Online multivariate time series prediction using SCKF-γESN model

•An online prediction model SCKF-γESN for multivariate time series is proposed.•The proposed model uses SCKF to update the unknown parameters of γESN.•Outlier detection algorithm is added into the process of SCKF.•It is applied for multivariate time series online prediction and performs well.

In this research, for online modeling and prediction of multivariate time series, we propose a novel approach termed squared root cubature Kalman filter-γ echo state network (SCKF-γESN). First, multivariate time series are modeled by using γ echo state network (γESN). Then, by using squared root cubature Kalman filter (SCKF), we update parameters of γESN and predict future observations online. Furthermore, we add a robust outlier detection algorithm to SCKF to protect SCKF-γESN from divergence caused by outliers. Finally, two numerical examples, by using a multivariate benchmark dataset and a real-world dataset, are conducted to substantiate the effectiveness and characteristics of the proposed SCKF-γESN.