论文标题
拟合广义钢化稳定分布：分数傅立叶变换（FRFT）方法
Fitting Generalized Tempered Stable distribution: Fractional Fourier Transform (FRFT) Approach
论文作者
论文摘要
该论文研究了丰富的通用钢化稳定分布，一种正态分布的替代方案以及$α$稳定的分布，用于建模资产回报以及许多物理和经济系统。首先，我们探讨了广义钢化稳定（GTS）分布的一些重要特性。开发的理论工具用于执行经验分析。使用S＆P 500，间谍ETF和比特币BTC拟合GTS分布。分数傅立叶变换（FRFT）技术在最大似然过程中评估了概率密度函数及其衍生物。根据统计推断和Kolmogorov-Smirnov（K-S）拟合优度的结果，GTS分布符合间谍ETF回报的基本分布。比特币BTC返回的右侧，标准普尔500标准普尔500返回分布的左侧适合钢化稳定分布；虽然比特币BTC返回的左侧和标准普尔500返回分布的右侧是由复合泊松过程建模的
The paper investigates the rich class of Generalized Tempered Stable distribution, an alternative to Normal distribution and the $α$-Stable distribution for modelling asset return and many physical and economic systems. Firstly, we explore some important properties of the Generalized Tempered Stable (GTS) distribution. The theoretical tools developed are used to perform empirical analysis. The GTS distribution is fitted using S&P 500, SPY ETF and Bitcoin BTC. The Fractional Fourier Transform (FRFT) technique evaluates the probability density function and its derivatives in the maximum likelihood procedure. Based on the results from the statistical inference and the Kolmogorov-Smirnov (K-S) goodness-of-fit, the GTS distribution fits the underlying distribution of the SPY ETF return. The right side of the Bitcoin BTC return, and the left side of the S&P 500 return underlying distributions fit the Tempered Stable distribution; while the left side of the Bitcoin BTC return and the right side of the S&P 500 return underlying distributions are modelled by the compound Poisson process
