The Stock Market Long Memory Empirical Research

The long memory of time series array firstly was found by Hurst in 1951, and then was established mathematical foundation by introducing fraction Brownian movement and conception of fractal by Mandelbrot. In the recent 20 years, research on long memory has been expanded to the domain of economics and finance from natural science field. Especially, long memory of financial time series array becomes study focus at home and abroad.It is very important to analysis the long memory about stock market. According to the Efficient Market Hypothesis(EMH), if a stock market is efficient, the price of the stock should be random. And the price is more random, the efficiency is more obvious. The existence of long memory about capital market strongly challenges EMH. It makes the price regular and the classical short memory time series array models useless. What's more, investors can forecast future prices of stock by studying its historical information.As the most important part of Chinese security market, Chinese stock market has developed for near 20 years, but it is still very different from foreign mature stock market. Therefore, we can't directly copy foreign test method to examine long memory about Chinese stock market.This paper chooses Composite Index of Shanghai, Component Index of Shenzhen and 10 vocation indexes on Chinese stock market as sample, mathematical and quantitative analysis as main research methods. The first chapter introduces practical meaning and domestic and international research dynamics of financial time series array. The second chapter and the third chapter systematically introduce theory and methods about long memory property. The fourth chapter is the demonstration part of this paper, while the last chapter is the conclusion of all demonstrations. According to the empirical result, there is no obvious long memory characteristic of returns about indexes in China stock market except four vocation indexes in Shenzhen stock market. But the variance of returns about index in China stock market.There's some innovations in this paper. Besides composite indexes, vocation indexes are added as research samples. The modified R/S analysis is improved in order to promote its accuracy. Meanwhile, the parameters of ARFIMA(p,d,q) model are calculated by two-step method.