Chaotic analysis of predictability versus knowledge discovery techniques: Case study of the Polish stock market

Increasing evidence over the past decade indicates that financial markets exhibit nonlinear dynamics in the form of chaotic behavior. Traditionally, the prediction of stock markets has relied on statistical methods including multivariate statistical methods, autoregressive integrated moving average models and autoregressive conditional heteroskedasticity models. In recent years, neural networks and other knowledge techniques have been applied extensively to the task of predicting financial variables. This paper examines the relationship between chaotic models and learning techniques. In particular, chaotic analysis indicates the upper limits of predictability for a time series. The learning techniques involve neural networks and case-based reasoning. The chaotic models take the form of R/S analysis to measure persistence in a time series, the correlation dimension to encapsulate system complexity, and Lyapunov exponents to indicate predictive horizons. The concepts are illustrated in the context of a major emerging market, namely the Polish stock market.