Statistical Analysis and Data Analysis of Stock Market by Interacting Particle Models

The statistical analysis of Chinese stock market fluctuations modeled by the interacting particle systems has been done in this paper. The contact model and voter model of the interacting particle systems are presented in this paper, where they are the continuous time Markov processes. One interpretation of contact model is as a model for the spread of an infection. One interpretation of voter model is, an individual reassesses his view by choosing a neighbor at random with certain probabilities and then adopting his position. In the first part of this paper, based on the contact process, a new stochastic stock price model of stock markets is modeled. From it, the statistical properties of Shenzhen Composite Index are studied. The data of Shenzhen Stock Exchange (SZSE) Composite Index is analyzed, and the corresponding simulation is made by the computer computation, and we further investigate the statistical properties, fat tails phenomena and the power-law distributions of returns. The methods of Skewness-Kurtosis test, Kolmogorov-Smirnov test are applied to study the fluctuation behavior of the returns for the stock price and Index. In the second part of this paper, based on the voter model, we study the statistical properties of prices changes for the different dimensions, intensity of the model and initial density θ .