Chaos-based Modified GM(1,1) Power Model in Time Series Prediction

A novel chaos prediction method, which applies modified GM(1,1) power model to study evolution laws of phase point L-1 norm in reconstructed phase space, is proposed in this paper. In the first stage, phase space delay coordinate reconstitution theory is used to reconstruct the unobserved phase space for chaotic time series, and L-1 norm series of phase points can be obtained in the reconstructed phase space. In the second stage, the kernel predictor of modified GM(1,1) power model, which is improved by optimizing background value and optimizing original condition, is constructed for forecasting. The measured data from stabilized platform experiment is applied to evaluate the performance of the proposed model. The empirical results are encouraging, and three accuracy evaluation standards indicate that the newly proposed method is excellent in model fitting and forecasting.