Chaotic Time Series Analysis And Its Application To Stock Index

Chaotic time series analysis methods is used to study the movement of stock prices and analyze the chaotic property of the series. Chaotic time series prediction is used for prediction. The dissertation is arranged as follows:Firstly, basic theory and method is reviewed.Secondly, two exponential time series are examined. Power Spectral is used to find the nonperiodic movement of data structure. Frequency shows that there exists distinction between the above data and normal distribution. PCA shows the data is not noise sequence but chaotic. The above analysis shows that both time series have chaotic property. Besides analysis from qualitative prospective, Lyapunov exponent、 correlation dimension and Kolmogorov is used to analyze the time series from quantitative angle. C-C method, G-P are used, respectively, to restructure the phase-space and compute correlation dimension。 Kolmogorov entropy is positive, which shows that the two series converge. Wolf and largest Lyapunov rosenstein are used to compute largest Lyapunov exponent, the results of which are both positive. Hence, the series are in chaotic state.Thirdly, local prediction method and largest lyapunov exponent are used to predict100steps and20steps prediction. Comparison between prediction and the actual value is made, which shows the steps of AOLMM are shorter than largest Lyapunov exponent. AOLMM is better than largest Lyapunov exponent in the first and twentieth step prediction while largest Lyapunov exponent is better in the100th prediction with slow fluctuation in error.