Time Series Analysis Based On Chaotic Theory

Chaotic theory has been proved to be an important and useful theory algorithm. The natural tightly connection between chaos and fracture is due to the infinite similarities of strange attractor of chaotic dynamic system. Nonlinear time series analysis based on chaotic theory cross through traditional frame of subjective model,draw out prediction on on the inner rules of chaotic time series data.In this article ,an equivalent definition of reconstruct function is drew in the state space reconstruct by time delay chaotic time series, that lead the prediction more conveniently. Then introduce a weighted distance to depict neighbour points of prediction which insured the similarity of the neighbour points. With the help of several neighbour points ,a average unbiased prediction is got, which is more accurate than traditional prediction. Lyapunov exponent depict the discrete extent of chaotic dynamic system. There propose an estimation of one step prediction error based on Lyapunov exponent, the estimation express the reliability of prediction numerically. At the same time, in order to improve the predictive precision it drew out an error complement methods creatively to correct one step prediction.With the answer of one step prediction, a creative interval prediction is got by the applied of non-parameter statistics method. Point prediction pay attention to prediction precision while interval prediction to reliability. The later enlarged the use area of chaotic time series analysis.