Residual GM(1,1) Model-Based Prediction Method for Chaotic Time Series

Aiming at the problems existing in previous grey-chaos prediction methods, with phase space reconstruction theory and residual GM(1,1) model, a novel prediction method based on L-1 norm of reconstructed phase points is proposed in the paper. For chaotic time series, phase space delay coordinate reconstitution theory is applied to reconstruct phase space firstly, and then residual GM(1,1) model is used to study the change law of phase point L-1 norm, finally predicted values of time series are obtained with the L-1 norm inverse solution. To test the prediction method, three criteria of MAPE, MSE and FEM are employed here. And at the end, simulation with measured data from stabilized platform experiment demonstrates that the newly proposed method is effective, and it can overcome the difficulties existing in some previous grey-chaos prediction methods.