Multivariate chaotic time series prediction based on Hierarchic Reservoirs

Chaotic time series prediction has received considerable attention in the last few years. Although many studies have been conducted in the field, there is little attention focused on multivariate time series prediction. Considering this problem, the Hierarchic Reservoirs (HR) prediction model is proposed for multivariate chaotic time series prediction in this paper. The basic idea is using multiple reservoirs to predict multivariate chaotic time series directly without using phase space reconstruction. Each single reservoir of the hierarchic reservoirs prediction model extract the features of a time series of the multivariate chaotic time series. Then, the features are composed to represent the target value of the time series. Two simulation examples, prediction of Lorenz chaotic time series and prediction of sunspots and the Yellow River annual runoff time series are conducted to demonstrate the effectiveness of the proposed method.