The Parameters Estimation Of ARCH Model Based On VG Distribution

Autoregressive conditional heteroskedasticity model， also calledARCH model，is proposed by Engle in1982，which were used to described the volatility of Financial time series data，and developed to generalizedAutoregressive conditional heteroskedasticity model (GARCH model) byBollerslev in1986. these models which can accurately describe thevolatility of Financial time series data’s rate of return,and are wildly usedin all fieldes of economy and finance，especially in Analysis of FinancialTime Series datas. however，one of the most important steps to discribethe volatility accurately is the model’s parameter estimation.Traditional econometrics models are usually estimated by leastsquare method，Generalized moment estimate method and The maximumlikelihood estimation method. Among these methods, the maximumlikelihood estimation method is the most wildspread method used toestimate ARCH model’s Parameters,which has a very important positionin economics research，especially in theoretical research,thoug thismethod is not as widely as the least square method. ARCH modelrequires it’s disturbance is normal distribution.But a lot of empiricalanalysis show that the distribution of finacial time series usually have ahigh kurtosis，a heavy tail and asymmetric. the hypothesis of normaldistribution can’t meet the need of the realistic economic and the analysis of financial time series data, and commonly result in that theconclusion don’t fit to the actual situation. According to this situation,many scholars have done a lot of researches about the distribution offinancial time series data. VG distribution is one of those researcheswhich can discribe the high kurtosis,heavy tail very well. using thisdistribution replace the normol distribution of Disturbance can fit toreality better.The maximum likelihood estimation method need to write out theformula of Logarithm likelihood function，and then get the values of eachparameters via solving the Logarithm likelihood function’s maximum.this method can get the result which have a big error，due to thecomplexity of the formula of VG distributiong’sLogarithm likelihoodfunction and the limitations of optimization methods. So many scholarswant to find a new method to estimate the parameters of ARCH model，such as MCMC method,At the same time, these studies restrict thedevelopment of maximum likelihood estimation method. This article usethe genetic algorithm to estimate the parameters of ARCH model whiththe disturbance is VG distribution. The result of estimation is moreaccurate than traditional maximum likelihood estimation method.Andexpand ARCH model’s theory.