Prediction of multivariate time series with sparse Gaussian process echo state network

In this paper, we present an echo state network model based on sparse Gaussian process regression, which has been successfully applied to multivariate time series prediction. While combining the Gaussian process with Echo State Network, the computational complexity of the model is very high. We consider using a group of limited basis functions instead of the original covariance function, which reduces the computational complexity and maintains the prediction performance of the model. In the framework of Bayesian inference, the model can combine prior knowledge and observation data perfectly and provide prediction confidence. The model realizes adaptive estimation of the hyper-parameters by using maximum likelihood approach and avoids complex computation process. Two simulation results show the effectiveness and practicality of the proposed method.