Modelling volatility in financial time series.
The objective of this dissertation is to model the volatility of financial time series data using ARCH, GARCH and stochastic volatility models. It is found that the ARCH and GARCH models are easy to fit compared to the stochastic volatility models which present problems with respect to the distributional assumptions that need to be made. For this reason the ARCH and GARCH models remain more widely used than the stochastic volatility models. The ARCH, GARCH and stochastic volatility models are fitted to four data sets consisting of daily closing prices of gold mining companies listed on the Johannesburg stock exchange. The companies are Anglo Gold Ashanti Ltd, DRD Gold Ltd, Gold Fields Ltd and Harmony Gold Mining Company Ltd. The best fitting ARCH and GARCH models are identified along with the best error distribution and then diagnostics are performed to ensure adequacy of the models. It was found throughout that the student-t distribution was the best error distribution to use for each data set. The results from the stochastic volatility models were in agreement with those obtained from the ARCH and GARCH models. The stochastic volatility models are, however, restricted to the form of an AR(1) process due to the complexities involved in fitting higher order models.