Output prediction summary deep echo state network for multivariate chaotic time series forecasting

Abstract In this paper, a novel multi-reservoir model called output prediction summary deep echo state network (OPS-DESN) is proposed for multivariate time series forecasting. OPS-DESN consists of a series of chain-connected feature extraction modules and a re-prediction module. Firstly, the input sequence is chosen by calculating the Pearson correlation coefficient between each dimensional component of the original data and the target output. Secondly, the number of feature extraction modules in OPS-DESN equals the dimension of the input sequence. The single dimensional components in the input sequence are allocated to each feature extraction module in descending order of correlation degree. Each external input component is combined with the previous module output, they are input into the current module for prediction. The outputs of all feature extraction modules are collected and used as input to the re-prediction module for re-fitting. Thirdly, to further enhance the prediction accuracy of OPS-DESN, grey wolf optimizer is selected as the parameter tuning method. Finally, prediction experiments conducted on two sets of theoretical and two sets of actual series verify the prediction performance of OPS-DESN.