Efficient Bayesian Inference for Univariate and High-Dimensional Stochastic Volatility Models

This thesis deals with statistical inference in nonlinear state space models that allow for dynamic and nondeterministic autoregressive evolutions of variances and co­variances, commonly referred to as stochastic volatility (SV). The models are specified within the frame­work of Bayesian statistics; estimation is carried out via several variants of Markov chain Monte Carlo (MCMC) samplers. These algorithms enable simulation of random draws from the high-dimensional posterior distribution through sequential draws from conditional distributions. A weakness of this procedure is that samples obtained through MCMC commonly show considerable auto­correlation, making the draws less informative about the distribution of interest and thus rendering the algorithm less efficient or even practically useless for certain data sets. As a result, the careful design of efficient samplers presents an active area of research to which this thesis aims to contribute. The dissertation comprises four research articles. The first one focuses on the estimation of univariate SV models. Several variants of MCMC algorithms are investigated and statistical inference is carried out by using different parameterizations. It turns out that the sampling efficiency and the optimal choice of parameterization heavily depend on certain features of the underlying data. To overcome this deficiency, we consider an ancillarity-sufficiency interweaving strategy (ASIS) which allows for a combination of complementary parameterizations and greatly improves sampling efficiency throughout the entire parameter range at hardly any additional computational cost.