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Tilted Nonparametric Estimation of Volatility Functions With Empirical Applications

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  • Ke-Li Xu
  • Peter C. B. Phillips

Abstract

This article proposes a novel positive nonparametric estimator of the conditional variance function without reliance on logarithmic or other transformations. The estimator is based on an empirical likelihood modification of conventional local-level nonparametric regression applied to squared residuals of the mean regression. The estimator is shown to be asymptotically equivalent to the local linear estimator in the case of unbounded support but, unlike that estimator, is restricted to be nonnegative in finite samples. It is fully adaptive to the unknown conditional mean function. Simulations are conducted to evaluate the finite-sample performance of the estimator. Two empirical applications are reported. One uses cross-sectional data and studies the relationship between occupational prestige and income, and the other uses time series data on Treasury bill rates to fit the total volatility function in a continuous-time jump diffusion model.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:jnlbes:v:29:y:2011:i:4:p:518-528 DOI: 10.1198/jbes.2011.09012
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    Cited by:

    1. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, pages 94-112.
    2. repec:eee:econom:v:201:y:2017:i:1:p:1-18 is not listed on IDEAS
    3. repec:cep:stiecm:/2014/573 is not listed on IDEAS
    4. Matthieu Garcin & Clément Goulet, 2015. "Non-parameteric news impact curve: a variational approach," Documents de travail du Centre d'Economie de la Sorbonne 15086rr, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Feb 2017.
    5. Giuseppe Cavaliere & Peter C. B. Phillips & Stephan Smeekes & A. M. Robert Taylor, 2015. "Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 34(4), pages 512-536, April.
    6. Taisuke Otsu & Ke-Li Xu & Yukitoshi Matsushita, 2013. "Estimation and Inference of Discontinuity in Density," Journal of Business & Economic Statistics, Taylor & Francis Journals, pages 507-524.
    7. 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, pages 135-159.
    8. 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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