Research On Multivariate Time Series Prediction And Reservoir Learning Method

Due to the multivariate chaotic time series with high dimension, nonlinear and high redundancy degree, traditional forecasting models lack of effective mechanisms to deal with nonlinear problem so that the predictive accuracy is low, which limit the application and promotion of traditional forecasting model. The newly proposed method reservoir method can map multi-variable nonlinear feature to the high-dimensional space of reservoir, which is changed into state variables with linear features, fully reflect the multi-variable nonlinear dynamic characteristics of chaotic systems. However, the reservoir application studies in multivariate chaotic time series prediction involves less. In addition, its structure and learning algorithm in prediction accuracy in terms of generalization performance are inadequate.Based on this, this paper make the multivariate chaotic time series mapped into the high-dimensional space of the reservoir, which makes the complex nonlinear sequence processed and solve a very difficult nonlinear problem. Then, high precision accuracy LM learning algorithm instead of the pseudo-inverse method is to train the output weight of the network. In addition, according to the properties of multivariate chaotic time series, multi-reservoir structure is proposed, which use Bayesian methods to optimize the estimation of model parameters, that improves forecast accuracy. However, the corresponding complexity of the model is increased. On that basis, a non-mercy relevance vector machine is proposed in this paper, that is, the output weights of the reservoir is added with a certain constraint, making the prediction model reduce the complexity and achieve the better prediction results. To improve the generalized performance of the prediction model, an ensemble ESN is presented by using AdaBoost.RT which boosts the generalization performance and prediction accuracy of individual ESN. In order to verify the effectiveness of the proposed methods above, all methods have been used in simulation examples. The simulation data sets are generated by manual numerical experiment and the actual hydrological multivariate observations. The final results show that the proposed methods can effectively improve the prediction accuracy of multivariate series.