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Bias Reduction In Nonparametric Diffusion Coefficient Estimation

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  • Nicolau, Jo o
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    Abstract

    In this paper, we quantify the asymptotic bias of the Florens-Zmirou (1993, Journal of Applied Probability 30, 790 804) and Jiang and Knight (1997, Econometric Theory 13, 615 645) estimator for the diffusion coefficient when the step of discretization is fixed, and then we propose a bias adjustment that partially compensates for the distortion. Also, we show that our estimators have all the asymptotic properties of the Florens-Zmirou and Jiang and Knight estimator when the step of discretization goes to zero. We provide some examples.I thank the editor Peter C.B. Phillips and the two referees for comments and suggestions that led to considerable improvement of the paper. I am also grateful to Carlos Braumann and Tom Kundert for helpful comments. This research was supported by the Funda o para a Ci ncia e a Tecnologia (FCT) and by POCTI.

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    Bibliographic Info

    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 19 (2003)
    Issue (Month): 05 (October)
    Pages: 754-777

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    Handle: RePEc:cup:etheor:v:19:y:2003:i:05:p:754-777_19

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    Cited by:
    1. Yamamura, Mariko & Shoji, Isao, 2010. "A nonparametric method of multi-step ahead forecasting in diffusion processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2408-2415.
    2. Kristensen, Dennis, 2011. "Semi-nonparametric estimation and misspecification testing of diffusion models," Journal of Econometrics, Elsevier, vol. 164(2), pages 382-403, October.
    3. Arapis, Manuel & Gao, Jiti, 2004. "Empirical comparisons in short-term interest rate models using nonparametric methods," MPRA Paper 11974, University Library of Munich, Germany, revised 23 Dec 2005.
    4. Xu, Ke-Li, 2010. "Reweighted Functional Estimation Of Diffusion Models," Econometric Theory, Cambridge University Press, vol. 26(02), pages 541-563, April.
    5. Gao, Jiti & Casas, Isabel, 2006. "Specification testing in discretized diffusion models: Theory and practice," MPRA Paper 11980, University Library of Munich, Germany, revised Aug 2007.
    6. Xu, Ke-Li, 2009. "Empirical likelihood-based inference for nonparametric recurrent diffusions," Journal of Econometrics, Elsevier, vol. 153(1), pages 65-82, November.
    7. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    8. Fuchun Li, 2005. "Testing the Parametric Specification of the Diffusion Function in a Diffusion Process," Working Papers 05-35, Bank of Canada.
    9. Nikolay Gospodinov & Masayuki Hirukawa, 2008. "Nonparametric Estimation of Scalar Diffusion Processes of Interest Rates Using Asymmetric Kernels," Working Papers 08011, Concordia University, Department of Economics, revised Dec 2008.

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