Gamma test analysis tools for non-linear time series

This thesis is concerned with the development of new tools for non-linear time series modelling and prediction, and the subsequent application of these tools to the problems of crime prediction and global climate modelling. We review the state of time series modelling for conventional stochastic time series. After describing the Gamma test and related background material, we extend the available tools by developing a new M -test based heuristic for Gamma test confidence intervals. We go on to study and develop new results describing the effects of measurement error on modelling and predicting noisy time series. We then describe the application of new techniques, based around the Gamma test, that are capable of selecting predictively useful input variables for modelling and predicting non-linear time series. In the process of this work we developed a much sought after suite of R-tools which are now freely distributed on the R web-site (http://www.r-project.org). Finally, we illustrate the use of these tools by examining two very different types of time series data. The first relates to the problem of crime prediction, where the data emerged as inadequate to support the aspirations of the original researchers. The second modelling exercise takes available data sets for climate modelling and develops predictive models for global surface temperature. Gamma test analysis tools for non-linear time series Samuel Kemp

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