基于Copula函数的黄金价格与美元指数的相关性分析

发布时间：2018-05-28 02:46

本文选题：Copula函数 + GARCH模型　；参考：《华中科技大学》2012年硕士论文

【摘要】：线性相关系数和Granger因果关系分析是最传统的相关性分析方法，而这两种方法只适合于有线性相关关系的变量，大多数金融变量之间都呈现出非线性关系，用线性相关系数来描述它们之间的相关性会存在一些误导。Copula函数是将若干个边缘分布连接起来形成联合分布的连接函数，由它推导出来的相关性测度在非线性单调增变换下保持不变，能够克服线性相关系数使用中的局限性，在描述金融变量间的相关性及相关结构方面有较多的优势。本文在介绍时间序列和Copula函数基础理论的基础上，选取2009年9月2日到2011年12月16日的国际黄金价格和美元指数作为样本，通过建立Copula模型来描述黄金价格和美元指数之间的相关性。模型的建立分两步完成：首先，确定边缘分布，它描述了黄金价格和美元指数收益率的分布特征；其次，选取适合的Copula函数，它描述的是两者之间的相关结构。本文采用金融时间序列模型来确定边缘分布，通过Eviews6.0软件对样本数据进行分析并做适当的处理，选用GARCH模型来估计黄金价格和美元指数收益率的边缘分布，并用分位数-分位数图评价了模型的拟合效果；对于Copula函数的选择，本文从二元正态Copula、二元t-Copula、GumbelCopula、ClaytonCopula及FrankCopula这五种Copula函数入手，通过估计线性相关参数、求相关性测度、绘制Copula函数的分布函数和密度函数，舍弃不适合的Copula函数，选择用二元正态Copula、二元t-Copula和FrankCopula来描述黄金价格和美元指数的相关结构，最后通过引入经验Copula函数，得出二元t-Copula拟合效果最好的结论。本文最终确定用t-Copula-GARCH模型来模拟黄金价格和美元指数之间的相关性及相关结构，并给出了结论所有具有的理论和现实意义，为投资者进行投资分析提供了良好的建议，，提醒投资者在投资黄金时应特别留意美元指数的急剧变化，以规避风险。
[Abstract]:Linear correlation coefficient and Granger causality analysis are the most traditional correlation analysis methods. It is misleading to use linear correlation coefficient to describe the correlation between them. Copula function is a join function that connects several edge distributions together to form a joint distribution. The correlation measure derived from it is invariant under the condition of nonlinear monotone increasing transformation, which can overcome the limitation of the use of linear correlation coefficient, and has many advantages in describing the correlation between financial variables and related structures. Based on the introduction of time series and the basic theory of Copula function, this paper selects the international gold price and dollar index from September 2, 2009 to December 16, 2011 as samples. Copula model is established to describe the correlation between gold price and dollar index. The establishment of the model is divided into two steps: first, the marginal distribution is determined, which describes the distribution characteristics of gold price and the dollar index yield; secondly, the appropriate Copula function is selected, which describes the correlation structure between the two. In this paper, the financial time series model is used to determine the edge distribution, the Eviews6.0 software is used to analyze and process the sample data, and the GARCH model is used to estimate the marginal distribution of gold price and dollar index yield. The fitting effect of the model is evaluated by quartile-quartile graph. For the selection of Copula function, this paper starts with five Copula functions, namely binary normal Copula, binary t-Copula GumbelCopula Clayton Copula and FrankCopula, and obtains the correlation measure by estimating the linear correlation parameters. The distribution function and density function of Copula function are drawn, and the unsuitable Copula function is given up. The binary normal Copula, binary t-Copula and FrankCopula are chosen to describe the related structure of gold price and dollar index. Finally, the empirical Copula function is introduced. The conclusion that binary t-Copula fitting is the best. In this paper, t-Copula-GARCH model is used to simulate the correlation and structure between gold price and dollar index, and the conclusion is all theoretical and practical significance, which provides a good suggestion for investors to carry out investment analysis. Investors are reminded to pay special attention to the sharp changes in the dollar index when investing in gold in order to avoid risk.
【学位授予单位】：华中科技大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F831.5;F224

【参考文献】