Multivariate nonlinear time series prediction by chain-structure echo state network

For multivariate nonlinear time series, most existing prediction models are directly established based on the historical information of variable itself or some related variables. However, it is generally challenging to fully map and mine the internal characteristics, due to the strong coupling existing among multiple variables. In addition, when the system information is only partially known, it is also very difficult to develop a more accurate prediction model, under the condition of specific prediction technology and limited data sets. In this paper, a chain-structure echo state network (CESN) is developed to enhance the data mining ability and prediction accuracy of traditional models. A CESN consists of multiple series ESN modules, which are responsible for portraying complicated dynamics of nonlinear systems. In CESN, the predicted output of a certain ESN module is concatenated with external input to form the new input signals for the sequentially connected module. Compared with classical prediction models, more related information is therefore mined and adopted by CESN. The network structure, mathematical model and stability analysis are studied for CESN, respectively. Two different simulation examples are given to verify the effectiveness of CESN, and simulation results demonstrate that CESN outperform than traditional ESN models.