非对称两参数与三参数Laplace分布的统计分析

发布时间：2019-02-18 22:16

【摘要】：股指收益率分布一直是金融研究中的一个重要问题。研究股指收益率分布,不仅有助于认识股票市场的内在运行规律,而且还可以帮助股指期货投资者进行正确的风险度量,以便进行资产定价与资产组合选择。提出能够更好地拟合金融资产收益率的分布,并对其进行统计分析已成为金融研究的新的重要课题之一。本文首先对非对称两参数Laplace分布的统计分析进行了研究。运用矩估计,极大似然等方法进行了参数估计,证明了极大似然估计法与矩估计2的结果实际是一致的。并用Monte-Carlo模拟综合比较了几种估计方法,得出矩估计2比矩估计1精度更好的结论。其次,本文研究了非对称三参数Laplace分布的统计分析及参数估计。从现有文献来看,关于非对称三参数Laplace分布的参数估计都是通过极大似然的方法获得,但其极大似然估计的存在性和唯一性理论证明并不完善。本文给出一种较为简单的处理方法。并用模拟综合比较了几种参数估计方法。接着,本文指出了周静怡[23]一文中参数估计值的错误并给出了修正后的参数估计值,进行了拟合优度检验。同时运用上文中提出的参数估计方法,对文章中的数据进行了参数估计,拟合优度检验后的结果表明非对称三参数Laplace分布能够较好的描述样本数据尖峰,厚尾,偏态的特征。最后,本文对沪,深两市股指日,周收益率进行了实证研究。研究结果表明,非对称三参数Laplace分布比正态分布能够更好的拟合沪,深两市股指日,周收益率。
[Abstract]:The distribution of stock index yield is always an important problem in financial research. The study of the distribution of stock index yield is not only helpful to understand the inherent law of stock market, but also helps investors to measure the risk correctly, so as to make asset pricing and portfolio selection. It is proposed that the distribution of the return rate of financial assets can be fitted better and the statistical analysis of it has become one of the new and important subjects in financial research. In this paper, the statistical analysis of asymmetric two-parameter Laplace distribution is studied. The method of moment estimation, maximum likelihood and so on is used to estimate the parameters, and it is proved that the results of maximum likelihood estimation and moment estimation are in good agreement with each other. Several estimation methods are synthetically compared with Monte-Carlo simulation. It is concluded that the moment estimation 2 is more accurate than the moment estimation 1. Secondly, this paper studies the statistical analysis and parameter estimation of asymmetric three parameter Laplace distribution. According to the existing literatures, the parameter estimation of asymmetric three-parameter Laplace distribution is obtained by the method of maximum likelihood, but the existence and uniqueness theory of maximum likelihood estimation is not perfect. In this paper, a relatively simple treatment method is given. Several parameter estimation methods are compared by simulation. Then, this paper points out the error of parameter estimation in Zhou Jingyi [23], gives the revised parameter estimate, and tests the goodness of fit. At the same time, the parameter estimation method mentioned above is used to estimate the parameters of the data in this paper. The results of goodness of fit test show that the asymmetric three-parameter Laplace distribution can well describe the peak, thick tail and skewness characteristics of the sample data. Finally, this paper makes an empirical study on the daily and weekly returns of stock indexes in Shanghai and Shenzhen stock markets. The results show that the asymmetric three-parameter Laplace distribution can better fit the daily and weekly returns of Shanghai and Shenzhen stock indexes than the normal distribution.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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