Nonlinear Time Series Prediction Based On Echo State Network

With the development of nonlinear science, people find that nonlinear systems are everywhere. The number of biological populations, the temperature of a region, the stock index in Nasdaq, all are nonlinear time series. Therefore, modeling and predicting nonlinear time series is a very important work.Most of the traditional prediction methods are based on Takens theory, where reconstructing phase space is needed before prediction. So the accuracy of prediction is limited by the correctness of phase space reconstructing. Echo state network is a recently proposed large-scale recurrent neural network. It can be used to model and predict nonlinear time series without phase space reconstructing. Besides this, the model is easy to train and test, and the prediction accuracy are significantly improved.However, the main problem in echo state network is the ill-posed problem. Many researchers handle this problem by regularization method or by adding random noise. In this paper, wavelet echo state network (WESN) is proposed to overcome this problem. Experiment result illustrates that WESN can overcome the ill-posed problem without adding extra noise signal. What’s more, empirical mode decomposition is also employed to handle the ill-posed problem in traditional echo state network, and empirical mode decomposition echo state network (EMDESN) is proposed. Experiment results also show the effectiveness of this method. Finally, we focus on the structure and echo state network, and put forward that small-world network can be used to replace the randomly generated reservoir network in ESN. The new model is named small-world echo state network (SWESN). Many time series are used to test SWESN, results show that SWESN can achieve higher prediction accuracy, especially in real world time series.