Multi-step forecasting using echo state networks

Echo state networks (ESNs) have been recently proposed as a special class of recurrent neural networks (RNNs), which help to avoid the possibility of vanishing gradient associated with RNNs, and also computational less complex. Online training of ESNs has previously been implemented using an RLS-type algorithm. Our approach aims at avoiding the numerical disadvantages inherent to the RLS algorithm by switching to a simpler and less computationally-intensive gradient descent algorithm. Simulations performed on benchmark AR, nonlinear and chaotic signals suggest that the performance of ESNs in single-step and multistep-ahead prediction is not sacrificed by the proposed method.