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-tailness as well as leverage effects. An efficient Markov chain Monte Carlo estimation
method is described exploiting a normal variance-mean mixture representation of
the error distribution with an inverse gamma distribution as a mixing distribution. The
proposed method is illustrated using simulated data, daily TOPIX and S&P500 stock
returns. The model comparison for stock returns is conducted based on the marginal
likelihood in the empirical study. The strong evidence of the leverage and asymmetric
heavy-tailness is found in the stock returns. Further, the prior sensitivity analysis is
conducted to investigate whether obtained results are robust with respect to the choice
of the priors.
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