Smith, Peter Jeffry (1988)
Estimation techniques for ARMA time series models and random geometric series.
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The thesis falls naturally into two sections. Firstly is a study of estimation techniques for ARMA models. Secondly is the work on random geometric series stemming from industrial collaboration with G.E.C. Telecommunications Laboratories. The unifying theory between these topics is discussed in the introduction.In the first section of the thesis the problem of estimation for ARMA models is considered. This is of long standing interest and the problem of maximum likelihood estimation is substantially solved. However the relationship between approximate and exact maximum likelihood estimation is less well known. The approximate procedures of A.M. Walker and E.J. Godolphin are considered in detail. Some results are produced which compare the two methods to each other and to various exact procedures. These comparisons are used to evaluate the success of some well known approximations. Finally a new approach to exact maximum likelihood estimation is developed which is simple to formulate and implement. This is used to study some numerical problems in estimation which occur near the boundary of the unit circle.The random geometric series considered in the second section have applications in both statistics and telecommunications. Specific examples of these series have been used to study infinite Bernoulli convolutions, intersymbol interference, error detection and many other subjects. In most applications it is the distribution of the series that is of interest. Initially the problem of calculating the distribution is considered in detail for a specific example concerning error detection. Several approaches are developed and compared to existing methods. It is shown that the most effective procedure is dependent on numerical properties of the series. Finally the new methods are extended to give two techniques, which can be used in all situations. These procedures are based on the semi-contraction mapping principles and the use of the Poisson summation formula to invert Fourier transforms.
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in Royal Holloway Research Online.Last modified on 31-Jan-2017
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Institution: University of London, Royal Holloway and Bedford New College (United Kingdom).