Chaotic Time Series Prediction using Improved ANFIS with Imperialist Competitive Learning Algorithm

Abstract—This paper presents an improved adaptive Neuro-fuzzy inference system (ANFIS) for predicting chaotic time series. The previous learning algorithms of ANFIS emphasized on gradient based methods or least squares (LS) based methods, but gradient computations are very computationally and difficult in each stage, also gradient based algorithms may be trapped into local optimum. This paper introduces a new hybrid learning algorithm based on imperialist competitive algorithm (ICA) for training the antecedent part and least square estimation (LSE) method for optimizing the conclusion part of ANFIS. This hybrid method is free of derivation and solves the trouble of falling in a local optimum in the gradient based algorithm for training the antecedent part. The proposed approach is used in order to modeling and prediction of three benchmark 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. Index Terms—chaotic time series, Gradient based, imperialist competitive algorithm, Fuzzy systems, ANFIS, least square estimation. I