Local Functional Coefficient Autoregressive Model for Multistep Prediction of Chaotic Time Series

A new methodology, which combines nonparametric method based on local functional coefficient autoregressive (LFAR) form with chaos theory and regional method, is proposed for multistep prediction of chaotic time series. The objective of this research study is to improve the performance of long-term forecasting of chaotic time series. To obtain the prediction values of chaotic time series, three steps are involved. Firstly, the original time series is reconstructed in m-dimensional phase space with a time delay τ by using chaos theory. Secondly, select the nearest neighbor points by using local method in the m-dimensional phase space. Thirdly, we use the nearest neighbor points to get a LFAR model. The proposed model’s parameters are selected by modified generalized cross validation (GCV) criterion. Both simulated data (Lorenz and Mackey-Glass systems) and real data (Sunspot time series) are used to illustrate the performance of the proposed methodology. By detailed investigation and comparing our results with published researches, we find that the LFAR model can effectively fit nonlinear characteristics of chaotic time series by using simple structure and has excellent performance for multistep forecasting.