Weighted Least Absolute Deviation Estimatation For A GARCH Process With Infinite Variance And Asymptotic Properties

In the long-term empirical study,it is found that as stock prices financial time series is usually gathered(volatility clustering) features.The so-called clustering of the financial markets is often accompanied by large fluctuations in another great fluctuatious. So how accurate characterization of this market volatility heteroskedasticity (Heteoskedastic) features,and future market fluctuations as much as possible to make accurate predictions,the theory of financial research and financial supervision policy formulation has an extremely important theoretical significance and the practical significance.Usually the hypothesis that the sequence is subject to normal distribution, breached the reality for the convenience of solution the problem.When it is greater difference with practice under this assumption,the parameter estimation methods, testing methods and the choice of models will have a larger deviations.Thus it will lead to the conclusion error even wrong.At the same time,financial time series also displayed the "heavy-tailed" phenomenon.This phenomenon should not be ignored.In the field of fluctuations research,Eagle and Tim Bollerslev has put the ARCH(autoregressive conditional heteroskedasticity) and GARCH(generalized autoregressive Conditional heteroskedasticity) model.Becanse of the financial time series to the "heavy-tailed" and "heteroscedasticity" more successful characterization,measurement, so were many financial scholars favour.However,Mikosch Starica found that when the error is subject to normal,the tail of GARCH(1,1) model of is thinner than the actual data.Therefore,how to construct appropriate model and reasonable estimation method under heteroscedasticity and heavy-tailed,for today it is center of theoretical circles and the business community.This paper focused on parameter estimation problem under heavy-tailed and Heteroscedasticity in the model.This paper systematically explain heavy-tailed distribution model and the strict stationary ergodic GARCG,and recalled the GARCH model parameters estimated historical process.It summed up parameter estimation method of the GARCH model with residual subject to different assumptions.When the time series show heavy tail, GARCH model discusses in detail quasi maximum likelihood estimation(QMLE),and least absolute deviations estimation(LADE),and improves the LADE,as weighed-least absolute deviations estimation(WLADE).Monte-Carlo simulates a group of heavytailed, heteroskedasticity of the data,and respectively QMLE,LADE,WLADE three estimation method estimate and compare construction of GARCH model.Subsequently the two cities of Shanghai and Shenzhen stock index data is empirical analysised. Calculated results show that,at the Shanghai and Shenzhen stock index benefits of a heavy tail,heteroscedasticity.At the same time,GARCH model is established by WLADE.volatility is forecasted and given to the calculation of VAR.The empirical results show that,the value of VAR is more precise by using of WLADE.Main conclusion of this paper as follows:Overall,in a heavy tail,aggregation of financial time series,to the application WLADE to establish GARCH model can be a satisfactory outcome,WLADE method is better than LADE,QMLE methods.When the tailed data is more thick,the WLADE method will be more accurate and the impact based on anomalies will be weak.