Wavelet Transform, Neural Networks and The Prediction of S&P Price Index: A Comparative Study of Backpropagation 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.