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

Testing Continuous-Time Models of the Spot Interest Rate

Fuchun Li

Journal of Financial Econometrics, 2021, vol. 19, issue 5, 789-822

Abstract: 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.

Keywords: diffusion matrix; continuous-time Markov process model; affine term structure model (search for similar items in EconPapers)
JEL-codes: C12 C14 E17 E43 G12 (search for similar items in EconPapers)
Date: 2021
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