Ishihara, Tsunehiro, Yasuhiro Omori and Manabu Asai

A multivariate stochastic volatility model with the dynamic correlation and the cross leverage effect is described and its efficient estimation method using Markov chain Monte Carlo is proposed. The time-varying covariance matrices are guaranteed to be positive denite by using a matrix exponential transformation. Of particular interest is our approach for sampling a set of latent matrix logarithm variables from their con- ditional posterior distribution, where we construct the proposal density based on an approximating linear Gaussian state space model. The proposed model and its extend- ed models with fat-tailed error distribution are applied to trivariate returns data (daily stocks, bonds, and exchange rates) of Japan. Further, a model comparison is conducted including constant correlation multivariate stochastic volatility models with leverage.