China's Stock Market Rate Of Return And Its Fluctuations In Long-term Memory Research

Since Hurst (1951) had found the Long Memory of the time array of hydrology and Mandelbrot's (1960 ,1971 ) introduction of fraction Brownian movement and conception of fractal had established mathematical foundation of Long memory research, Research on Long Memory was extensively expanded in the domain of the social sciences field and natural science field. Greene and Fielitz (1977 ) was the first person who had carried on research to the behavior of Long Memory of stock markets. Recently, researchers have paid more attention to Long Memory of financial time array. It becomes research hotspot in domestic and international financial economics field. And it becomes an important special topic for non-linear study in the financial market.Non-linear characteristic and theory analysis using together, quantitative analysis and qualitative analysis using together were the main research method in this paper. On the basis of existing research results, I choose Index of Shanghai Stock Exchange, the composite index and Shanghai Stock Exchange A, B-share index of Shenzhen Stock Exchange, Shenzhen Stock Exchange A, B-share component index as research object. Econometrics method adopted, I systematically researched Long Memory characteristic of returns and their variance of Chinese stock markets.This paper is mainly divided into five chapters.Chapter one, introduction of the general characteristic of Chinese stock markets fluctuation, and I draw proposition from this. It mainly introduced returns and its variance characteristic of Chinese stock market which including remarkable characteristic, such as fat tails of distribution, excess variation, clustering fluctuation. At the same time, it introduced Leverage of variation.Chapter second, I introduced the main models about research on Long Memoryof characteristic in return and variance of Chinese stock market, and I pointed out the nature, strongpoint and shortcoming of these models. In order to study Long Memory more deeply, I has revised the model; The model includes ARMA mode, ARCH model, GARCH model, ARFMA model and ARFIMA-GARCH-t model. Revised models involves GARCH-GED model, ARFIMA-GARCH-t model and ARFMA-GARCH mixed normality model.Chapter third, I have provided two kinds of Long Memory definition of pedigree method and relevant method. I have summarized the commonly using study method. I briefly survey domestic and international research dynamic. I have explained the main research meaning of this paper. The method of inspection includes analytic approach of the auto-correlation function, traditional R/S analytic method, Revised R/S analytic method, GPH analytic method.Chapter forth, is the positive research on Long Memory characteristics of returns and returns of variance about index. Revised R/S analysis and GPH regression were utilized as research methods. I mainly researched on return array of stock index, its standard variance array and its variance array. It was a general study of Long Memory in Chinese stock markets. The standard variance array and variance array achieved from estimation of variance equation of ARFIMA-GARCH-t model.Chapter five: is the main research conclusion of this paper. In the meanwhile, I preferred some shortcoming on my research.