Research On Predictive Model Of Chaotic Time Series

"Preparedness ensures success,unpreparedness spells failure",which fully demonstrates the importance of the prediction in the decision-making.But for the non-linear characteristics of the research subject such as the complexity,diversity, and uncertainty,the prediction sometimes is difficult and requires people to explore the new predictive model continuously according to-the specific circumstances.Chaotic theory is an important part of non-linear theory which can grasp the characteristics from the seemingly irregular motion in the non-linear system such as the sensitivity to initial conditions,aperiodic variation and the existence of strange attractors.So it can excellently describe the motion law in the nonlinear system and open up new ideas for the research of predictive model.Chaotic theory is applied to time series prediction in this thesis.On the basis of the analysis of research status at home and abroad about chaotic time series prediction model study,a comparatively systematic and deep study is carried out.The main research contents are as follows:(1) The theory of phase space reconstruction is studied.According to the mathematical definition the chaotic nature is discussed.The selection of tWo important parameters in the-phase space reconstruction which are called embedding dimension and delay time is researched.Autocorrelation method,average displacement method,complex autocorrelation method,and mutual information method of delay time selection are realized.False nearest neighbours method and Cao's method of embedding dimension selection are realized.At the same time the combined selection of embedding dimension and delay time which is called C-C method is also realized.(2) The method of chaotic characteristics identification is studied.Three important characteristic values of chaotic system which are called Lyapunov exponent, correlation dimension and Kolmogorov entropy are analyized.From the qualitative and quantitative points of view,the chaotic characteristics of time series is identifid. Power spectrum method and Poincare section method of qualitative identification are realized.Wolf method,small data method,G-P algorithm and least square method of quantitative identification are realized.(3) Self-adaptive predictve model and RBF neural network predictve model are established.From the analysis of traditional linear predictive models,the inner limitations are found.Subsequently some commonly used chaotic time series predictive models such as the weighted one-rank local-region method and largest Lyapunov exponent method are researched,whose advantages are showen by the simulation experiment.At the same time aiming at the problems of learning disability in commonly used chaotic time series predictive models,the new predictive models such as self-adaptive and RBF neural network models are established.The predictive precision and accuracy is improved through simulation experiments and the valid predictive time is also extended.(4) The above algorithms are integrated on MATLAB,and a preliminary chaotic test platform is established.Three modules of phase space reconstruction, chaotic identification,and chaotic prediction are contained in the platform,which provides the test means for the follow-up study.