author
Van Rooy, Herculaas Frederik
2008-07-07T09:27:52Z
2008-07-07T09:27:52Z
2008-07-07T09:27:52Z
http://hdl.handle.net/10210/760
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 process. We propose a statistical model that incorporates
both the unequally spaced transaction times (the points) as well as the movements of the
associated returns (the marks). In all data sets investigated, no change in the value of the
mark accounts for more that half the observations. If no change is considered as the
censoring of some underlying process, we can explicitly model both the censoring of marks
and the underlying process by utilizing methods for Markov chains and missing values.
All models considered hitherto in the literature assume homogeneity of structure within
a UHF data set. Data analyses indicate strongly that such an assumption is not justi
ed.
The proposed model aims to exploit this observation. The diurnal (time of day) e¤ect is
a form of non-stationarity commonly found in UHF data sets. We show that the method
currently considered standard practice is inadequate and we will propose modi
cations of it.
Consideration is given to the classi
cation of heterogeneous subsets that arises naturally in
UHF data, for instance daily subsets of a UHF data set. We
nd evidence in support of
some market microstructure theories, but no theory is supported by all data sets considered.
We pay attention to technical issues surrounding the application of certain tests to large
samples. As large samples are common in UHF data sets methods that are sensitive to large
sample size, for example the Ljung-Box test, are not suitable.
Professor Freek Lombard
en
Finance
Time and economic reactions
Johannesburg Stock Exchange
Mathematical models
On the modelling of ultra high frequency financial data on the Johannesburg Stock Exchange
Thesis