In this thesis, identification of periodically varying orders of univariate
Periodic Autoregressive Moving-Average (PARMA) processes is mainly studied.
The identification of the varying orders of PARMA process is carried
out by generalizing the well-known Box-Jenkins techniques to a seasonwise
manner. The identification of pure periodic moving-average (PMA) and pure
periodic autoregressive (PAR) models are considered only. For PARMA model
identification, the Periodic Autocorrelation Function (PeACF) and Periodic Partial
Autocorrelation Function (PePACF), which play the same role as their ARMA
counterparts, are employed.
For parameter estimation, which is considered only to refine model
identification, the conditional least squares estimation (LSE) method is used
which is applicable to PAR models. Estimation becomes very complicated,
difficult and may give unsatisfactory results when a moving-average (MA)
component exists in the model. On account of overcoming this difficulty,
seasons following PMA processes are tried to be modeled as PAR processes
with reasonable orders in order to employ LSE. Diagnostic checking, through
residuals of the fitted model, is also performed stating its reasons and methods.
The last part of the study demonstrates application of identification
techniques through analysis of two seasonal hydrologic time series, which
consist of average monthly streamflows. For this purpose, computer programs
were developed specially for PARMA model identification.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/1083682/index.pdf |
| Date | 01 September 2003 |
| Creators | Akgun, Burcin |
| Contributors | Oztas, Ayhan H. |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | M.S. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for public access |
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