Adaptive Neuro-Fuzzy Inference System with Self-Feedback and Imperialist Competitive Learning Algorithm for Chaotic Time Series Prediction

Prediction of chaotic time series based on the phase space reconstruction theory has been applied in many research fields. In this paper, we propose an improved adaptive neuro-fuzzy inference system (ANFIS) with self-feedback and imperialist competitive learning algorithm for the application of chaotic time series prediction. Since the ANFIS is based on a feed-forward network structure, it is limited to static problems and cannot effectively cope with dynamic properties such as the time series. To surmount this trouble, we suggested an improved version of ANFIS by introducing self-feedback connections from previous outputs that model the temporal dependence. Also we suggested a new hybrid learning algorithm based on imperialist competitive algorithm (ICA) and least square estimation (LSE) to train this new ANFIS structure. This hybrid learning algorithm is free of derivation and solves the trouble of falling in local optimum in the gradient based algorithm for training the antecedent part. The proposed approach is used to model and predict the six benchmarks of chaotic time series. Analysis of the prediction results and comparisons with recent and old studies demonstrates the promising performance of the proposed approach for modeling and prediction of nonlinear and chaotic time series.