二元Archimedean Copula函数选择的新方法及相关模型的改进
发布时间：2018-09-18 09:48
【摘要】：随着世界贸易深度不断地扩大,加强了地区与地区、国家与国家之间的经济交流和合作,经济全球化、一体化的趋势愈加明显,使得影响经济发展的因素不再单一。而各个因素之间的关系变得错综复杂,所以传统的基于线性相关分析金融市场风险的模型已经不再适用于愈加复杂的经济体系。以往度量金融序列间相关关系时,我们习惯性地假设它们的边缘分布为正态分布或t分布,以此来减少运算量。但是,这样的假设时常与金融数据具有尖峰厚尾的特征相矛盾。为了化解这一矛盾,Copula理论的出现为分析金融序列相关性这类问题提供了一条崭新的思路,Copula函数的优点主要有两点:一是能够将变量的边缘分布和联合分布分开研究,且边缘分布的设定也不再局限于正态分布或t分布这类少数的几种概率分布,可以根据实际情况选择恰当的分布;二是由Copula导出的相关性度量,不仅能描述序列间存在的线性相关关系,更能捕捉到非线性、非对称的相关关系,在具体应用中更贴近真实性。Archimedean Copula函数的生成元具有构造简单、计算方便的特性,且作为Copula函数的一个重要分支,能有效地刻画金融领域中多元变量间复杂的非线性的相关关系。但实践经验表明当选择不同的Archimedean Copula函数会得到截然不同的结果。所以,如何选择恰当的Archimedean Copula函数来刻画金融数据间的相关关系就至关重要。本文以二元Archimedean Copula函数为研究对象,从Copula分布函数?tk?出发,构造了一个比分布函数?tk?的非参数估计量??tk?更有效的估计量?tk?,再根据?tk?,?tk?两者间的距离选择恰当的Archimedean Copula函数。实证分析表明新方法能够有效的选择二元Archimedean Copula函数模型。在度量金融序列间的相关性时常常会建立会选择建立Copula-GPD模型和Copula-GARCH-GPD模型,但这两个模型存在一定的缺陷。Copula-GPD模型没有考虑序列存在的条件异方差和波动聚集性,且两个模型都是选择单个的Copula函数进行序列间相关程度的分析,得到的结果并不全面。本文试着建立了M-Copula-TGARCH-GPD模型,M-Copula是指采用混合Copula来描述序列相关性,TGARCH是充分考虑金融序列存在的非对称性,GPD是用极值理论对尾部进行拟合。实证分析表明M-Copula-TGARCH-GPD模型能更好的体现金融序列间的相关性。
[Abstract]:With the expansion of the depth of world trade, the economic exchange and cooperation between regions, countries and countries, the trend of economic globalization and integration is becoming more and more obvious, which makes the factors affecting economic development no longer single. The relationship between various factors becomes complicated, so the traditional model based on linear correlation analysis of financial market risk is no longer suitable for increasingly complex economic systems. In the past, when we measured the correlation between financial sequences, we used to assume that their edge distribution is normal distribution or t distribution, so as to reduce the amount of computation. However, such assumptions are often contradicted by the peak and thick tail characteristics of financial data. In order to resolve this contradiction, the emergence of Copula theory provides a new way of thinking for the analysis of financial sequence correlation. The advantages of Copula function are as follows: first, it is possible to study the marginal distribution and joint distribution of variables separately. Moreover, the setting of edge distribution is no longer limited to a few probability distributions such as normal distribution or t distribution, and the proper distribution can be selected according to the actual situation. Not only can the linear correlation between sequences be described, but also the nonlinear and asymmetric correlation can be captured. In practical applications, the generator of the real. Archimedean Copula function has the characteristics of simple construction and convenient calculation. As an important branch of Copula function, it can effectively depict the complex nonlinear correlation among multivariate variables in the field of finance. But practical experience shows that when different Archimedean Copula functions are selected, the results are very different. Therefore, how to choose the appropriate Archimedean Copula function to describe the correlation between financial data is very important. In this paper, the binary Archimedean Copula function is taken as the research object, and the Copula distribution function is used as the object of study. A specific distribution function is constructed. The nonparametric estimator tk? A more effective estimate will be based on the TKM? The distance between the two select the appropriate Archimedean Copula function. Empirical analysis shows that the new method can effectively select the binary Archimedean Copula function model. When we measure the correlation between financial sequences, we often choose to establish Copula-GPD model and Copula-GARCH-GPD model, but the two models have some defects. Copula-GPD model does not take into account the conditional heteroscedasticity and volatility aggregation. Both models select a single Copula function to analyze the correlation between sequences, and the results are not comprehensive. This paper attempts to establish a M-Copula-TGARCH-GPD model in which mixed Copula is used to describe the sequence correlation. TGARCH is an asymmetric M-Copula-TGARCH-GPD model which considers the existence of financial sequences. The extreme value theory is used to fit the tail. Empirical analysis shows that M-Copula-TGARCH-GPD model can better reflect the correlation between financial sequences.
【学位授予单位】：西华师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：F224
[Abstract]:With the expansion of the depth of world trade, the economic exchange and cooperation between regions, countries and countries, the trend of economic globalization and integration is becoming more and more obvious, which makes the factors affecting economic development no longer single. The relationship between various factors becomes complicated, so the traditional model based on linear correlation analysis of financial market risk is no longer suitable for increasingly complex economic systems. In the past, when we measured the correlation between financial sequences, we used to assume that their edge distribution is normal distribution or t distribution, so as to reduce the amount of computation. However, such assumptions are often contradicted by the peak and thick tail characteristics of financial data. In order to resolve this contradiction, the emergence of Copula theory provides a new way of thinking for the analysis of financial sequence correlation. The advantages of Copula function are as follows: first, it is possible to study the marginal distribution and joint distribution of variables separately. Moreover, the setting of edge distribution is no longer limited to a few probability distributions such as normal distribution or t distribution, and the proper distribution can be selected according to the actual situation. Not only can the linear correlation between sequences be described, but also the nonlinear and asymmetric correlation can be captured. In practical applications, the generator of the real. Archimedean Copula function has the characteristics of simple construction and convenient calculation. As an important branch of Copula function, it can effectively depict the complex nonlinear correlation among multivariate variables in the field of finance. But practical experience shows that when different Archimedean Copula functions are selected, the results are very different. Therefore, how to choose the appropriate Archimedean Copula function to describe the correlation between financial data is very important. In this paper, the binary Archimedean Copula function is taken as the research object, and the Copula distribution function is used as the object of study. A specific distribution function is constructed. The nonparametric estimator tk? A more effective estimate will be based on the TKM? The distance between the two select the appropriate Archimedean Copula function. Empirical analysis shows that the new method can effectively select the binary Archimedean Copula function model. When we measure the correlation between financial sequences, we often choose to establish Copula-GPD model and Copula-GARCH-GPD model, but the two models have some defects. Copula-GPD model does not take into account the conditional heteroscedasticity and volatility aggregation. Both models select a single Copula function to analyze the correlation between sequences, and the results are not comprehensive. This paper attempts to establish a M-Copula-TGARCH-GPD model in which mixed Copula is used to describe the sequence correlation. TGARCH is an asymmetric M-Copula-TGARCH-GPD model which considers the existence of financial sequences. The extreme value theory is used to fit the tail. Empirical analysis shows that M-Copula-TGARCH-GPD model can better reflect the correlation between financial sequences.
【学位授予单位】：西华师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：F224
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