Effective prediction of future financial states has been a major quest for groups ranging from national governments to individual investors. The size, diversity and complexity of financial markets make traditional statistical methods ineffective in predicting beyond a very short time frame. Alternative models using artificial neural networks and fractal time series have had better results in long-term predictions, but still do not work in all situations. This dissertation combined features of artificial neural networks and fractal time series to create a fractal neural network. Fractals exhibit repetitive patterns when a unit is broken down into its components. This similarity property was used to create a fractal neural network that could be broken out into separate, smaller neural networks. The recurring nature of the fractal pattern indicates that phenomena exhibiting repetitive patterns may be effectively modeled with fractal neural networks. Computer models of fractal time series, artificial neural networks and fractal neural networks were constructed and used to analyze and predict the exchange rate between the Deutschemark and the US Dollar and between the US dollar and the British Pound. Results confirmed that the exchange rates for 1994 to 1995 exhibit fractal patterns. Three layer artificial neural networks and fractal neural networks were constructed, trained on the 1994 data, and used to predict exchange rates for the first half of 1995. The number of correct predictions of the direction of change of the exchange rates calculated by the fractal neural network exceeded those produced by the artificial neural network for weekly Deutschemark and daily and weekly Pound exchange rates. When the predicted values were compared to actual values and used to form an investment strategy, the fractal network consistently produced a profit that exceeded that of the artificial neural network.
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