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Specification testing in discretized diffusion models: Theory and practice

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Author Info
Gao, Jiti
Casas, Isabel

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Abstract

We propose two new tests for the specification of both the drift and the diffusion functions in a discretized version of a semiparametric continuous-time financial econometric model. Theoretically, we establish some asymptotic consistency results for the proposed tests. Practically, a simple selection procedure for the bandwidth parameter involved in each of the proposed tests is established based on the assessment of the power function of the test under study. To the best of our knowledge, this is the first approach of this kind in specification of continuous-time financial econometrics. The proposed theory is supported by good small and medium-sample studies.

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Publisher Info
Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 147 (2008)
Issue (Month): 1 (November)
Pages: 131-140
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Handle: RePEc:eee:econom:v:147:y:2008:i:1:p:131-140

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Web page: http://www.elsevier.com/locate/jeconom

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Related research
Keywords: Continuous-time diffusion process Kernel method Nonparametric testing Power function Size function Time series econometrics;

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References listed on IDEAS
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  1. Yacine Aït-Sahalia, 1999. "Transition Densities for Interest Rate and Other Nonlinear Diffusions," Journal of Finance, American Finance Association, vol. 54(4), pages 1361-1395, 08. [Downloadable!] (restricted)
  2. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May. [Downloadable!] (restricted)
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  3. Manuel Arapis & Jiti Gao, 2006. "Empirical Comparisons in Short-Term Interest Rate Models Using Nonparametric Methods," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 310-345. [Downloadable!] (restricted)
    Other versions:
  4. Dennis Kristensen, 2004. "Estimation in Two Classes of Semiparametric Diffusion Models," FMG Discussion Papers dp500, Financial Markets Group. [Downloadable!] (restricted)
  5. Li, Fuchun, 2007. "Testing The Parametric Specification Of The Diffusion Function In A Diffusion Process," Econometric Theory, Cambridge University Press, vol. 23(02), pages 221-250, April. [Downloadable!]
  6. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December. [Downloadable!] (restricted)
  7. Yanqin Fan & Oliver Linton, 1997. "Some Higher Order Theory for a Consistent Nonparametric Model Specification Test," Cowles Foundation Discussion Papers 1148, Cowles Foundation, Yale University. [Downloadable!]
  8. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September. [Downloadable!] (restricted)
  9. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-90, July. [Downloadable!] (restricted)
  10. Nicolau, Jo o, 2003. "Bias Reduction In Nonparametric Diffusion Coefficient Estimation," Econometric Theory, Cambridge University Press, vol. 19(05), pages 754-777, October. [Downloadable!]
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