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Reweighted Nadaraya-Watson estimator of scalar diffusion models by using asymmetric kernels

Author

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  • Muhammad Hanif

    (Department of Mathematics, Zhejiang University, Hangzhou, China, 310027)

Abstract

The nonparametric estimation of first and second infinitesimal moments describe by using the reweighted Nadaraya-Watson of scalar diffusion model. We used the symmetric kernels instead of standard kernel smoothing. We prove that the proposed estimators are consistence and asymptotically follow normal distribution under the condition of recurrence and stationarity.

Suggested Citation

  • Muhammad Hanif, 2011. "Reweighted Nadaraya-Watson estimator of scalar diffusion models by using asymmetric kernels," Far East Journal of Psychology and Business, Far East Research Centre, vol. 4(5), pages 53-69, July.
    • Handle: RePEc:fej:articl:v:4a:y:2011:i:5:p:53-69
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    References listed on IDEAS

    as
    1. Jiang, George J. & Knight, John L., 1997. "A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model," Econometric Theory, Cambridge University Press, vol. 13(5), pages 615-645, October.
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    3. 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.
    4. Olivier SCAILLET, 2001. "Density Estimation Using Inverse and Reciprocal Inverse Guassian Kernels," LIDAM Discussion Papers IRES 2001017, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    5. Marcelo Fernandes & Paulo Monteiro, 2005. "Central limit theorem for asymmetric kernel functionals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(3), pages 425-442, September.
    6. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 471-480, September.
    7. Xu, Ke-Li, 2010. "Reweighted Functional Estimation Of Diffusion Models," Econometric Theory, Cambridge University Press, vol. 26(2), pages 541-563, April.
    8. 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.
    9. 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.
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    11. Stanton, Richard, 1997. "A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1973-2002, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Beta kernel; Gamma kernel; Harris recurrence; Local time; Nonparametric estimation; Reweighted Nadaraya-Watson estimator; Stochastic differential equation;
    All these keywords.

    JEL classification:

    • M1 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration

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