Dependence phenomenon analysis of the stock market

Institute of Financial Mathematics and Financial Engineering, School of Science, Beijing Jiaotong University Beijing 100044, China

^(a) wangjun@bjtu.edu.cn

Received: 8 November 2012
Accepted: 23 March 2013

Abstract

A random financial stock price model is developed by the interacting contact process, which is one of the statistical-physics systems. The contact process is a continuous-time Markov process, one interpretation of this process is as a model for the spread of an infection, where the epidemic spreading mimics the interplay of local infections and the recovery of individuals. We investigate and analyze the long-term memory, the nonlinear correlations and the multifractal phenomenon of normalized returns of the price model by statistical analysis methods, which include autocorrelation analysis, the Gaussian copula method and the multifractal analysis method. Moreover, we consider the daily returns of the Shanghai Stock Exchange Composite Index and the Shenzhen Stock Exchange Composite Index, and the comparisons of statistical behaviors of returns between the actual data and the simulation data are presented.