C++ Neural Networks and Fuzzy Logic: Preface

The S&P 500 and Sunspot Predictions

Michael Azoff in his book on time−series forecasting with neural networks (see references) creates neural

network systems for predicting the S&P 500 index as well as for predicting chaotic time series, such as

sunspot occurrences. Azoff uses feedforward backpropagation networks, with a training algorithm called

adaptive steepest descent, a variation of the standard algorithm. For the sunspot time series, and an

architecture of 6−5−1, and a ratio of training vectors to trainable weights of 5.1, he achieves training set error

of 12.9% and test set error of 21.4%. This series was composed of yearly sunspot numbers for the years 1706

to 1914. Six years of consecutive annual data were input to the network.

One network Azoff used to forecast the S&P 500 index was a 17−7−1 network. The training vectors to

trainable weights ratio was 6.1. The achieved training set error was 3.29%, and on the test set error was

4.67%. Inputs to this network included price data, a volatility indicator, which is a function of the range of

price movement, and a random walk indicator, a technical analysis study.