Multivariate Chaotic Time Series Prediction Using a Wavelet Diagonal Echo State Network

Echo state networks have become increasingly popular for its superior performance in the field of time series prediction. However, it is difficult to implement the complicated ESN topologies in practice. To solve the problem, we propose a diagonal connected reservoir structure with composite functions inside the nodes. The input is first processed by wavelet functions and then passes through sigmoid activation functions. This increases the diversity of the reservoir. A selection method that takes into account the domain of the input data is applied to initialize the wavelet translation and dilation parameters. The output weights are efficiently computed by the least square method after the reservoir state matrix is formed. We exhibit the merits of our model on a benchmark multivariate chaotic dataset and a real-world application. Experimental results substantiate that the proposed model can achieve significantly good performance with a low-dimensional reservoir.