上证指数的混沌特性分析

Analysis of Chaotic Properties for Shanghai Stock Indices

通过计算得到上证指数的最大李雅普诺夫（Ｌｙａｐｕｎｏｖ）指数为正值，表明上证指数具有混沌特性．通过上证指数的相关积分关于相空间维数的数值计算发现，当相空间维数大于１０以后，相关积分趋于平稳，从而确定上证指数的嵌入维数约为１１，这时对应的相关积分可以看作为它的分数维，约等于１．１．

It is shown through numercal simulation that the largest Lyapunov exponent of the Shanghai Stock Index is positive.This implies that the index series is chaotic. The correlated integration with respect to the dimension of the state space is calculated. When the dimension is larger than 10, the correlated integration approaches to 1.1 which can be considered as the fractal dimension.Thus shows that the optimal embedding dimension of the index series is 11.