Three essays in neural networks and financial prediction

The first essay studies the theoretical links between Radial Basis Functions, Fuzzy Logic Systems and Feedforward Neural Networks. Conditions under which all of the above can be derived from the Sigma-Pi Neural Network as the single unique superstructure are provided. This nestedness and the theory of metric entropy allow for a comparison of the average relative densities of the nonlinear approximators in function space. While this type of model selection criterion can theoretically discriminate between the different nonlinear network-based models a priori the asymptotic nature of the metric entropy results limit its practical value.; Hence the second essay focuses on an applied evaluation of Fuzzy Logic Systems, Sigma and Sigma-Pi networks in a directional prediction context. The comparative implications of signal-to-noise ratio, training data set size and non-stationary parameters are studied using simulated data. The directional forecasting performance of nonlinear models for predictable functions of financial data such as squared returns or absolute returns is highly dependent on these three criteria. From my models, Sigma Neural Networks provide the most reliable network-based predictor specification, this is verified on several financial data sets.; In the third essay I use the nonlinear specifications Fuzzy Logic System, Sigma and Sigma-Pi network to test the efficiency of the S&P 500 index with respect to its derivative market, the SPX options market. Using a trading strategy based on the directional volatility forecasts and including transactions costs one finds some limited inefficencies in the option price process. The speculative returns are very risky which gives a good illustration that deviations between theoretical considerations and empirical observations do not necessarily imply exploitable profit opportunities if market imperfections are taken into account.