The Parameters Estimate And Useless For ARCH Family Model

With the development of the modern world,economy play a very important role in world stage .At the mean time , the research field of social science and natural science which are associated with economy have been made a profound improvement consequently .Among these ,in the field of statistics ,the topic of finance and economy turn to be the most prevailed one.Owing to propose the conditional heteroscedasticity model,Engle was awarded Nobel Price of economy in 2003.For the time varying volatility is the main character of financial series data,it is no doubt that ARCH models have brought a momentous and profound influence into the field of finance.The article elementarily discusses the parameters estimate for ARCH family model and use them to evaluate VaR of China stock marketing comparatively.The main conclusions are as follows:1, A new β — GARCH model with GED ,is proposed for modelling nonlin-uj: time series stationary and existence of moments conditions of the model arederived. The estimation of the parameters of the β — GARCH model take time series heavy-tailed nature into account,and it can be easily done through BHHH algorithm.2, A new mixture autoregressive conditional heteroscedastic model with a generalized error distribution ,is proposed for modelling nonlinear time series .The estimation of the parameters of the mixture autoregressive conditional heteroscedastic model take the time series heavy-tailed mature into account ,and detect that the index r corresponding to the tail-thickness index. The estimation of the parameters can be easily done through EM algorithm and the order model is also easily selected by BIC criterion.3, we analyze ARCH family such as GARCH ,EGARCH ,PARCH ,and computes VaR about index of Shanghai stock exchange ,Shenzhen in normal distribution separately and t-distribute,GED distribute.we got some new results and we can use them to evaluate China stock exchange.