【作者】 蒙坚玲；

【导师】 司继文； 龚朴；

【作者基本信息】 华中科技大学 ， 工程力学， 2004， 硕士

【摘要】 相关性一直是人们关注的一个焦点问题。在风险分析中,忽略了事物之间的相互关系可能会低估或高估了风险。常用的相关性度量ρ只是一个线性的度量,对于非正态分布和非线性的情况并不适用。而且,简单相关系数受其他因素的影响,反映的往往是表面的、非本质的联系。对于风险管理者来说,仅仅知道不同随机变量之间存在相关关系还不够,还必须知道它们之间的相互影响。本文从风险分析的角度,提出了一种基于copula函数来分析相依时间序列的方法。不同时间序列之间的相依关系分析包括协整分析、简单相关分析、偏相关分析、因果分析以及尾部的相关分析。Copula是一个函数,它主要用来刻画随机变量之间的相关性,它与面向均值、方差和线性相关的建模方法不同。Copula模型是对整个联合分布建模,因此可以提供更多有用信息,特别是可以捕捉到非正态、非对称分布的尾部信息。而且,若对变量作单调增的变换,由copula函数导出的一致性和相关性度量的值不会改变。Copula理论的出现和应用可以说将风险分析和多变量时间序列分析推向了一个新阶段。本文介绍了copula函数的概念和性质,并提出了一种估计copula函数的方法。在风险分析中,随机变量的尾部一直是风险分析的重点,因为灾难事件往往就在这个区域里发生。Copula函数包含了尾部相关的全部信息,因此它可以更全面、更深入地刻画随机变量之间的尾部相关关系。文中导出了copula函数和尾部相关系数之间的关系。最后,用一个具体的算例阐述了以上分析方法的具体应用。更多还原

【Abstract】 A dependence study for different random variables is carried through from the view of risk analysis and the method for dependence study is introduced. It is well known that the coefficient is a measure of linear correlation. To measure dependence through computation of correlations reveals adequate in the context of multivariate normally distributed risks or in assessing linear dependence, but it is not appropriate to measure the nonlinear dependence withρij. The concordance measure Kendall’s tau is presented which has no limitation for the distribution of random variable. Being affected by other factors, simple correlation coefficients often indicate the nonessential relationship between variables. To obtain the essential relationship, the concept of partial correlation coefficient and the method of calculation are presented in this work. For a risk manager, it is not enough to know the relationship between different random variables only. They want to know more, such as the interactional relationship between variables. The Granger causality test is introduced and the application is presented with an example. If regression is carried for nonstationary time series, the spurious regression will be produced. To resolve that, the method of cointegration is introduced. Eventually, to obtain more information about dependence relationship and quantitate risk, the concept of copula and the estimate method of copula function are introduced and applied to calculate the tail dependence. The tail of random variable’s distribution is the focus of the risk analysis because the event with small probability often occurs in this area. The concept of tail dependence is introduced here to analyze the tail risk of random variable. Since copula function contains all the information of tail dependence, it can depict the tail dependence relationship between variables comprehensively. In the last section of this paper, an example is presented to demonstrate the application of the method mentioned above.更多还原