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Nonparametric Estimation and Misspecification Testing of Diffusion Models

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Author Info
Dennis Kristensen () (School of Economics and Management, University of Aarhus, Denmark and CREATES)

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Abstract

A nonparametric kernel estimator of the drift (diffusion) term in a diffusion model are developed given a preliminary parametric estimator of the diffusion (drift) term. Under regularity conditions, rates of convergence and asymptotic normality of the nonparametric estimators are established. We develop mis- specification tests of parametric diffusion models based on the nonparametric estimators, and derive the asymptotic properties of the tests. We also propose a Markov Bootstrap method for the test statistics to improve on the finite-sample approximations. The finite sample properties of the estimators are examined in a simulation study.

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Publisher Info
Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2007-01.

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Length: 31
Date of creation: 11 May 2007
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Handle: RePEc:aah:create:2007-01

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Web page: http://www.econ.au.dk/afn/

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Related research
Keywords: Diffusion; fixed-time distance asymptotics; kernel estimation; misspecification test; nonparametric;

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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  3. Federico M. Bandi & Peter C.B. Phillips, 2005. "A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions," Cowles Foundation Discussion Papers 1522, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  4. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May. [Downloadable!] (restricted)
    Other versions:
  5. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
    Other versions:
  7. Lars Peter Hansen & Jose Alexandre Scheinkman, 1993. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," NBER Technical Working Papers 0141, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  8. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 12(4), pages 721-62.
  9. Darolles, Serge & Gourieroux, Christian, 2001. "Truncated dynamics and estimation of diffusion equations," Journal of Econometrics, Elsevier, vol. 102(1), pages 1-22, May. [Downloadable!] (restricted)
  10. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June. [Downloadable!]
  11. Dennis Kristensen & Yongseok Shin, 2008. "Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood," CREATES Research Papers 2008-58, School of Economics and Management, University of Aarhus. [Downloadable!]
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