基于交互作用系统的股票价格波动相关性

Correlation analysis of price fluctuation of stock market by stochastic interacting system

根据随机交互作用系统之一的接触过程理论,构造了一个股票价格模型来模拟金融市场股票价格时间序列及其收益率序列.重点讨论了模拟收益率序列的相关性,并与实际数据上证综指(SSE)、深证成指(SZSE)进行了对比分析.在交叉相关性分析中,分别研究了不同的信息传播速率和初始信息携带率之间的交叉相关性,并用实际数据对SSE与SZSE作对照,发现它们之间都是存在交叉相关性的;在自相关性分析中,采用了常规自相关函数、q阶自相关函数以及多重自相关函数分别对单个模拟数据以及实际数据进行分析,从3种结果中都可以看出模拟数据的收益率序列同实际数据一样是具有波动集簇性的.

A stochastic financial price model for simulation of stock prices and returns on the basis of contact process theory, which is one of the stochastic interacting systems is introduced in this paper. We study the correlation behaviors of the simulation return series from the proposed rood el,comparing the simulation results with the actual data including Shanghai Stock Exchange Composite Index （SSE） and Shenzhen Stock Exchange Component Index （SZSE）. In the cross- correlation analysis, the cross-correlation between different intensity and initial density is analyzed and compared with the actual data from SSE and SZSE. It is found that they are cross correlated. Besides, in the autocorrelation analysis, the common autocorrelation function, q- order autocorrelation function and multi-autocorrelation function are applied to study the single return series from simulation and real financial market, respectively. From the three results can be seen both the simulation data and actual data have volatility clustering.