Validating forecasts of the joint probability density of bond yields: Can affine models beat random walk?

Most existing empirical studies on affine term structure models (ATSMs) have mainly focused on in-sample goodness-of-fit of historical bond yields and ignored out-of-sample forecast of future bond yields. Using an omnibus nonparametric procedure for density forecast evaluation in a continuous-time framework, we provide probably the first comprehensive empirical analysis of the out-of-sample performance of ATSMs in forecasting the joint conditional probability density of bond yields. We find that although the random walk models tend to have better forecasts for the conditional mean dynamics of bond yields, some ATSMs provide better forecasts for the joint probability density of bond yields. However, all ATSMs considered are still overwhelmingly rejected by our tests and fail to provide satisfactory density forecasts. There exists room for further improving density forecasts for bond yields by extending ATSMs.