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This paper chooses the relatively persuasive stock index in China, Shanghai Composite Index (1), using data from December 31, 1997 to April 4, 2018 as the sample of the paper and then calculate them according to the logarithmic rate of return. By using EVIEWS 7 software to test the effect of these samples, this paper select and establish the relevant model, and the fluctuation characteristics of return series are analyzed briefly. Due to the discovery of stock market returns has obvious ARCH effect and through repeated attempts, the author finds that GARCH (1, 1) model is more appropriate when describing the characteristics of the fluctuation of stock index compared with other similar models. Through the descriptive statistical test and the ADF unit root test, it is found that the fluctuation of equity market has the characteristics of "thick" and "clustering". The volatility of the stock returns has a "cluster" character and the financial time series is stable and has the conditional heteroscedasticity. Good news on the impact of the market and investment is weaker than bad news, investors and the market is more sensitive to the bad news. At the end of the empirical analysis, by drawing the information impact curve, we can intuitively see the traits of the financial time series, that is, leverage effect. Keywords—log return rate; GARCH model family; asymmetry; lever age effect; information impact

proceedings of the 3rd international conference on judicial, administrative and humanitarian problems of state structures and economic subjects (jahp 2018)

The Analysis of the Volatility of China's Stock Market Taking Shanghai Composite Index as an Example