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POT极值模型参数的准确估计是计算金融资产回报厚尾分布市场风险的关键.由n阶概率加权矩得到参数的二项式回归估计,而将参数的零、一阶概率加权矩估计予以推广.极大似然估计中,将极大化似然函转化为二元函数无条件极值问题,其他参数估计方法的结果作为迭代的初始值,通过它们的似然函数值和极大似然函数值的比较以及迭代次数判断方法的优劣.实证研究表明:参数的零、一阶概率加权矩估计较接近于真值,随着阶数的提高,二项式回归参数估计的误差很大.参数的极大似然估计优于非线性回归估计优于零、一阶概率加权矩估计.在此基础上计算上证A股指数VaR值.
The accurate estimation of POT extremum model parameters is the key to calculate the market risk of the fat tail distribution of financial assets return.The binomial regression estimation of the parameters is obtained from the n-th probability weighted moment, while the zero and first-order probability weighted moment estimates are generalized In maximum likelihood estimation, the maximization likelihood function is transformed into the unconditional extreme value problem of binary functions, and the results of other parameter estimation methods are used as the initial values of iteration. Through their likelihood function values and maximum likelihood function The comparison of values and the determination of the number of iterations.The empirical study shows that the zero and first-order probability weighted moments of the parameters are closer to the true value, and the error of the binomial regression parameter estimation is very large with the increase of order. The maximum likelihood estimation of the parameters is superior to the non-linear regression estimation, which is better than zero and the first-order probability weighted moment estimation, and the VaR of Shanghai A-share Index is calculated.