重尾分布的尾部指数估计及沪深股市实证分析  

Tail Index Estimation of Heavy-tailed Distribution and Empirical Analysis of China's Stock Markets

作　　者：刘维奇[1,2] 赫英迪[2,3] 陈琳[2,4] 

机构地区：[1]山西大学管理科学与工程研究所,山西太原030006 [2]山西大学数学科学学院,山西太原030006 [3]广东茂名职业技术学院,广东茂名525000 [4]山西大学工程学院,山西太原030013

出　　处：《数学的实践与认识》2011年第6期1-13,共13页Mathematics in Practice and Theory

基　　金：教育部人文社会科学研究项目(07JA630027;06JA630035);山西省高校人文社科重点研究基地项目(20083006)

摘　　要：重尾分布尾部指数α的估计依赖于样本中所用顺序统计量个数k的选取.本文介绍了估计α时选择k的两类不同的方法:Sum-plot方法和Bootstrap方法,并对Hall提出的Bootstrap方法作了改进,称为M-Bootstrap方法.本文利用上述方法对已知分布进行Monte-Carlo模拟,研究它们的可行性,然后对上海和深圳两市股指数据进行了实证分析.计算结果表明,上海和深圳股指收益率具有重尾性.是右偏态的,右尾厚于左尾.通过几种方法计算的结果比较发现Sum-plot方法和M-Bootstrap方法在估计重尾指数上精确性较高一些,而且不受异常值的影响.Estimating the tail index α of a heavy-tailed distribution depends oil the choice of the number k of upper order statistics used in the estilnation. In this paper, we introdllce two different kinds of methods which are used to choose the value k in tile estimating α, Sumplot method and Bootstrap method. And also improve the Bootstrap method proposed by Hall, it is called M-Bootstrap method. Firstly, using tile above methods, we simulate known distributions and prove feasibility of these methods by Monte-Carlo method. Then, we make empirical analysis basing on Shanghai and Shenzhen＇s stock index data. These results show that China＇s stock index returns rate is of thick tail, and expose right skewness, that is, right tail is heavier on left tail. By comparing results obtained in several different methods, indicate that Sum-plot method and M-Bootstrap method is more precise in estimating heavy-tailed index and is immune to anomalous value.

关 键 词：重尾分布 重尾指数 Hill估计 Sum—plot方法 BOOTSTRAP方法 

分 类 号：O211.3[理学—概率论与数理统计]