中国证券市场的非线性特征与分形维分析

采用Cao方法清楚地观测到中国证券市场的月收益率序列是确定性混沌序列,而日收益率序列和周收益率序列却接近于随机波动信号,不适宜做分形维的研究.对我国股市各指数分别作了分形维计算后,同时用替代数据法进行非线性检验,拒绝了中国股市为线性过程的可能性,从而保证了非线性前提下分维数结果的可靠性.结果显示:深证A股市场最为复杂,需要五个变量来建立动力学模型(D2=4 6150),而上证A股需要四个变量来建立模型(D2=3 2411).因此,深圳股市的效率弱于上海股市.而我国B股市场已经接近于发达国家股市的复杂性程度(D2=3 3195(上B);D2=2 5875(深B)),说明B股的效率比A股的效率高.

Nonlinear Characteristics and Fractal Dimension Analysis of Chinese Stock Markets

Cao's method is employed in this article to make sure the monthly return series of Chinese Stock Market is chaotic but daily return series and weekly return series were found noisy. Thus monthly return series were analyzed using correlation dimension as well as its surrogate data. Apparent difference of correlation dimension from the monthly return series and its surrogate data rejects the null hypothesis that the monthly return series is derived from a linear system, which confirms that the fractal dimension of Chinese Stock Market stems from an inner nonlinear dynamics. It was concluded that Shanghai A Share's efficiency outweighs Shenzheng A Share's and in general B Share's efficiency outweighs A Share's. Shenzheng A Share is most complex (D_2=4.6150) compared with its Shanghai's counterpart (D_2=3.2411). B Share (D_2=3.3195 (Shanghai B); D_2=2.5875 (Shenzheng B)) approaches the stock complexity of Western countries'.