W. Pedrycz & S.-M. Chen (Eds.): Time Series Analysis, Model. & Applications, ISRL 47, pp. 229–247. DOI: 10.1007/978-3-642-33439-9_11 © Springer-Verlag Berlin Heidelberg 2013 Chapter 11 Neural Networks and Wavelet De-Noising for Stock Trading and Prediction Lipo Wang and Shekhar Gupta * Abstract. In this chapter, neural networks are used to predict the future stock prices and develop a suitable trading system. Wavelet analysis is used to de-noise the time series and the results are compared with the raw time series prediction without wavelet de-noising. Standard and Poor 500 (S&P 500) is used in experi- ments. We use a gradual data sub-sampling technique, i.e., training the network mostly with recent data, but without neglecting past data. In addition, effects of NASDAQ 100 are studied on prediction of S&P 500. A daily trading strategy is employed to buy/sell according to the predicted prices and to calculate the direc- tional efficiency and the rate of returns for different periods. There are numerous exchange traded funds (ETF’s), which attempt to replicate the performance of S&P 500 by holding the same stocks in the same proportions as the index, and therefore, giving the same percentage returns as S&P 500. Therefore, this study can be used to help invest in any of the various ETFs, which replicates the perfor- mance of S&P 500. The experimental results show that neural networks, with appropriate training and input data, can be used to achieve high profits by invest- ing in ETFs based on S&P 500. 1 Introduction Stock prices are highly dynamic and bear a non-linear relationship with many variables such as time, crude oil prices, exchange rates, interest rates, as well as factors like political and economic climate. Hence stock prices are very hard to model by even the best financial models. Future stock prices can be studied mere- ly by historical prices. Lipo Wang · Shekhar Gupta School of Electrical and Electronic Engineering Nanyang Technological University Block S1, 50 Nanyang Avenue, Singapore 639798 e-mail: elpwang@ntu.edu.sg