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Reweighted Functional Estimation Of Diffusion Models

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  • Xu, Ke-Li

Abstract

The local linear method is popular in estimating nonparametric continuous-time diffusion models, but it may produce negative results for the diffusion (or volatility) functions and thus lead to insensible inference. We demonstrate this using U.S. interest rate data. We propose a new functional estimation method of the diffusion coefficient based on reweighting the conventional Nadaraya–Watson estimator. It preserves the appealing bias properties of the local linear estimator and is guaranteed to be nonnegative in finite samples. A limit theory is developed under mild requirements (recurrence) of the data generating mechanism without assuming stationarity or ergodicity.

Suggested Citation

  • Xu, Ke-Li, 2010. "Reweighted Functional Estimation Of Diffusion Models," Econometric Theory, Cambridge University Press, vol. 26(02), pages 541-563, April.
  • Handle: RePEc:cup:etheor:v:26:y:2010:i:02:p:541-563_10
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    References listed on IDEAS

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    Cited by:

    1. repec:spr:annopr:v:256:y:2017:i:2:d:10.1007_s10479-016-2273-6 is not listed on IDEAS
    2. Ye, Xu-Guo & Lin, Jin-Guan & Zhao, Yan-Yong & Hao, Hong-Xia, 2015. "Two-step estimation of the volatility functions in diffusion models with empirical applications," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 135-159.
    3. Ke-Li Xu & Peter C. B. Phillips, 2011. "Tilted Nonparametric Estimation of Volatility Functions With Empirical Applications," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 518-528, October.
    4. 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.
    5. Peter C.B. Phillips & Ke-Li Xu, 2007. "Tilted Nonparametric Estimation of Volatility Functions," Cowles Foundation Discussion Papers 1612, Cowles Foundation for Research in Economics, Yale University, revised Jul 2010.
    6. Yunyan Wang & Lixin Zhang & Mingtian Tang, 2012. "Re-weighted functional estimation of second-order diffusion processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1129-1151, November.

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