Bayesian analysis of stochastic volatility-in-mean model with leverage and asymmetrically heavy-tailed error using generalized hyperbolic skew Student's t-distribution.

A stochastic volatility-in-mean model with correlated errors using the generalized hyperbolic skew Student-t (GHST) distribution provides a robust alternative to the parameter estimation for daily stock returns in the absence of normality. An efficient Markov chain Monte Carlo (MCMC) sampling algorithm is developed for parameter estimation. The deviance information, the Bayesian predictive information and the log-predictive score criterion are used to assess the fit of the proposed model. The proposed method is applied to an analysis of the daily stock return data from the Standard & Poor's 500 index (S&P 500). The empirical results reveal that the stochastic volatility-in-mean model with correlated errors and GH-ST distribution leads to a significant improvement in the goodness-of-fit for the S&P 500 index returns dataset over the usual normal model.