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Title: Bayesian forecasting with state space models
Author: Key, Peter Bernard
Awarding Body: University of London
Current Institution: Royal Holloway, University of London
Date of Award: 1986
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This thesis explores the use of State-Space models in Time Series Analysis and Forecasting, with particular reference to the Dynamic Linear Model (DLM) introduced by Harrison and Stevens. Concepts from Control Theory are employed, especially those of observability, controllability and filtering, together with Bayesian inference and classical forecasting methodology. First, properties of state-space models which depart from the usual Gaussian assumptions are examined, and the predictive consequences of such models are developed. These models can lead to new phenomena, for example it is shown that for a wide class of models which have a suitably defined steady evolution the usual properties of classical steady models (such as exponentially weighted moving averages) do not apply. Secondly, by considering the forecast functions, equivalence theorems are proved for DLMs in the steady state and stationary Box-Jenkins models. These theorems are then extended to include both time-varying and non-stationary models thus establishing a very general predictor equivalence. However it is shown that intuitively appealing DLMs which have diagonal covariance matrices are restricted by only covering part of the equivalent stability / invertibility region, and examples are given to illustrate these points. Thirdly, some problems of inference involving state-space models are looked at, and new approaches outlined. A class of collapsing procedures based upon a distance measure between posterior components is introduced. This allows the use of non-normal errors or Harrison-Stevens Class II models by condensing the normal-mixture posterior distribution to prevent an explosion of information with time, and avoids some of the problems of the Harrison-Stevens solution. Finally, some examples are given to illustrate the way in which some of these models and collapsing procedures might be used in practice.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Statistics