Research On Analysis Of Correlation And Prediction Modeling For Multivariate Chaotic Time Series

Analyzing the evolvement rule of the observed time series is an important means to understand the dynamical characteristic of system. Based on the prediction method of univariate time series, and according to the proper selection of dimension and delay time, the time series can be predicted precisely. However, in practical problems, due to limited length of the univariate time series and containing noise, the track of the dynamic system can not be described accurately, so that it is very significant to do some research on the analysis and modeling of the multivariate time series. However, how to identify the characteristics of the systems and build predictive models is a hot topic in the nature and social science. Neural networks with strong nonlinear map ability have been applied in nonlinear pattern recognition. However, it is difficult using the neural networks to cope with multi-variable time series, because the multi-variable time series contain too much redundant information which make the structure of models more complicated and caustic the generalized ability.For the problems mentioned above, variable selection and neural networks are employed to analyze and predict multivariate time series, and the prediction method of chaotic time series which is based on the correlation analysis of multivariate. Because chaotic time series have special analysis and prediction approach, so that in order to detect the chaotic characteristics, an improved Rosentein's algorithm based combination of phase spaces is presented for calculating the noisy chaotic time series' Largest Lyapunov Exponent which provides the basis of prediction. To deal with the multivariate chaotic time series, the paper make use of causality analysis based on Plus-predictability and Reverse-predictability to mine the hidden relationship, and select the most correlative time series, and fulfill the prediction using combination of PCA and four-level forward neural networks. In order to find out better prediction model, Bayesians echo state network and complex-values echo state network are proposed. The Bayesians echo state network avoid over-fitting problem faced by original ESN, meanwhile can also automatic estimate the hyper-parameters of the model. And the complex-values echo state network extends the ESN from real number to complex-value number, converting the two variables to the complex data, and it offer a new solution to cope with multivariate prediction. All algorithms proposed in the paper have been used in the predictive simulation (Dalian rainfall and temperature, sunspots and runoff of Yellow River), and the results show that these algorithms can efficiently find out the correlation between multivariate chaotic time series, improve the accuracy of the prediction and reveal the dynamic characteristic of the complex system.