Analysis Of The Stock Log-return Distribution Function And Prediction Of The Stock Price

When we study stock market, we usually think that the model of stock price obeys Brownian movement, which log-return characterize normal distribution. It is the foundation that we define a lot of financial derivative which take stock as thing marked. But Statistics result of actual market indicate most log-return of stock disobey normal distribution.In the article we at first discuss the kind of stock log-return distribution. We find that 7 kinds function can describe stock log-return form their works: Gausses of normal distribution, Levy distribution, t distribution, spike attitude distribution, random fluctuating model, ARCH-GARCH model, divide shape Brownian movement .We have introduced brief these seven kinds of function.Then we had examined several stocks of the stock market of Shanghai with Partial degreeand kurtosis examination and x 2 examination. We find that stock log-return disobeys normaldistribution with one day. Then we fit to the function of the stock log-return, The first method adopt method of Mantegna and Stanley in studying the log-return of S&P500 index distribution of stock exchange of New York in 1995 to fitted to Shanghai Stock Exchange's composite index. We find stable Levy distribution can describe Shanghai Stock Exchange's composite index. The second kinds of methods are that compared Laplace distribution with normal distribution to see Laplace distribution is more superior than normal distribution. We finds that all stock log-return of day we study disobey normal distribution. More stock log-return obeye Laplace distribution. But with we enlarging interval of time, the stocks which obey normal distribution increases gradually, This is unanimous with Fama's assumption that the long-term log-return obey normal distribution. We have started put forward a simple stock price model from investor on stock market, and utilize this model to analyse the stock log-return function.At last, we set up two kinds of models to predict the stock price, the first kind is Grey-Markov model, find it's accuracy more than Grey model, The second kind is revised arrays model of time.