Statistical Analysis On Correlations Of Stochastic Financial System Based On Percolation And Voter Model

This paper aims at studying the correlations in financial markets by utilizing perco-lation model and voter model from statistical physics system, combing with stochastic process theory to construct the fluctuation process of stock price and return. It is a new attempt to introduce statistical physics models to economy. We treat physical particle as investors in financial markets and mutual impacts among particle as influence of in-vestment attitudes and communications. Based on the hypothesis of "herd behavior", the investors who hold the same investment attitude would eventually affect the stock price.We select the return interval series and return series as our paper’s static in or-der to analyze the correlations in two pairs of return interval series and return series. In particular, firstly we employ two tests to testify the power-law cross-correlation be-tween two pairs of return interval series and return series; secondly we use multifractal detrended cross-correlation analysis to study the properties about multifractality and cross-correlation between return interval series in SSE and SZSE and employ Copula function to research the tail dependence and concordance between the return series of SSE and SZSE in Chinese market. Meanwhile we also conduct the same analysis of multifractal detrended cross-correlation and tail dependence to the simulative return in-terval series and return series derived from the percolation model and voter model for comparison with the outcomes of actual data.The result shows that Chinese stock markets have the characters of multifractality and not efficient markets, real return interval series and simulative return interval series appear a weak positive multifractal detrended cross-correlation while both real return series and simulate return series have a considerably strong tail dependence and strong concordance. It also indicates that our models can reflect some important characters of real markets when the parameters are in proper range, which supply the rationality, help and support for further study on fluctuations of stock.