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Nonparametric Localized Bandwidth Selection for Kernel Density Estimation

Author

Listed:
  • Tingting Cheng

    ()

  • Jiti Gao

    ()

  • Xibin Zhang

    ()

Abstract

As conventional cross-validation bandwidth selection methods do not work properly in the situation where the data are serially dependent time series, alternative bandwidth selection methods are necessary. In recent years, Bayesian based methods for global bandwidth selection have been studied. Our experience shows that a global bandwidth is however less suitable than a localized bandwidth in kernel density estimation based on serially dependent time series data. Nonetheless, a difficult issue is how we can consistently estimate a localized bandwidth. This paper presents a nonparametric localized bandwidth estimator, for which we established a completely new asymptotic theory. Applications of this new bandwidth estimator to the kernel density estimation of Eurodollar deposit rate and the S&P 500 daily return demonstrate the effectiveness and competitiveness of the proposed localized bandwidth.

Suggested Citation

  • Tingting Cheng & Jiti Gao & Xibin Zhang, 2016. "Nonparametric Localized Bandwidth Selection for Kernel Density Estimation," Monash Econometrics and Business Statistics Working Papers 7/16, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2016-7
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    References listed on IDEAS

    as
    1. Peter Hall & Qi Li & Jeffrey S. Racine, 2007. "Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 784-789, November.
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    3. Zhang, Xibin & King, Maxwell L. & Hyndman, Rob J., 2006. "A Bayesian approach to bandwidth selection for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3009-3031, July.
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    6. Qi Li & Juan Lin & Jeffrey S. Racine, 2013. "Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 57-65, January.
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    More about this item

    Keywords

    density estimation; localized bandwidth; GARCH model;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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