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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.

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  • 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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    Full references (including those not matched with items on IDEAS)

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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, vol. 186(1), pages 94-112.
    2. Xu, Ke-Li, 2017. "Regression discontinuity with categorical outcomes," Journal of Econometrics, Elsevier, vol. 201(1), pages 1-18.
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    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. Zhang, Hongfan, 2018. "Quasi-likelihood estimation of the single index conditional variance model," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 58-72.
    7. Marc G. Genton & Peter Hall, 2016. "A tilting approach to ranking influence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 77-97, January.
    8. Isabel Casas & Xiuping Mao & Helena Veiga, 2018. "Reexamining financial and economic predictability with new estimators of realized variance and variance risk premium," CREATES Research Papers 2018-10, Department of Economics and Business Economics, Aarhus University.
    9. Yuping Song & Weijie Hou & Zhengyan Lin, 2022. "Double Smoothed Volatility Estimation of Potentially Non‐stationary Jump‐diffusion Model of Shibor," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 53-82, January.
    10. Taisuke Otsu & Ke-Li Xu & Yukitoshi Matsushita, 2013. "Estimation and Inference of Discontinuity in Density," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 507-524, October.
    11. Ke-Li Xu & Jui-Chung Yang, 2015. "Towards Uniformly Efficient Trend Estimation Under Weak/Strong Correlation and Non-stationary Volatility," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 63-86, March.
    12. Enno Mammen & Jens Perch Nielsen & Michael Scholz & Stefan Sperlich, 2019. "Conditional Variance Forecasts for Long-Term Stock Returns," Risks, MDPI, vol. 7(4), pages 1-22, November.
    13. Christopher F. Parmeter & Valentin Zelenyuk, 2019. "Combining the Virtues of Stochastic Frontier and Data Envelopment Analysis," Operations Research, INFORMS, vol. 67(6), pages 1628-1658, November.
    14. Zheng Li & Guannan Liu & Qi Li, 2017. "Nonparametric Knn estimation with monotone constraints," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 988-1006, October.
    15. Song Yuping & Hou Weijie & Zhou Shengyi, 2019. "Variance reduction estimation for return models with jumps using gamma asymmetric kernels," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(5), pages 1-38, December.
    16. 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.
    17. Ilya Kuzminov & Dirk Meissner & Alina Lavrynenko & Elena Tochilina, 2018. "Technology Classification for the Purposes of Futures Studies," HSE Working papers WP BRP 78/STI/2018, National Research University Higher School of Economics.
    18. 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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