The Improvement Of The GARCH Model And Its Application In The Analysis Of Stock Market Volatility

Over the years,the research of the stock market’s return volatility has been one key issue in the financial time series, which is also the most concerned measure of the National Regulatory Authorities, because volatility is one of the most simple and most effective indicators of comprehensive reflection of the stock market price behavior,at the same time, it is also closely related to the business investment, financial decision-making and consumer behavior.In recent years, China’s stock market is booming, and the measure of the stock volatility change’s demand is increasingly strong.GARCH model is a conditional heteroskedasticity model,which is specifically made the amount of body for the financial data, especially for the stock market’s return volatility analysis, GARCH model (Generalized Auto Regressive Conditional Heteroskedasticity Model) is the promote form of ARCH model (Auto Regressive Conditional Heteroskedasticity Model), which fully describes the wave process of the assets return rate.Financial time series’features are volatility clustering, asymmetry, fat tail. In general, volatility clustering can be described by ARCH model and its general form GARCH model, Another typical feature of financial time series is asymmetry, GARCH model generally assume that residual item obey normal distribution, can’t express this characteristic. First,this paper builds time sequence on volatility asymmetric properties of the TAR-GARCH model, test the stock market return volatility on its relevance’s differences, as well as on positive and negative information’s differences.Second,this paper bring in dummy variable, adopt the stock market gains dummy variable GARCH model to depict the asymmetry of the financial time series, through the improvements in GARCH models, better reflects the characteristics of financial time series and the change of the stock’s volatility, so we get a better simulation result. This article will apply the dummy variable GARCH model to the volatility study of the Shanghai Composite Index, expand the GARCH model in the application of the stock market. Research shows that GARCH model’s improvements have important theoretical and practical significances, not only can help investors to analyze the specific situation, but also for policy makers have great reference value.Finally,compare the dummy variable GARCH model and GARCH model variants(i.e. asymmetric GARCH model) in the example analysis, explain the applicability of this paper’s the innovations more, especially suitable for fluctuation analysis, this analysis can play an important role, its significance exceed the numerical itself analysis.