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Gaussian kernel GARCH models

Author

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  • Xibin Zhang

    ()

  • Maxwell L. King

    ()

Abstract

This paper aims to investigate a Bayesian sampling approach to parameter estimation in the GARCH model with an unknown conditional error density, which we approximate by a mixture of Gaussian densities centered at individual errors and scaled by a common standard deviation. This mixture density has the form of a kernel density estimator of the errors with its bandwidth being the standard deviation. This study is motivated by the lack of robustness in GARCH models with a parametric assumption for the error density when used for error-density based inference such as value-at-risk (VaR) estimation. A contribution of the paper is to construct the likelihood and posterior of the model and bandwidth parameters under the kernel-form error density, and to derive the one-step-ahead posterior predictive density of asset returns. We also investigate the use and benefit of localized bandwidths in the kernel-form error density. A Monte Carlo simulation study reveals that the robustness of the kernel-form error density compensates for the loss of accuracy when using this density. Applying this GARCH model to daily return series of 42 assets in stock, commodity and currency markets, we find that this GARCH model is favored against the GARCH model with a skewed Student t error density for all stock indices, two out of 11 currencies and nearly half of the commodities. This provides an empirical justification for the value of the proposed GARCH model.

Suggested Citation

  • 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.
  • Handle: RePEc:msh:ebswps:2013-19
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    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp19-13.pdf
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. repec:eee:eneeco:v:67:y:2017:i:c:p:346-354 is not listed on IDEAS
    3. Tingting Cheng & Jiti Gao & Xibin Zhang, 2014. "Semiparametric Localized Bandwidth Selection in Kernel Density Estimation," Monash Econometrics and Business Statistics Working Papers 14/14, Monash University, Department of Econometrics and Business Statistics.
    4. Haotian Chen & Xibin Zhang, 2014. "Bayesian Estimation for Partially Linear Models with an Application to Household Gasoline Consumption," Monash Econometrics and Business Statistics Working Papers 28/14, Monash University, Department of Econometrics and Business Statistics.
    5. 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.

    More about this item

    Keywords

    Bayes factors; Gaussian kernel error density; localized bandwidths; Markov chain Monte Carlo; value-at-risk;

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