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Nonparametric specification testing for continuous-time models with application to spot interest rates


  • Hong, Yongmiao
  • Li, Haitao


We propose two nonparametric transition density-based speciþcation tests for continuous-time diffusion models. In contrast to marginal density as used in the literature, transition density can capture the full dynamics of a diffusion process, and in particular, can distinguish processes with the same marginal density but different transition densities. To address the concerns of the þnite sample performance of nonparametric methods in the literature, we introduce an appropriate data transformation and correct the boundary bias of kernel estimators. As a result, our tests are robust to persistent dependence in data and provide reliable inferences for sample sizes often encountered in empirical þnance. Simulation studies show that our tests have reasonable size and good power against a variety of alternatives in þnite samples even for data with highly persistent dependence. Besides the single-factor diffusion models, our tests can be applied to a broad class of dynamic economic models, such as discrete time series models, time-inhomogeneous diffusion models, stochastic volatility models, jump-diffusion models, and multi-factor term structure models. When applied to daily Eurodollar interest rates, our tests overwhelmingly reject some popular spot rate models, including those with nonlinear drifts that some existing tests can not reject after correcting size distortions. We þnd that models with nonlinear drifts do not signiþcantly improve the goodness-of-þt, and the main source of model inadequacy seems to be the violation of the Markov assumption. We also þnd that GARCH, regime switching and jump diffusion models perform signiþcantly better than single-factor diffusion models, although they are far from being adequate to fully capture the interest rate dynamics. Our study shows that nonparametric methods are a reliable and powerful tool for analyzing þnancial data.

Suggested Citation

  • Hong, Yongmiao & Li, Haitao, 2002. "Nonparametric specification testing for continuous-time models with application to spot interest rates," SFB 373 Discussion Papers 2002,32, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:200232

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    References listed on IDEAS

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    Cited by:

    1. Isao Ishida, 2005. "Scanning Multivariate Conditional Densities with Probability Integral Transforms," CIRJE F-Series CIRJE-F-369, CIRJE, Faculty of Economics, University of Tokyo.
    2. Xiaohong Chen & Yanqin Fan, 2002. "Evaluating Density Forecasts via the Copula Approach," Vanderbilt University Department of Economics Working Papers 0225, Vanderbilt University Department of Economics, revised Sep 2003.
    3. Li, Fuchun & Tkacz, Greg, 2006. "A consistent bootstrap test for conditional density functions with time-series data," Journal of Econometrics, Elsevier, vol. 133(2), pages 863-886, August.
    4. Hamilton, James D. & Wu, Jing Cynthia, 2014. "Testable implications of affine term structure models," Journal of Econometrics, Elsevier, vol. 178(P2), pages 231-242.
    5. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    6. Yanqin Fan & Xiaohong Chen & Andrew Patton, 2004. "(IAM Series No 003) Simple Tests for Models of Dependence Between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates," FMG Discussion Papers dp483, Financial Markets Group.
    7. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
    8. Durham, Garland B., 2007. "SV mixture models with application to S&P 500 index returns," Journal of Financial Economics, Elsevier, vol. 85(3), pages 822-856, September.

    More about this item


    Boundary bias; Continuous-time model; Hellinger metric; Kernel method; Parameter estimation uncertainty; Probability integral transform; Quadratic form; Short-term interest rate; Transition density;

    JEL classification:

    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
    • G0 - Financial Economics - - General


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