Analysis and modeling of multivariate chaotic time series based on neural network

A new nonlinear multivariate technique is proposed for modeling and predicting chaotic time series with a view to improve estimates and predictions. With analysis of the relations among different state spaces by the proposed method, which introduces the reverse-predictability and time spans to discover the underlying relationship, the connections among multivariate time series are discussed before prediction. Then we predict the time series by multivariate prediction. Though multivariate time series can bring more information about the complex system, which can enhance the accuracy of prediction, they also bring a too large number of input variables which may result in overfitting and poor generalization abilities. To overcome the shortcomings, principal component analysis (PCA) based on singular value decomposition (SVD) is used to extract main features of multivariate time series and reducing the dimension of the model inputs. Then based on Takens’ delay time theory, the multivariate time series are reconstructed. Subsequently, a four-layer feedforward neural network is trained as the multivariate predictive model. Three simulation examples, that are coupled Henon equation and two set of real world time series, are used to demonstrate the validity of the proposed method.