Doctoral Degrees (Statistics and Actuarial Science)

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Browsing Doctoral Degrees (Statistics and Actuarial Science) by Subject "Dissertations -- Statistics"

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    Time series forecasting and model selection in singular spectrum analysis
    (Stellenbosch : Stellenbosch University, 2002-11) De Klerk, Jacques; De Wet, Tertius; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
    ENGLISH ABSTRACT: Singular spectrum analysis (SSA) originated in the field of Physics. The technique is non-parametric by nature and inter alia finds application in atmospheric sciences, signal processing and recently in financial markets. The technique can handle a very broad class of time series that can contain combinations of complex periodicities, polynomial or exponential trend. Forecasting techniques are reviewed in this study, and a new coordinate free joint-horizon k-period-ahead forecasting formulation is derived. The study also considers model selection in SSA, from which it become apparent that forward validation results in more stable model selection. The roots of SSA are outlined and distributional assumptions of signal senes are considered ab initio. Pitfalls that arise in the multivariate statistical theory are identified. Different approaches of recurrent one-period-ahead forecasting are then reviewed. The forecasting approaches are all supplied in algorithmic form to ensure effortless adaptation to computer programs. Theoretical considerations, underlying the forecasting algorithms, are also considered. A new coordinate free joint-horizon kperiod- ahead forecasting formulation is derived and also adapted for the multichannel SSA case. Different model selection techniques are then considered. The use of scree-diagrams, phase space portraits, percentage variation explained by eigenvectors, cross and forward validation are considered in detail. The non-parametric nature of SSA essentially results in the use of non-parametric model selection techniques. Finally, the study also considers a commercial software package that is available and compares it with Fortran code, which was developed as part of the study.