Bayesian analysis of non-Gaussian state space models with applications in financial econometrics

Non-Guassian state space models have an important role to play in empirical finance. The primary aim of this thesis is to develop Bayesian methods for estimating such models. Initia focus is given to a particular non-Gaussian state space model used in the analysis of transactions data: the stochastic conditional duration (SCD) model. Markov chain Monte Carlo (MCMC) methods are developed for the SCD model and used in an empirical analysis. Simulation experiments demonstrate that the finite sample performance of the Bayesian approac is superior, overall, to that of quasi-maximum likelihood (QML). The effect of parameterisation on the simulation effciency of the MCMC estimators of both the SCD and another non-Gaussian state space model, the stochastic volatility (SV) model, is examined. Four alternative parameterisations are considered and it is shown that large gains in simulation efficiency can be achieved through simple re-parameterisation of both models. Particle filtering methods are introduced and developed for the SCD and SV models. Initial attention is given to the case where the state is sequentially updated given each new observation and for fixed values of the parameters. These methods are extended to allow for the situation of the unknown parameters of both models and are evaluated using both simulated and empirical data sets.