Bayesian Analysis of Additive Factor Volatility Models with Heavy-Tailed Distributions with Specific Reference to S&P 500 and SSEC Indices

The distribution of the financial return series is unsuitable for normal distribution. The distribution of financial series is heavier than the normal distribution. In addition, parameter estimates obtained in the presence of outliers are unreliable. Therefore, models that allow heavy-tailed distribution should be preferred for modelling high kurtosis. Accordingly, univariate and multivariate stochastic volatility models, which allow heavy-tailed distribution, have been proposed to model time-varying volatility. One of the multivariate stochastic volatility (MSVOL) model structures is factor-MSVOL model. The aim of this study is to investigate the convenience of Bayesian estimation of additive factor-MSVOL (AFactor-MSVOL) models with normal, heavy-tailed Student-t and Slash distributions via financial return series. In this study, AFactor-MSVOL models that allow normal, Student-t, and Slash heavy-tailed distributions were estimated in the analysis of return series of S&P 500 and SSEC indices. The normal, Student-t, and Slash distributions were assigned to the error distributions as the prior distributions and full conditional distributions were obtained by using Gibbs sampling. Model comparisons were made by using DIC. Student-t and Slash distributions were shown as alternatives of normal AFactor-MSVOL model.