| In this article, some methods are used to test the volatility characteristics of returns on the indices of stock shares in China's stock markets. In chapter 2, we use the ICSS:MV algorithm (Bos and Hoontrakul,2002), which extends the algorithm of Iterative Cumulative Sums of Squares to Mean and Variance, to estimate the structural breakpoints of series of share indexes returns in Shanghai and Shenzhen stock markets. Some results are obtained in this section. 1) The volatility of China's stock markets is higher than that of developed stock markets. 2)The volatility of Shenzhen Sample Index returns becomes more and more higher, this suggests that its role as a market radiator is more and more weaker. 3) Most of the breakpoints are aroused from variance changing, this supports the hypothesis that mean is constant but variance varies in one financial series. 4) It's improper to divide the episodes of China's stock market to macro extent according to the breakpoints estimated through ICSS:MV, for there are so many breakpoints. 5) The volatility in China's stock market has become more and more rational since the rule of raising limit was established in 1996. In chapter 3, the model of TGARCH ( Glosten, Jagannathan, and Runkle, 1993) is used to test the volatility of these stock shares indices. The results in this section suggest that the phenomena of thick tails, volatility clustering, leverage effects and so on, are still exist in China's stock markets. According to some researchers in china, the leverage effects in Chinese stock markets are contrary to these in developed stock markets (i.e., bad news affection is higher than good news). But in my opinion, the reason may be the selection of data sample. And in chapter 4,we test the co integration between the two stock markets. Our empirical results are as follows:1) the co-integration exists in the long run, and 2)the volatility in the short run affects the markets, especially the Shanghai market.
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