The Application Of The GARCH Model In The Analysis Of Stock Market Volatility

Volatility is a hot research topic in the analysis of economic and financial areas, In the early stage, we used constant standard deviation or variance to measure volatility. But in the financial markets,volatility will change over time, the traditional statistical methods can't reflect these features, many scholars began to try to use other methods to analyze the problem about volatility in finance. In 1982, the ARCH model( Auto Regressive Conditional Heteroskedasticity Model)were proposed by Robert F.Engle, it is used to analyze the time series with different variances and get good results. Since then, ARCH model got rapid development, scholars get many improvements on the base of arch model, such as Bollerslev proposed the GARCH model(generalized autoregressive conditional heteroskedasticity model) in 1986.GARCH model is a generalized ARCH model, besides the basic features of the ARCH model, the GARCH model can react long term autocorrelation between data. the ARCH model is only suitable for the short-term auto-correlation process of the different variance function. The GARCH model can effectively simulate the long-term memory process of the different variance function. The GARCH model is the main time series model in this paper.This paper take the Shanghai Composite Index, Shenzhen component index and the gem index between 2013 and 2015 as the analysis object,use ARMA model and GARCH model to analyse the three stock markets' volatility. The analysis results show that the distribution of Shanghai stock index and Shenzhen stock index are almost unanimously, and their disturbance variance increases gradually, the reaction degree to the external information is that the gem is strongest, the Shanghai board and the Shenzhen board is weak.