On Flexible Linear Factor Stochastic Volatility Models

In this thesis I discuss flexible Bayesian treatment of the linear factor stochastic volatility model with latent factors, which proves to be essential in order to preserve parsimony when the number of cross section in the data grows. Based on the Bayesian model selection literature, I introduce a flexible prior specification which allows carrying out restriction search on the mean equation coefficients of the factor model – the loadings matrix. I use this restriction search as a data-based alternative to evaluate the cross sectional restrictions suggested by arbitrage pricing theory. A mixture innovation model is also proposed which generalizes the standard stochastic volatility specification and can also be interpreted as a restriction search in variance equation parameters. I comment on how to use the mixture innovation model to catch both gradual and abrupt changes in the stochastic evolution of the covariance matrix of high-dimensional financial datasets. This approach has the additional advantages of dating when large jumps in volatility have occurred in the data and determining whether these jumps are attributed to any of the factors, the innovation errors, or combinations of those.