Abstract
Ph.D.
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.