Nonparametric localized bandwidth selection for kernel density estimation

Tingting Cheng, Jiti Gao, Xibin Zhang

Research output: Contribution to journalArticleResearchpeer-review

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 establish 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.

Original languageEnglish
Pages (from-to)733-762
Number of pages30
JournalEconometric Reviews
Volume38
Issue number7
DOIs
Publication statusPublished - 2019

Keywords

  • Density estimation
  • GARCH model
  • localized bandwidth

Cite this

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Nonparametric localized bandwidth selection for kernel density estimation. / Cheng, Tingting; Gao, Jiti; Zhang, Xibin.

In: Econometric Reviews, Vol. 38, No. 7, 2019, p. 733-762.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Gao, Jiti

AU - Zhang, Xibin

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AB - 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 establish 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.

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