Application of neural networks to chaotic systems in economics.

Abstract

The understanding of the market forces that drive the economy, as exemplified in indices such as the S&P 500, is of vital importance for the modeling, prediction, and direction of both developed and emerging economies. Knowledge of or insight into the market’s future performance could reduce risk and increase profits for investors. However, previous attempts to find a predictive model to describe stock-market performance have met with limited success, due to the stochastic nature, non-linearity, and high degree of complexity of such systems. As a first step towards such an understanding of the market, here we analyze the relation between two fundamentals market features: the daily change in price and volume of the S&P 500. First, we use a simple statistical analysis to demonstrate the non-linear behavior of the index on short timescales. To quantify the dependence of the daily change in price on factors other than the change in volume, we have also analyzed the variation in price when the volume is more or less constant and find such other factors could be described as weak white noise. Finally, we train a single-layer neural network model with all neurons densely interconnected and show that although it can reproduce the training data, in agreement with the universal simulation theorem, it is unable to predict the test data, even at a semi-qualitative level. These results demonstrate the need for “deep learning” via multi-layer neural networks to describe the behavior of stock-market indices.