An investigation into the properties of Bayesian forecasting models

In the early 70's, Harrison and Stevens made a major contribution to the area of statistical forecasting. They adopted a Bayesian approach in conjunction with a fundamental model, first used by Kalman and called the Dynamic Linear Model (DLM). This thesis is concerned with the investigation of the properties of different Bayesian forecasting models and in particular of the Multi State Model (MSM). The latter is important in postulating that no single DLM can adequately describe a process with discontinuities and consequently the system defines a number of models characterising the most likely process states. A small number of parameters are shown to govern the behaviour of the MSM and the relationship between the choice of these parameters. and performance has been examined. It is shown that for a process exhibiting discontinuities, traditional forecasting criteria such as the mean square error are no longer appropriate. An alternative set of performance measures is proposed and used as the main language of understanding the variety of responses of the MSM to different types and sizes of discontinuities. The parameter representing the noise variance of the process is shown to be critical to the performance of both the MSIl and other single state Bayesian models. A number of on line variance estimation methods are proposed and tested on artificial and real data. The methods are shown to be robust and lead to improved performance not only of the MSM but the other Bayesian single state models which of course require a noise variance estimate. Finally, alternative formulations of the MSM are proposed, leading to significant reduction in the computational and storage requirements while at the same time improving the response of the MSM.