非对称广义正态分布的估计及应用

Estimation and Application of Asymmetric Generalized Normal Distribution

为更好地刻画金融市场收益率数据的尖峰厚尾带偏特征,本文将广义正态分布推广为非对称广义正态分布,给出该分布的三种表达式和概率性质,利用极大似然估计方法和小批量梯度下降算法进行参数估计和数值模拟。针对标准普尔500指数(S&P 500)和上海证券交易所综合指数(SSEC)的日收益率数据集,对比分析非对称广义正态分布及其3种退化分布的拟合效果。实证结果表明,非对称广义正态分布更好地拟合了日收益率数据的尖峰厚尾带偏特征,在金融市场数据建模中具有较好应用价值。

In order to better characterize the characteristics of peak and thick tail bias for financial market yield data,this paper extends the generalized normal distribution to the asymmetric generalized normal distribution,gives three expressions and probability properties of the distribution,uses maximum likelihood estimation method and small batch gradient descent algorithm to estimate parameters and conduct numerical simulation.Based on the data sets of daily returns of S&P 500 and SSEC,the fitting effects of asymmetric generalized normal distribution and its three degenerate distributions are compared and analyzed.The empirical results show that the asymmetric generalized normal distribution better fits the peak fat tail bias characteristics of daily yield data,and has good application value in financial market data modeling.