Akram, Muhammad (1984) Generalised exponentially weighted regression and dynamic Bayesian forecasting models. PhD thesis, University of Warwick.

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Abstract

In this dissertation a new Forecasting Methodology, called Generalised Exponentially Weighted Regression (G.E.W.R) is presented. This Methodology is based on Linear Filtering using an Exponentially Weighted System and a Bayesian formulation developed. It is particularly designed to analyse discrete time series driven by Autoregressive and Moving Average type Coloured Noise processes. In order to elaborate the theory various theorems and corollaries are given.

For the implementation of G.E.W.R. various parsimonious Bayesian Dynamic Linear Models and Normal Discount Models for Low and High Frequency Components of time series with or without Seasonality and Cyclicity are introduced.

For theoretical and computational purposes recurrence relations for the Precision and Transformation Matrices are developed.

For the unknown variance case an automatic (self-tuning) on line Bayesian Learning Procedure is introduced.

For Complex Systems a procedure to construct the State Space Models is given and, for practitioners, methods of reparameterising Dynamic Linear Models is given.

In order to demonstrate the performance of G.E.W.R. the theory is applied to various simulated data sets and real life economic and industrial time series. In all cases the Methodology not only generates one-step ahead optimum forecasts in a Minimum Mean Square Error (M.M.S.E.) sense but also provides reasonable long term forecasts.

Item Type:	Thesis (PhD)
Subjects:	H Social Sciences > HA Statistics Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Regression analysis -- Mathematical models, Forecasting -- Mathematical models, Bayesian statistical decision theory, Forecasting -- Methodology
Official Date:	April 1984
Dates:	Date Event April 1984 Submitted
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Harrison, P. J.
Extent:	viii, 207 leaves
Language:	eng

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