We propose solutions to two statistical problems using the frequency domain approach to time series analysis. In both problems the data at hand can be described by the well known signal plus noise model.
The first problem ...
During the last few years the number of known variable stars which show periodic light level changes has grown by several tens of thousands. The aim of the research reported here was to extend the suite of statistical ...
Most people in the world rely on a well-functioning and stable financial system. Problems
experienced by financial institutions, such as too little liquidity or large amounts
of bad debt, can easily influence companies ...
We often wish to determine whether observations occurring in a natural time sequence
are from the same distribution or whether changes in distribution have taken place at
certain points in time. These time points are ...
The Christmas and Easter holiday periods have a large influence on electricity load.
Forecasting the load for these periods is difficult since the changes in the load patterns
are sudden and substantial. Furthermore, the ...
In this dissertation we investigate the South-African interest rate market by analyzing the
Johannesburg Interbank Agreed rate (JIBAR) and the South-African three-month treasurybill
rate. In particular, we assess the ...
We consider two problems relating to location-scale families of distributions. Firstly,
we consider methods of parameter estimation when two samples come from the same
type of distribution, but possibly differ in terms ...
Fractional Brownian motion and its increment process, fractional Gaussian noise, are syn-
onymous with the concept of long range dependence. A strictly stationary time series is
said to exhibit long range dependence or ...
There have been two rather distinct approaches to the analysis of time series: the time domain approach and frequency domain approach. The former is exemplified by the work of Quenouille (1957), Durbin (1960), Box and ...
A concern for astronomers is to determine whether the period of a variable star stays
constant over time. One aspect that has been neglected in the past when testing for constant
period is that the variance of the observed ...
This thesis considers the modelling of ultra high frequency (UHF) …nancial data from South
African markets. The approach to be taken is that such irregularly spaced data can be viewed
as a realization of a marked point ...
Comparison of two distributions via use of the quantile comparison function is carried
out specifically from possibly censored data. A semi-parametric method which
assumes linearity of the quantile comparison function ...
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 ...
At the very roots of this dissertation lies a commercial process with many as yet unexplored characteristics that will be thoroughly examined, using a rich variety of statistical methods and techniques. Broadly speaking, ...
The brightness of many stars vary over time. A plot of the brightness against
time is known as a light curve. The fall and rise times of the light curve can be
modelled by two cross-correlated white noise processes.
We ...