Fuzzy modelling of the Johannesburg Security Exchange overall index
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University of Cape Town
This thesis focuses on the empirical analysis of the fuzzy feature of the Johannesburg Stock Exchange Overall Index using fuzzy logic techniques. The data for the periods 1985 - 2001 is used in the analysis. Description of the fuzzy feature is crucial to the proper understanding of the movement of the JSE Overall Index and the South African economy. The fuzzy feature of the Johannesburg Security Exchange Overall Index if understood would impact on the ﬁnancial and economical decisions. A preliminary Fractal analysis is carried out before the fuzzy analysis to investigate the nature of the Johannesburg Security Exchange Overall Index. The Johannesburg Security Exchange Overall Index experiences the Hurst phenomena of long memory for periods of 100 days (approximately three months). Outside the long memory periods, the Johannesburg Security Exchange Overall Index is found to exhibit antipersistent or short-range dependency characteristics. The fuzzy feature of the Johannesburg Security Exchange Overall Index is described by many aspects of fuzzy logic. The analysis of the fuzzy feature is carried out according to time periods of approximately 4 years each of the Johannesburg Security Exchange Overall Index. The index in each time period is partitioned in three fuzzy states: "low", "middle" and "high". The fuzzy states are important in assessing the fuzzy nature of the Johannesburg Security Exchange Overall Index. The partitioning reveals that the fuzzy states of the Johannesburg Security Exchange Overall Index do not possess sharp boundaries. The sizes of the fuzzy states are found to change with time. This reﬂects changes in the forces behind the dynamics of the index.
Bibliography: leaves 181-206.
Musongole, C. 2002. Fuzzy modelling of the Johannesburg Security Exchange overall index. University of Cape Town.