the general perception in the literature, nonparametric methods are a reliable and powerful tool for analyzing Þnancial data.