Bahadur Representation And Asymptotic Normality Of VaR Quantile Estimator Under Negatively Associated Conditions

VaR (Value at risk) technique is a new risk management tool which has been developed after the nineties, it can measure risk scientificly, accurately, comprehensively, so it is generally welcome by the international financial community.It is known to us that VaR (Value at risk)has close relationship with quantile estimator. In real life, what we meet most of the financial and economic time series are not independent but dependent, this shows that researching quantile estimator is significance of estimating the value of VaR under the conditions of the dependent.In this paper, under the conditions of NA (negatively associated), we give Bahadur's rep-resentation of VaR sample quantile. On the basis of(2008) article, we optimize the conver-gence rate of Bahadur's representation of VaR sample quantile, the speed by O(τn) increased to O(τnn-1/4), and prove asymptotic normality of Bahadur's representation of VaR sample quan-tile. We give the confidence interval of sample quantile VaR estimates under confidence level 1-α. Finally, we use two common time series models to do the numerical simulation of the VaR sam-ple quantile estimation, and tests its accuracy; Meanwhile, we analysis the Haiyue shares and Tianrun Crankshaft, under different probability levels, we give two stocks the value of VaR of logarithmic rate of return, VaR estimates of Tianrun Crankshaft is less than the VaR estimates of Haiyue shares, overall, this shows that investing in Haiyue shares has more risk than Tianrun Crankshaft.