Multi-state delayed echo state network with empirical wavelet transform for time series prediction

In this paper, considering the effect of multiple delayed states on the reservoir itself, based on the advantage of the empirical wavelet transform, an improved ESN with multiple delayed states is proposed, called multi-state delayed echo state network with empirical wavelet transform (EWT-MSD-ESN). Firstly, the empirical wavelet transform is used to decompose the input signal, and then the main features of all decomposed components of the input signal can be extracted. Secondly, considering the multi-state delayed capability of the reservoir, the reservoir state equation of the EWT-MSD-ESN can be adjusted adaptively by using the autocorrelation coefficient of the input signal, such that the intrinsic characteristics of different learning tasks can be fully reflected. Finally, four numerical simulation examples and two actual examples are used to validate the predictive performance of EWT-MSD-ESN.