上证指数收益率分布的拟合研究  

Study on fitting the return distribution of Shanghai stock index

作　　者：任芳玲[1] 刘龙 REN Fangling;LIU Long(College of Mathematics and Computer Science,Yan’an University,Yan’an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《延安大学学报（自然科学版）》2024年第4期88-92,98,共6页Journal of Yan'an University：Natural Science Edition

基　　金：陕西省大学生创新创业训练计划项目(S202410719092);延安大学教学改革研究项目(YDJGZD23-05)。

摘　　要：采用近十一年上证指数数据,研究其收益率分布情况。首先,验证了上证指数收益率不符合正态分布,具有尖峰厚尾和非对称性质;其次,采用logistics分布、t分布、q-高斯分布、g-h分布以及正态逆高斯分布分别进行参数估计和图像拟合;最后,通过比较5种分布的分布函数曲线与数据的累积概率分布曲线,计算拟合优度和均方误差根进行优度检验,得出正态逆高斯分布拟合结果最优的结论。Using the data of Shanghai stock index in recent 11 years,the distribution of its return rate is studied.Firstly,it is verified that the return of Shanghai stock index does not conform to the normal distribution,and has the properties of sharp peak,thick tail and asymmetry.Secondly,logistics distribution,t distribution,q-Gaussian distribution,g-h distribution and normal inverse Gaussian distribution are used for parameter estimation and image fitting respectively.Finally,by comparing the distribution function curves of the five distributions with the cumulative probability distribution curves of the data,the goodness of fit and the mean square error root are calculated to perform the goodness test,and the conclusion is drawn that the fitting results of the normal inverse Gaussian distribution are optimal.

关 键 词：收益率分布 尖峰厚尾 正态逆高斯分布 G-H分布 

分 类 号：F830.9[经济管理—金融学]