On The Volatility Of Shanghai Securities Market Grail Index By Wavelet Packet Denoising And GARCH Model

With the policy of transformation and opening, great change has happened in the macroeconomic and microeconomic environment at home and abroad, which makes the domestic financial markets experience profound transformation, and the financial market volatility and the financial risks had increased rapidly. The financial volatility is one of the most important characteristics in stock market. At present our stock market is in the development of new and transition period, which ont only has the characteristics of common stock market, but also has its own characteristics. It is important to know how to measure the financial fluctuations,depict and analyze the characteristics of financial volatility,which is helpful to understand and master the rules and structures of fluctuations in the financial markets. And the measurement and analysis of financial volatility must be realized through scientific methods and tools.In the light of modern finance theory, modern statistics theory and wavelet packet denoising theory, with the volatility of Shanghai composite index, the author systematically makes a theoretical and empirical research into the characteristics of China's stock market fluctuation.In this paper, wavelet packet denoising theory , stock volatility theory and the determination methods of the stock market volatility are introduced firstly; with the help of wavelet packet denoising theory, time series of Shanghai composite index are denoised after its deformation, then a statistical description is analyzed; at last, the most appropriate GARCH model is established by the comparison of all kinds of GARCH models.The research results indicate that: Shanghai securities market grail index accords with the general financial data, which can be undertaken the general statistical analysis and can build GARCH model to analyze; GARCH model which is used the wavelet packet to denoise is obviously superior to that is not used, which shows that the wavelet packet denoising is more effective; from the comparison and analysis of all kinds of GARCH models, we can see the asymmetry of Shanghai securities index, namely "leverage effect" that the same bad news than good news on the market volatility is of a greater impact.