Bayesian Student-T Stochastic Volatility Models Via Scale Mixtures

33 Pages Posted: 20 Aug 2009

See all articles by Boris Choy

Boris Choy

University of Sydney Business School

Wai Yin Wan

NSW Bureau of Crime Statistics and Research

Chun Man Chan

affiliation not provided to SSRN

Date Written: August 18, 2009

Abstract

The normal error distribution for the observations and log-volatilities in a stochastic volatility (SV) model is replaced by the Student-t distribution for robustness consideration. The model is then called the t-t SV model throughout this paper. The objectives of the paper are two-fold. Firstly, we introduce the scale mixtures of uniform (SMU) and the scale mixtures of normal (SMN) representations to the Student-t density and show that the setup of a Gibbs sampler for the t-t SV model can be simplified. For example, the full conditional distribution of the log-volatilities has a truncated normal distribution which enables an efficient Gibbs sampling algorithm. These representations also provide a means for outlier diagnostics. Secondly, we consider the so-called t SV model with leverage where the observations and log-volatilities follow a bivariate t distribution. Returns on exchange rates of Australian dollar to ten currencies are fitted by the t-t SV model and the t SV model with leverage, respectively.

Keywords: GARCH, Scale mixtures of normal, Scale mixture of uniform, Gibbs sampler, Outlier diagnostics, Leverage

JEL Classification: C11, C15, C32

Suggested Citation

Choy, S. T. Boris and Wan, Wai Yin and Chan, Chun Man, Bayesian Student-T Stochastic Volatility Models Via Scale Mixtures (August 18, 2009). Available at SSRN: https://ssrn.com/abstract=1456822 or http://dx.doi.org/10.2139/ssrn.1456822

S. T. Boris Choy (Contact Author)

University of Sydney Business School ( email )

Cnr. of Codrington and Rose Streets
Sydney, NSW 2006
Australia

Wai Yin Wan

NSW Bureau of Crime Statistics and Research ( email )

St James Centre
111 Elizabeth Street
SYDNEY NSW, 2000
Australia

Chun Man Chan

affiliation not provided to SSRN ( email )

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