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.