Echo state network (ESN) is a new kind of recurrent neural network with a randomly generated reservoir structure and an adaptable linear readout layer. It has been widely employed in the field of time series prediction. However, when high-dimensional reservoirs are utilized to predict multivariate time series, there may be a collinearity problem. In this paper, to overcome the collinearity problem and obtain a sparse solution, we propose a new model-adaptive elastic ESN, in which adaptive elastic net algorithm is used to calculate the unknown weights. It combines the strengths of the quadratic regularization and the adaptively weighted lasso shrinkage. Hence, the proposed model can deal with the collinearity problem and enjoy the oracle property with an unbiased estimation. We exhibit the merits of our model on two benchmark multivariate chaotic datasets and two real-world applications. Experimental results substantiate the effectiveness and characteristics of the proposed model.
