Bayesian semiparametric GARCH models

Xibin Zhang () and Maxwell King

No 24/11, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: This paper aims to investigate a Bayesian sampling approach to parameter estimation in the semiparametric 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. The proposed investigation is motivated by the lack of robustness in GARCH models with any parametric assumption of the error density for the purpose of error-density based inference such as value-at-risk (VaR) estimation. The contribution of the paper is to construct the likelihood and posterior of model and bandwidth parameters under the proposed mixture error density, and to forecast the one-step out-of-sample density of asset returns. The resulting VaR measure therefore would be distribution-free. Applying the semiparametric GARCH(1,1) model to daily stock-index returns in eight stock markets, we find that this semiparametric GARCH model is favoured against the GARCH(1,1) model with Student t errors for five indices, and that the GARCH model underestimates VaR compared to its semiparametric counterpart. We also investigate the use and benefit of localized bandwidths in the proposed mixture density of the errors.

Keywords: Bayes factors; kernel-form error density; localized bandwidths; Markov chain Monte Carlo; value-at-risk (search for similar items in EconPapers)
JEL-codes: C11 C14 C15 G15 (search for similar items in EconPapers)
Pages: 38 pages
Date: 2011-11-03
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-for, nep-ore and nep-rmg
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Citations: View citations in EconPapers (7)

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