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

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 compo...

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Bibliographic Details
Published in:Journal of financial econometrics 2021, Vol.19 (5), p.789-822
Main Author: Li, Fuchun
Format: Article
Language:English
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Summary: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.
ISSN:1479-8409
1479-8417
DOI:10.1093/jjfinec/nbz026