A Market Fraction Model Based On General Function And Empirical Analysis

This article is based on a market fraction of Xuezhong He and Youwei Li?2015?^[1],A general function of market price and mean value of historical price differences is intro-duced to trend followers,a new random model is established.Firstly,we discuss the equilibrium solution of the deterministic model,the stable region and its branches when the basic price of the risk asset is equal to the long-term basic operating price.Secondly,the influence of two noise processes on the volatility clustering and its autocorrelation of the return,absolute return and square return in the random model is also studied.It is concluded that the the basic process of noise plays an important role in the clustering phenomenon of market price fluctuation,and also plays a key role in the autocorrelation mode of absolute return and square return.The excess demand of noise plays an im-portant role in the autocorrelation mode of returns.The simulation results show that a realistic price sequence can be generated when all two noises appear.Finally,the model is compared with the original model,the Shanghai stock index and its three kinds of stocks.This model in non symmetry by the test results,the long memory and volatility clustering than the original model close to the real market data,the effect of this model is consistent with the original model in the test of stability.It can be concluded that the model can not only reflect a series of facts,but also show the changing roles of the stock in China's stock market.