Recurrence relationships and model monitoring for dynamic linear model

This thesis considers the incorporation and deletion of information in Dynamic Linear Models together with the detection of model changes and unusual values. General results are derived for the Normal Dynamic Linear Model which naturally also relate to second order modelling such as occurs with the Kalman Filter, linear least squares and linear Bayes estimation. The incorporation of new information, the assessment of its influence and the deletion of old or suspect information are important features of all sequential models. Many dynamic sequential models exhibit conditioned, independence properties. Important results concerning conditional independence in normal models are established which provide the framework and the tools necessary to develop neat procedures and to obtain appropriate recurrence relationships for data incorporation and deletion. These are demonstrated in the context of dynamic linear models, with particularly simple procedures for discount regression models. Appropriate model and forecast monitoring mechanisms are required to detect model changes and unusual values. Cumulative Sum (Cusum) techniques widely used in quality control and in model and forecast monitoring have been the source of inspiration in this context. Bearing in mind that a single sided Cusum may be regarded essentially as a sequence of sequential tests, such a Cusum is, in many cases, equivalent to a Sequence of Sequential Probability Ratio Tests in many cases, as for example in the case of the Exponential Family. A relationship between Cusums and Bayesian decision is established for a useful class of linear loss functions. It is found to apply to the Normal and other important practical cases. For V- mask Cusum graphs, a particularly interesting result which emerges is the interpretation of the distance of the V vertex from the latest plotted point as the prior precision in terms of a number of equivalent observations