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Specification testing in discretized diffusion models: Theory and practice

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  • Gao, Jiti
  • Casas, Isabel

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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File URL: http://www.sciencedirect.com/science/article/B6VC0-4TDVMJY-3/2/c45e6745d432808f5e7c1472325ea18e
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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
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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

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Find related papers by JEL classification:
  • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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  1. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, vol. 71(1), pages 241-283, January.
  2. Manuel Arapis & Jiti Gao, 2006. "Empirical Comparisons in Short-Term Interest Rate Models Using Nonparametric Methods," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(2), pages 310-345.
  3. Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc.
  4. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May.
  5. Dennis Kristensen, 2004. "Estimation in Two Classes of Semiparametric Diffusion Models," FMG Discussion Papers dp500, Financial Markets Group.
  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.
  7. 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.
  8. Yanqin Fan & Oliver Linton, 1997. "Some Higher Order Theory for a Consistent Nonparametric Model Specification Test," Cowles Foundation Discussion Papers 1148, Cowles Foundation for Research in Economics, Yale University.
  9. Corradi, Valentina & Swanson, Norman R., 2005. "Bootstrap specification tests for diffusion processes," Journal of Econometrics, Elsevier, vol. 124(1), pages 117-148, January.
  10. Li, Q. & Wang, Suojin, 1998. "A simple consistent bootstrap test for a parametric regression function," Journal of Econometrics, Elsevier, vol. 87(1), pages 145-165, August.
  11. Nicolau, Jo o, 2003. "Bias Reduction In Nonparametric Diffusion Coefficient Estimation," Econometric Theory, Cambridge University Press, vol. 19(05), pages 754-777, October.
  12. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
  13. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
  14. Fuchun Li, 2005. "Testing the Parametric Specification of the Diffusion Function in a Diffusion Process," Working Papers 05-35, Bank of Canada.
  15. Chen, Song Xi & Gao, Jiti & Tang, Chenghong, 2005. "A test for model specification of diffusion processes," MPRA Paper 11976, University Library of Munich, Germany, revised Feb 2007.
  16. Yongmiao Hong, 2005. "Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 37-84.
  17. Gao, Jiti & King, Maxwell, 2004. "Adaptive Testing In Continuous-Time Diffusion Models," Econometric Theory, Cambridge University Press, vol. 20(05), pages 844-882, October.
  18. 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.
  19. Chen, Song Xi & Gao, Jiti, 2007. "An adaptive empirical likelihood test for parametric time series regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 950-972, December.
  20. Fan, Yanqin & Li, Qi, 2000. "Consistent Model Specification Tests," Econometric Theory, Cambridge University Press, vol. 16(06), pages 1016-1041, December.
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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. 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, vol. 22(3), pages 361-411, September.
  3. 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.

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