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Testing the Parametric Specification of the Diffusion Function in a Diffusion Process

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  • Fuchun Li

Abstract

A new consistent test is proposed for the parametric specification of the diffusion function in a diffusion process without any restrictions on the functional form of the drift function. The data are assumed to be sampled discretely in a time interval that can be fixed or lengthened to infinity. The test statistic is shown to follow an asymptotic normal distribution under the null hypothesis that the parametric diffusion function is correctly specified. Monte Carlo simulations are conducted to examine the finite-sample performance of the test, revealing that the test has good size and power.

Suggested Citation

  • Fuchun Li, 2005. "Testing the Parametric Specification of the Diffusion Function in a Diffusion Process," Staff Working Papers 05-35, Bank of Canada.
  • Handle: RePEc:bca:bocawp:05-35
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Song, Zhaogang, 2011. "A martingale approach for testing diffusion models based on infinitesimal operator," Journal of Econometrics, Elsevier, vol. 162(2), pages 189-212, June.
    2. Gao, Jiti & Casas, Isabel, 2008. "Specification testing in discretized diffusion models: Theory and practice," Journal of Econometrics, Elsevier, vol. 147(1), pages 131-140, November.
    3. Chen, Bin & Hong, Yongmiao, 2011. "Generalized spectral testing for multivariate continuous-time models," Journal of Econometrics, Elsevier, vol. 164(2), pages 268-293, October.
    4. Kristensen, Dennis, 2011. "Semi-nonparametric estimation and misspecification testing of diffusion models," Journal of Econometrics, Elsevier, vol. 164(2), pages 382-403, October.
    5. repec:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-016-0685-z is not listed on IDEAS
    6. Chen, Bin & Song, Zhaogang, 2013. "Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach," Journal of Econometrics, Elsevier, vol. 173(1), pages 83-107.
    7. Zu, Yang & Boswijk, H. Peter, 2017. "Consistent nonparametric specification tests for stochastic volatility models based on the return distribution," Journal of Empirical Finance, Elsevier, vol. 41(C), pages 53-75.
    8. repec:wyi:journl:002142 is not listed on IDEAS
    9. Zu, Y., 2015. "Consistent nonparametric specification tests for stochastic volatility models based on the return distribution," Working Papers 15/02, Department of Economics, City University London.
    10. Chen, Qiang & Zheng, Xu & Pan, Zhiyuan, 2015. "Asymptotically distribution-free tests for the volatility function of a diffusion," Journal of Econometrics, Elsevier, vol. 184(1), pages 124-144.
    11. Fuchun Li, 2015. "Testing for the Diffusion Matrix in a Continuous-Time Markov Process Model with Applications to the Term Structure of Interest Rates," Staff Working Papers 15-17, Bank of Canada.
    12. repec:wyi:journl:002117 is not listed on IDEAS
    13. Monsalve-Cobis, Abelardo & González-Manteiga, Wenceslao & Febrero-Bande, Manuel, 2011. "Goodness-of-fit test for interest rate models: An approach based on empirical processes," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3073-3092, December.

    More about this item

    Keywords

    Econometric and statistical methods; Interest rates;

    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

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