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Re-weighted functional estimation of second-order diffusion processes

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Author Info

  • Yunyan Wang

    ()

  • Lixin Zhang

    ()

  • Mingtian Tang

    ()

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    Abstract

    Second-order diffusion process can not only model integrated and differentiated diffusion processes but also overcome the difficulties associated with the nondifferentiability of the Brownian motion, so these models play an important role in econometric analysis. In this paper, we propose a re-weighted estimator of the diffusion coefficient in the second-order diffusion model. Consistence of the estimator is proved under appropriate conditions and the conditions that ensure the asymptotic normality are also stated. The performance of the proposed estimator is assessed by simulation study. Copyright Springer-Verlag 2012

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    File URL: http://hdl.handle.net/10.1007/s00184-011-0372-6
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    Bibliographic Info

    Article provided by Springer in its journal Metrika.

    Volume (Year): 75 (2012)
    Issue (Month): 8 (November)
    Pages: 1129-1151

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    Handle: RePEc:spr:metrik:v:75:y:2012:i:8:p:1129-1151

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    Web page: http://www.springerlink.com/link.asp?id=102509

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    Related research

    Keywords: Asymptotic normality; Consistency; Diffusion process; Empirical likelihood; Re-weighted estimator;

    References

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    1. Arnaud Gloter, 2006. "Parameter Estimation for a Discretely Observed Integrated Diffusion Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 33(1), pages 83-104.
    2. Susanne Ditlevsen & Michael Sørensen, 2004. "Inference for Observations of Integrated Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 31(3), pages 417-429.
    3. Gobet, Emmanuel & Hoffmann, Marc & Reiß, Markus, 2002. "Nonparametric estimation of scalar diffusions based on low frequency data is ill-posed," SFB 373 Discussion Papers 2002,57, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Cai, Zongwu, 2001. "Weighted Nadaraya-Watson regression estimation," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 307-318, February.
    5. Xu, Ke-Li & Phillips, Peter C. B., 2011. "Tilted Nonparametric Estimation of Volatility Functions With Empirical Applications," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 518-528.
    6. Federico M. Bandi & Peter C.B. Phillips, 2001. "Fully Nonparametric Estimation of Scalar Diffusion Models," Cowles Foundation Discussion Papers 1332, Cowles Foundation for Research in Economics, Yale University.
    7. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(01), pages 169-192, February.
    8. Nicolau, Jo o, 2007. "Nonparametric Estimation Of Second-Order Stochastic Differential Equations," Econometric Theory, Cambridge University Press, vol. 23(05), pages 880-898, October.
    9. Xu, Ke-Li, 2010. "Reweighted Functional Estimation Of Diffusion Models," Econometric Theory, Cambridge University Press, vol. 26(02), pages 541-563, April.
    10. P. Hall & B. Presnell, 1999. "Intentionally biased bootstrap methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 143-158.
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