Using repetitive fuzzy method for chaotic time series prediction

Abstract

In this paper, a new perspective is presented for prediction of chaotic time series by combining the phase space reconstruction and fuzzy approach. Before applying time series to the predictor system, the reconstruction parameters, including embedding dimension and time delay, are determined in an off-line manner by using nearest neighbor and mutual information methods. Then, the structure of the fuzzy system is specified and the input number of fuzzy system is set to the embedding dimensions. According to the embedding dimension and time delay, the phase space is reconstructed point-by-point at the entry of the fuzzy system. Fuzzy system is composed of two separated parts: predictor and tracker. The predictor part forecasts the next point for new entry with fine-tuned parameters using the last step, and the tracker part adjusts the parameters for the next step. This adjustment is done iteratively. The proposed method is compared with some references' results. Simplicity and appropriate speed with sufficient accuracy are the advantages of this method.