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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]

Author

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  • Fuchun Li

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.

Suggested Citation

  • Fuchun Li, 2021. "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]," Journal of Financial Econometrics, Oxford University Press, vol. 19(5), pages 789-822.
    • Handle: RePEc:oup:jfinec:v:19:y:2021:i:5:p:789-822.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbz026
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    More about this item

    Keywords

    diffusion matrix; continuous-time Markov process model; affine term structure model;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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