Online prediction for multivariate time series by echo state network based on square-root cubature Kalman filter

Considering the problem of multivariate time series prediction, this paper proposes an online prediction model for multivariable time series by echo state network (ESN) based on square-root cubature Kalman filter. The model uses echo state network to map the nonlinear relationship between input and output, subsequently, updates the output weights of reservoir online by square-root cubature Kalman filter (SCKF) with three-order approximation for nonlinear functions. We add outlier detection into the filter algorithm, avoiding the adverse effect on the follow-up time series prediction. Experiment results on multivariate benchmark dataset and observed dataset demonstrate the effectiveness of the proposed model.