Bayesian graphical forecasting models for business time series

This thesis develops three new classes of Bayesian graphical models to forecast multivariate time series. Although these models were originally motivated by the need for flexible and tractable forecasting models appropriate for modelling competitive business markets, they are of theoretical interest in their own right. Multiregression dynamic models are defined to preserve certain conditional independence structures over time. Although these models are typically very non-Gaussian, it is proved that they are simple to update, amenable to practical implementation and promise more efficient identification of causal structures in a time series than has been possible in the past. Dynamic graphical models are defined for multivariate time series for which there is believed to be symmetry between certain subsets of variables and a causal driving mechanism between these subsets. They are a specific type of graphical chain model (Wermuth & Lauritzen, 1990) which are once again typically non- Gaussian. Dynamic graphical models are a combination of multiregression dynamic models and multivariate regression models (Quintana, 1985,87, Quintana & West, 1987,88) and as such, they inherit the simplicity of both these models. Partial segmentation models extend the work of Dickey et al. (1987) to the study of models with latent conditional independence structures. Conjugate Bayesian anaylses are developed for processes whose probability parameters are hypothesised to be dependent, using the fact that a certain likelihood separates given a matrix of likelihood ratios. It is shown how these processes can be represented by undirected graphs and how these help in its reparameterisation into conjugate form