Bayesian analysis of a stochastic volatility model with a generalized hyperbolic
(GH) skew Student's t-error distribution is described where we first consider an
asymmetric heavy-tailed error and leverage effects. An efficient Markov chain
Monte Carlo estimation method is described that exploits a normal variance-mean
mixture representation of the error distribution with an inverse gamma distribution
as the mixing distribution. The proposed method is illustrated using simulated
data, daily S&P500 and TOPIX stock returns. The models for stock returns
are compared based on the marginal likelihood in the empirical study. There is
strong evidence in the stock returns high leverage and an asymmetric heavy-tailed
distribution. Furthermore, a prior sensitivity analysis is conducted whether the
results obtained are robust with respect to the choice of the priors.
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