A Study On The Long-term Memory And System Dynamic Mechanism Of Stock Market

The Efficient Market Hypothesis(EMH)raised by Fama can be considered of the basis of modem financial theories,as so many famous financial models,including Capital Asset Pricing Model(CAPM)and option pricing model,are all built on the premise of a efficient market.However,EMH have always been controversial because of its overly strict assumptions.On the other hand,the real markets alway shows various "anomalies,that can't be explained by EMH,such as calendar effect,momentum effect,long-term memory and so on.Thus,it has been a research spot of many scholars to develop more reliable models or make the further study of the intermal dynamic mechanism of the market as a complex system.Among them,the Fractal Market Hypothesis(FMH)raised by Peters,the Minority Game model developed by Challet and the Sornette's Log-Periodic Power Law model inspire us most.This paper makes a further development of these predecessor's research.First,we use R/S algorithm to test whether there a long memory exists in the A-share.In this part,we calculate the Hurst index of the CSI300 Index,CSI500 Index and Growth Enterprise Index which represent large cap stock,medium cap stock and small cap stock respectively.The empirical results show that there do exist a long memory in stock markets,and the memory strength generally presents negatively with market cap.Namely that a stock with a smaller market cap always shows a more strong memory,and that may because of that small market cap stocks are more easily to be influenced by market and investor sentiment.In order to explore how market memory is generated,a self-organizing micro-market model under global information was constructed.In this model,investors need to take into account of the fundamental information and technical information to make decisions,they also need to communicate and interact with others adjacent.We make a computer simulation of this model and get a series of market return with statistical characteristics quite close with real market return.More than that,the model can also depict a reasonable market evolution process.Both of them imply that the model can generally characterize the micro-dynamic mechanism of the market well,and that the memory of the market also comes from the interaction between micro-individuals to some extent.The system dynamic mechanism of the stock market always presents a specific evolution model under specific conditions.For example,assets' price always presents an evolution model of Log-Periodic Power Law during the process of the accumulation of speculative bubbles.Thus,this paper applies the LPPL model to study the two financial crisis events in A-share market which happened in 2007 and 2015 respectively.When estimate the dynamic parameters of LPPL model,we happen to find that some parameters in the model can present specific evolution patterns around the peak of the stock price.Thus it suggests that we can use these patterns to identify a potential financial crisis and get a warning before its happening.