Discontinuous Regression Tree Estimation of Largest Lyapunov Exponent

Chaos theory in dynamics system is becoming more and more important in many fields, like signal processing. Largest Lyapunov exponent is a useful measure of the stability of a dynamics system and successful method to test for chaos. A new method to estimate largest Lyapunov exponent from observed time series is proposed. It fits the nonlinear function by stochastic gradient boosting of regression tree. Since regression trees are discontinuous, its Jacobian matrix doesn´t exist and regular methods based on function estimator fails, we directly calculate Lyapunov exponent from them without using Jacobian matrix of the fitted function. A simulation study to evaluate our method´s performance is reported. Two observed daily series are deduced not chaotic both by this method and artificial neural network.