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Testing The Parametric Specification Of The Diffusion Function In A Diffusion Process

Author

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  • Li, Fuchun

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.The author is grateful to Yacine Aït-Sahalia, John Knight, Oliver Linton (the co-editor), Greg Tkacz, Jun Yang, and three anonymous referees for helpful comments and suggestions. He also thanks seminar participants at the Bank of Canada, the 2004 Semiparametrics Conference in Rio de Janeiro, and the 2005 Econometric Study Group in Bristol. The views expressed in this paper are those of the author. No responsibility for them should be attributed to the Bank of Canada.

Suggested Citation

  • Li, Fuchun, 2007. "Testing The Parametric Specification Of The Diffusion Function In A Diffusion Process," Econometric Theory, Cambridge University Press, vol. 23(2), pages 221-250, April.
    • Handle: RePEc:cup:etheor:v:23:y:2007:i:02:p:221-250_07
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Tianshun Yan & Changlin Mei, 2017. "A test for a parametric form of the volatility in second-order diffusion models," Computational Statistics, Springer, vol. 32(4), pages 1583-1596, December.
    5. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    6. Adam Canopius, 2006. "Practitioners' Corner," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 346-351.
    7. 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.
    8. 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.
    9. Chen, Bin & Hong, Yongmiao, 2011. "Generalized spectral testing for multivariate continuous-time models," Journal of Econometrics, Elsevier, vol. 164(2), pages 268-293, October.
    10. repec:wyi:journl:002117 is not listed on IDEAS
    11. Kristensen, Dennis, 2011. "Semi-nonparametric estimation and misspecification testing of diffusion models," Journal of Econometrics, Elsevier, vol. 164(2), pages 382-403, October.
    12. repec:wyi:journl:002142 is not listed on IDEAS
    13. 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.
    14. 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.
    15. Zu, Y., 2015. "Consistent nonparametric specification tests for stochastic volatility models based on the return distribution," Working Papers 15/02, Department of Economics, City St George's, University of London.
    16. A. López-Pérez & M. Febrero-Bande & W. González-Manteiga, 2025. "Estimation and specification test for diffusion models with stochastic volatility," Statistical Papers, Springer, vol. 66(2), pages 1-36, February.
    17. John Knight & Fuchun Li & Mingwei Yuan, 2006. "A Semiparametric Two-Factor Term Structure Model," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 204-237.

    More about this item

    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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