Modelling of Chaotic Time Series Using Minimax Probability Machine Regression

A state-of-the-art regression method called minimax probability machine is introduced to modelling the chaotic time series. Since the positive global Lyapunov exponents cause the errors in modelling of the chaotic time series to grow exponentially rapidly, a weighted term to the cost function is introduced to compensate this effect. Power spectrum and dynamic invariants involving Lyapunov exponents and correlation dimension are used as criterions to estimate the performance and then apply our method to the Lorenz system. The simulation results show that the proposed method can capture the dynamics of the chaotic time series effectively.