Copula模型的变结构点检测研究

发布时间：2018-05-06 01:21

本文选题：Copula模型 + 变结构Copula模型　；参考：《浙江财经大学》2017年硕士论文

【摘要】：Copula模型因将联合分布与它们各自的边缘分布连接在一起,被人们称为连接函数,虽然起源较晚,但由于具有优良的特质,迅速在国内外得到了广泛的关注和快速的发展,并应用于金融、医学、质量工程等若干领域.特别在国际化与多元化发展影响下的金融市场,Copula模型克服了传统相关性工具的缺点,更好地描述了金融市场内外间呈现出的非线性、非对称和尾部相关特征.Copula模型的出现为研究相依性的学者也提供了特别的贡献,从而也促使了Copula模型的理论发展和实际应用.从形式上,由最初的二元Copula函数到多元Copula函数,由单一Copula模型到混合Copula模型,从静态Copula模型到动态Copula模型.从研究内容,包含模型选择、参数估计和拟合优度检验等,以及研究方法的参数估计方法,非参数估计方法和贝叶斯估计方法等方面都有了快速的发展.目前,关于Copula模型的理论研究主要集中在静态Copula模型、半参数及参数方法上.而动态Copula模型考虑了金融变量的波动传染机制,因此动态Copula模型可更好地刻画金融市场内外间的变结构相关关系.动态Copula模型可分为变结构Copula模型和时变Copula模型.本文基于非参数方法对变结构Copula模型进行变点检测分析研究.经验似然非参数方法由Owen(1988)提出,由于其优良性质,被广泛应用于各个学科及领域.本文在一定的假设条件与约束条件下,构造了检测Copula模型中的变结构点的经验似然比检验统计量,且给出了相应的渐近分布特征与大样本性质的证明,最后,通过相应的随机模拟和一个实证分析对本文提出的非参数经验似然方法进行验证.本文的主要研究内容可以归纳为以下几点:1.归纳总结变结构Copula模型的研究现状、背景及研究意义,提出本文的研究方法及研究内容.2.采用经验似然方法检测Copula模型中存在单一变结构点,构造相应的检验统计量,给出渐近分布和大样本性质的证明,最后进行了随机模拟与实例说明该方法的合理性与可行性.3.采用经验似然方法研究Copula模型中存在多个变结构点的情况,构造相应的检验统计量,给出渐近分布和大样本性质的证明,最后进行了随机模拟与实例分析来说明该方法的适用性与可行性.4.对论文进行总结概括,提出了论文中存在的优缺点,并对未来变结构Copula模型研究的发展方向进行了展望.
[Abstract]:The Copula model is called join function because it connects the joint distribution with their respective edge distribution. Although the origin is late, because of its excellent characteristics, it has been widely concerned and developed rapidly at home and abroad. And applied to finance, medicine, quality engineering and other fields. Especially under the influence of internationalization and diversification, the Copula model of financial markets overcomes the shortcomings of traditional correlation tools and better describes the nonlinearity in and out of financial markets. The emergence of asymmetric and tail-dependent characteristics. Copula model also provides a special contribution to the study of dependence of scholars, which also promotes the theoretical development and practical application of Copula model. Formally, from the initial binary Copula function to the multivariate Copula function, from the single Copula model to the hybrid Copula model, from the static Copula model to the dynamic Copula model. The research contents, including model selection, parameter estimation and goodness of fit test, as well as parameter estimation methods, non-parametric estimation methods and Bayesian estimation methods, have been developed rapidly. At present, the theoretical research on Copula model is mainly focused on static Copula model, semi-parameter and parametric method. The dynamic Copula model considers the volatility contagion mechanism of the financial variables, so the dynamic Copula model can better describe the variable structure correlation between the financial market and the outside. The dynamic Copula model can be divided into variable structure Copula model and time-varying Copula model. In this paper, the variable point detection of variable structure Copula model is studied based on nonparametric method. Empirical likelihood nonparametric method was proposed by Owenn 1988. It is widely used in various disciplines and fields because of its excellent properties. In this paper, under certain assumptions and constraints, empirical likelihood ratio test statistics for detecting variable structure points in Copula model are constructed, and the corresponding asymptotic distribution characteristics and properties of large samples are proved. The non-parametric empirical likelihood method proposed in this paper is verified by the corresponding stochastic simulation and an empirical analysis. The main contents of this paper can be summarized as follows: 1. The research status, background and significance of variable structure Copula model are summarized, and the research methods and contents of this paper are put forward. The empirical likelihood method is used to detect the existence of a single variable structure point in the Copula model. The corresponding test statistics are constructed, and the asymptotic distribution and the properties of large samples are proved. Finally, a stochastic simulation and an example are carried out to illustrate the rationality and feasibility of the method. The empirical likelihood method is used to study the existence of multiple variable structure points in the Copula model. The corresponding test statistics are constructed, and the asymptotic distribution and the properties of large samples are proved. Finally, random simulation and example analysis are carried out to illustrate the applicability and feasibility of the method. In this paper, the advantages and disadvantages of this paper are summarized, and the future research direction of variable structure Copula model is prospected.
【学位授予单位】：浙江财经大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F831.5

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