Wavelet Neural Networks: With Applications in Financial Engineering, Chaos, and Classification

10 Predicting Chaotic Time Series

One of the most common problems that financial managers have to face is the accurate prediction of time series. Various models are used for the modeling of stock returns and prices or levels of volatility. The usual approach that financial analysts follow to solve these problems is to employ statistical procedures such as the general family of ARFIMA and/or GARCH models. However, financial time series often exhibit chaotic behavior. As a result, the prediction power of linear models is limited, due to their inability to model the evolutionary dynamics of the process. The models mentioned previously do not have the ability to adapt to a change of the dynamics in a chaotic system.

Chaotic time series are dynamic systems that are extremely sensitive to initial conditions and can exhibit complex external behavior. Small differences in initial conditions can exhibit diverging results. Hence, it is difficult to find the dynamic system simply through observations of the outcome. As defined by Edward Lorenz, in chaos the present determines the future, but the approximate present does not approximately determine the future.

To improve the modeling of chaotic time series, a number of nonlinear prediction methods have been developed, such as polynomials, neural networks, genetic algorithms, dynamic programming, and swarm optimization. Recently, neural networks and local models have been employed directly for chaotic time-series prediction, and comparatively ...