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Gaussian kernel GARCH models

  • Xibin Zhang


  • Maxwell L. King


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.

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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 19/13.

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Date of creation: 2013
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Handle: RePEc:msh:ebswps:2013-19
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  6. Xibin Zhang & Maxwell L. King, 2004. "Box-Cox Stochastic Volatility Models with Heavy-Tails and Correlated Errors," Monash Econometrics and Business Statistics Working Papers 26/04, Monash University, Department of Econometrics and Business Statistics.
  7. Nakatsuma, Teruo, 2000. "Bayesian analysis of ARMA-GARCH models: A Markov chain sampling approach," Journal of Econometrics, Elsevier, vol. 95(1), pages 57-69, March.
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  24. 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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