Time series forecasting and model selection in singular spectrum analysis

[摘要] ENGLISH ABSTRACT:Singular spectrum analysis (SSA) originated in the field of Physics. The technique isnon-parametric by nature and inter alia finds application in atmospheric sciences,signal processing and recently in financial markets. The technique can handle a verybroad 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 isderived. The study also considers model selection in SSA, from which it becomeapparent that forward validation results in more stable model selection.The roots of SSA are outlined and distributional assumptions of signal senes areconsidered ab initio. Pitfalls that arise in the multivariate statistical theory areidentified.Different approaches of recurrent one-period-ahead forecasting are then reviewed.The forecasting approaches are all supplied in algorithmic form to ensure effortlessadaptation to computer programs. Theoretical considerations, underlying theforecasting algorithms, are also considered. A new coordinate free joint-horizon kperiod-ahead forecasting formulation is derived and also adapted for the multichannelSSA case.Different model selection techniques are then considered. The use of scree-diagrams,phase space portraits, percentage variation explained by eigenvectors, cross andforward validation are considered in detail. The non-parametric nature of SSAessentially results in the use of non-parametric model selection techniques.Finally, the study also considers a commercial software package that is available andcompares it with Fortran code, which was developed as part of the study.

[发布机构] Stellenbosch University