Testing for the Diffusion Matrix in a Continuous-Time Markov Process Model with Applications to the Term Structure of Interest Rates

For each component in the diffusion matrix of a d-dimensional diffusion process, we propose a test for the parametric specification of this component. Overall, d(d-1)/2 test statistics are constructed for the off-diagonal components, while d test statistics being for the main diagonal components. Using theories of degenerate U-statistics, each of all these test statistics is shown to follow an asymptotic standard normal distribution under null hypothesis, while diverging to infinity if the component is misspecified over a significant range. We obtain new empirical findings by applying our tests to evaluate a variety of three-factor affine term structure models in modeling the volatility dynamics of monthly U.S. Treasury yields.