Modeling volatility dynamics using non-Gaussian stochastic volatility model based on band matrix routine

Substantial evidence supports that financial returns time series exhibit abnormal properties including leptokurtosis, volatility clustering as well as intermittent jumps and leverage effects between returns and volatility processes. This paper studies a heavy-tailed stochastic volatility (SV) model with jumps components and leverage effects, and the Student's-t distribution is employed to describe the error innovations (SVJLt). Since the existence of high-dimensionality of the latent variables and the special structure of Hessian matrix of the stochastic volatility density, we develop an efficient Markov chain Monte Carlo (MCMC) posterior simulator exploiting the adaptive importance sampling technique based on band and sparse matrix routine rather than the conventional Kalman filter to estimate the new model. And the precision sampler is exploited due to the band structure of the inverse covariance matrix of the state variables. The model comparisons of returns volatility are conducted utilizing the observed-data based deviance information criterion (DIC) and the cross-entropy (CE) based marginal likelihood estimation. The effectiveness of the proposed model and the methodology are illustrated with applications in stock returns volatility forecast. Through employing several loss functions for evaluation, the empirical studies suggest strong evidence in heavy tailed distributions, jumps features and leverage effects simultaneously.