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Some aspects of harmonic time series analysis

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dc.contributor.advisor Prof. Freek Lombard en_US
dc.contributor.author Human, Johannes Urbanus
dc.date.accessioned 2012-01-17T07:53:53Z
dc.date.available 2012-01-17T07:53:53Z
dc.date.issued 2012-01-17
dc.date.submitted 2009
dc.identifier.uri http://hdl.handle.net/10210/4275
dc.description Ph.D. en_US
dc.description.abstract Harmonic time series are often used to describe the periodic nature of a time series, for example the periodic nature of a variable star’s observed light curve. Statistical methods for determining the number of harmonic components to include in harmonic time series are limited. In this thesis a stepwise bootstrap procedure based on a F-type statistic is suggested. The performance of the stepwise procedure is compared to that of Schwartz’s Bayesian Criterion (SBC) and a procedure based on a statistic described by Siegel (1980). Harmonic series with correlated noise terms and irregularly spaced observations are also considered. Tests to detect changes in harmonic parameters are also derived in this thesis. A cumulative sum statistic to test for constant amplitude is derived. It is shown that testing for constant amplitude is equivalent to testing for constant slope in simple linear regression. We also derive a likelihood ratio statistic to test for constant amplitude. It is shown that the latter likelihood ratio statistic is asymptotically equivalent to the cumulative sum statistic. These statistics are compared to a quadratic form statistic used by Koen (2009). Likelihood ratio tests are also derived for detecting changes in the frequency or phase of harmonic time series. Graphical devices to aid in diagnostic checking are suggested. en_US
dc.language.iso en en_US
dc.subject Harmonic analysis en_US
dc.subject Time-series analysis en_US
dc.title Some aspects of harmonic time series analysis en_US
dc.type Thesis en_US

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