Empirical Analysis Of Time Series Of Long Memory

The essential characteristic of time series is that, it is of dynamic and adjacent observations are dependent. What time series mention is the analytical technique to this kind of dependence. This requires found stochastic and dynamic models of time series. This kind of dynamic dependence of observations is the memory of time series. Economic time series is of obvious memory, represent as the series have remarkable autocorrelation, even apart of many spacing, the historical events would influence future events for a long time. That is long memory of time series.The stock data as one of economic data is the same as other economic data, is of long memory. The research on the long memory and fluctuate character of the yield rate of stock is important to analysis and understand the structure of stock market, judge the trend of stock market, evaluate the influence of Volatility to stock market risk and future change etc. doubtless. especially, under the background of all countries opening capital market,allowing the free flow of capital, it become terribly necessary.On the foundation of checking a great deal of literature, this thesis gives summarization to the detection, definition, test, kinds of modeling of long memory, strives to image the characters of long memory across-the-board. What's more, on the foundation of formerly scholars'researches, this article puts forward following guess: long memory reflects the memory of time sequence itself, while volatility persistence reflects the long memory character of variance of time series. And through the analysis of the long memory character of stock daily closing price data of A-indexes of shanghai stock market, uses statistic software SPSS and EVIEWS, this thesis establishes Long memory-autoregressive time-varying-variance model ARIMA-ARCH, and does long memory analysis, test, forecast on the daily closing price data of stock. At the same time, carries on correlative quality analysis to the return sequence of daily closing price of stocks which is connotative, points out that the motion regulation of the return sequence of daily closing price of stock is different to daily closing price's. This paper also studies the return sequence of daily closing price of stock with the statistical method, does qualitative analysis on it. It explains the causation of volatility phenomenon of the stock market from mathematics angle.