Dissertation (PhD)--University of Stellenbosch, 2002 / 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. / AFRIKAANSE OPSOMMING: Singulier spektraalanalise (SSA) het sy oorsprong in die Fisika. Die tegniek is nieparametries
van aard en vind toepassing in velde soos atmosferiese wetenskappe,
seinprossesering en onlangs in finansiële markte. Die tegniek kan 'n wye
verskeidenheid tydreekse hanteer wat kombinasies van komplekse periodisiteite,
polinomiese- en eksponensiële tendense insluit. Vooruitskattingstegnieke word ook in
hierdie studie beskou, en 'n nuwe koërdinaatvrye gesamentlike horison k-periodevooruitskattingformulering
word afgelei. Die studie beskou ook model seleksie in
SSA, waaruit duidelik blyk dat voorwaartse validasie meer stabiele model seleksie tot
gevolg het.
Die agtergrond van SSA word ab initio geskets en verdelingsaannames van seinreekse
beskou. Probleemgevalle wat voorkom in die meervoudige statistiese teorie word
duidelik geïdentifiseer.
Verskeie tegnieke van herhalende toepassing van een-periode-vooruitskatting word
daarna beskou. Die benaderings tot vooruitskatting word in algororitmiese formaat
verskaf wat die aanpassing na rekenaarprogrammering vergemaklik. Teoretiese
vraagstukke, onderliggend aan die vooruitskattings-algortimes, word ook beskou. 'n
Nuwe koërdinaatvrye gesamentlike horison k-periode-vooruitskattingsformulering
word afgelei en aangepas vir die multikanaal SSA geval.
Verskillende model seleksie tegnieke is ook beskou. Die gebruik van "scree"-
diagramme, fase ruimte diagramme, persentasie variasie verklaar deur eievektore,
kruis- en voorwaartse validasie word ook aangespreek. Die nie-parametriese aard van
SSA noop die gebruik van nie-parametriese model seleksie tegnieke.
Die studie vergelyk laastens 'n kommersiële sagtewarepakket met die Fortran
bronkode wat as deel van hierdie studie ontwikkel is.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/53190 |
| Date | 11 1900 |
| Creators | De Klerk, Jacques |
| Contributors | De Wet, T., Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 340 p. |
| Rights | Stellenbosch University |
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