上证指数收益率分布的拟合研究

Study on fitting the return distribution of Shanghai stock index

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.