Exploring Chaos with Sparse Kernel Machines

Chaotic behaviour has been shown to exist in financial data. This paper advances the use of the sparse kernel machine model for the prediction of directional change for this class of dynamical systems. The notions of low entropy trajectory sets and low entropy trajectory balls in phase space are defined as the building patterns for the predictor. The statistical stability and robustness of the sparse kernel machine is measured out-of-sample in three experiments. Results indicate the existence of a spatio-temporal dynamic of the trajectory in the state space of a currency time series, confirming results in the literature. Applied to the momentum indicator, our results show the ability of the sparse kernel machine to produce a statistically significant effect size for the directional prediction of the price series, compared to Multiple Back propagation Neural Networks. Tests run on the phase space of the market volatility show a high degree of predictability, considerably larger effect size and increased performance of the local model approach with sparse kernel machines compared to MBP neural networks.