Fractional Order Echo State Network for Time Series Prediction

摘要

In this brief, considering the infinite memory of fractional-order differential equation, a fractional-order echo state network (FESN) is given for time series prediction. For the FESN, the reservoir state differential equation is replaced with fractional-order differential equation. According to the advantages of FESN, the dynamic characteristics of a class of time series can be fully reflected. In order to improve the prediction performance of FESN, a fractional-order output weights learning method and a fractional-order parameter optimization method are given to train the output weights and optimize the reservoir parameters, respectively. Finally, two numerical examples are used to show the effectiveness of FESN.