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Semiparametric Localized Bandwidth Selection for Kernel Density Estimation

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  • Tingting Cheng
  • Jiti Gao
  • Xibin Zhang

Abstract

Since conventional cross–validation bandwidth selection methods don’t work for the case where the data considered are dependent time series, alternative bandwidth selection methods are needed. In recent years, Bayesian based global bandwidth selection methods have been proposed. Our experience shows that the use of a global bandwidth is however less suitable than using a localized bandwidth in kernel density estimation in the case where the data are dependent time series as discussed in an empirical application of this paper. Nonetheless, a difficult issue is how we can consistently estimate a localized bandwidth. In this paper, we propose a semiparametric estimation method, for which we establish a completely new asymptotic theory for the proposed semiparametric localized bandwidth estimator. Applications of the 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 semiparametric localized bandwidth.

Suggested Citation

  • Tingting Cheng & Jiti Gao & Xibin Zhang, 2014. "Semiparametric Localized Bandwidth Selection for Kernel Density Estimation," Monash Econometrics and Business Statistics Working Papers 27/14, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2014-27
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    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp27-14.pdf
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    References listed on IDEAS

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    1. Xibin Zhang & Maxwell L. King, 2013. "Gaussian kernel GARCH models," Monash Econometrics and Business Statistics Working Papers 19/13, Monash University, Department of Econometrics and Business Statistics.
    2. Max de Lima & Gregorio Atuncar, 2011. "A Bayesian method to estimate the optimal bandwidth for multivariate kernel estimator," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 137-148.
    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.
    4. Nils-Bastian Heidenreich & Anja Schindler & Stefan Sperlich, 2013. "Bandwidth selection for kernel density estimation: a review of fully automatic selectors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 403-433, October.
    5. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
    6. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-359, October.
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    Cited by:

    1. Tingting Cheng & Jiti Gao & Oliver Linton, 2017. "Multi-step non- and semi-parametric predictive regressions for short and long horizon stock return prediction," Monash Econometrics and Business Statistics Working Papers 13/17, Monash University, Department of Econometrics and Business Statistics.
    2. Sreevani, & Murthy, C.A., 2016. "On bandwidth selection using minimal spanning tree for kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 102(C), pages 67-84.

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