Wavelet Transform, Neural Networks and the Prediction of S&p Price Index: a Comparative Study of Back Propagation Numerical Algorithms

In this article, we explore the effectiveness of different numerical techniques in the training of backpropaqgation neural networks (BPNN) which are fed with wavelet-transformed data to capture useful information on various time scales. The purpose is to predict S&P500 future prices using BPNN trained with conjugate gradient (Fletcher-Reeves update, Polak-Ribiére update, Powell-Beale restart), quasi-Newton (Broyden-Fletcher-Goldfarb-Shanno, BFGS), and Levenberg-Marquardt (L-M) algorithm. The simulations results show strong evidence of the superiority of the BFGS algorithm followed by the L-M algorithm. Also, it is found that the L-M algorithm is faster than the other algorithms. Finally, we found that previous price index values outperform wavelet-based information to predict future prices of the S&P500 market. As a result, we conclude that the prediction system based on previous lags of S&P500 as inputs to the BPNN trained with BFGS provide the lowest prediction errors.