Long Term Prediction of Chaotic Time Series with the Aid of Neuro Fuzzy Models, Spectral Analysis and Correlation Analysis

This paper presents a novel methodology for long term prediction of chaotic time series based on spectral analysis and neuro fuzzy modeling. A main motivation of using spectral analysis is to find some long term predictable components which describe the time series dynamics properly. In addition, this paper proposes a novel input variables selection criterion which is based on correlation analysis. The objective of this algorithm is to maximize relevance between inputs and output and minimizes the redundancy of selected inputs. After selecting input variables, a locally linear neuro fuzzy model is optimized for each of the principal components obtained from singular spectrum analysis, and the multi step predicted values are recombined to make the natural chaotic phenomenon. Two case studies are considered in this paper. The method has been applied to the long-term prediction of disturbance storm time (DST) as a solar activity indexes and one time series from neural forecasting competitions NN3. Results depict the power of the proposed method in long-term prediction of chaotic time series.