Bayesian analysis of moving average stochastic volatility models: modeling in-mean effects and leverage for financial time series

We propose a moving average stochastic volatility in mean model and a moving average stochastic volatility model with leverage. For parameter estimation, we develop efficient Markov chain Monte Carlo algorithms and illustrate our methods, using simulated and real data sets. We compare the proposed specifications against several competing stochastic volatility models, using marginal likelihoods and the observed-data Deviance information criterion. We also perform a forecasting exercise, using predictive likelihoods, the root mean square forecast error and Kullback-Leibler divergence. We find that the moving average stochastic volatility model with leverage better fits the four empirical data sets used.