Bayesian Inference for Discrete Time Stochastic Volatility

This thesis investigates Bayesian inference for latent state-space models, focusing on stochastic volatility (SV) models for financial return series. A unified Bayesian framework is developed for estimation, prediction, and model comparison in nonlinear latent-variable systems. The analysis considers several univariate SV specifications, including Gaussian, heavy-tailed, and leverage models, as well as multivariate Factor Stochastic Volatility (FSV) models for modeling time-varying dependence structures. Practical applications are conducted using daily returns of the iShares STOXX Europe 600 ETF and eleven European sector ETFs from 2015 to 2024. The results indicate highly persistent volatility dynamics across all model specifications. For the univariate analysis, models with Student-t innovations generally outperform the Gaussian benchmark, highlighting the importance of accommodating extreme return realizations. Leverage effects provide additional but comparatively modest predictive improvements. For the multivariate analysis, FSV models capture the dominant dependence structure among sectoral returns through a small number of latent factors while maintaining a parsimonious representation of dynamic covariance relationships. The findings also illustrate the trade-off between model flexibility and computational efficiency as model complexity increases.