Matrix exponential stochastic volatility with cross leverage

A multivariate stochastic volatility model with the dynamic correlation and the cross leverage effect is described and its estimation using Markov chain Monte Carlo is proposed. The time-varying covariance matrices are guaranteed to be positive definite by using a matrix exponential transformation. Of particular interest is our approach for sampling a set of latent matrix logarithm variables from their conditional posterior distribution, where we construct the proposal density based on an approximating linear Gaussian state space model. The proposed model and its extensions 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 and diagonal multivariate GARCH models.