Pair-Copula自回归模型及其在股票指数中的应用

发布时间：2018-01-06 13:11

本文关键词：Pair-Copula自回归模型及其在股票指数中的应用　出处：《吉林大学》2017年硕士论文　论文类型：学位论文

更多相关文章： Pair-Copula Construction 藤 COPAR

【摘要】：Copula不受边缘分布选择的限制,可以灵活地构造多元分布,被应用在越来越多的领域中.本文回顾和总结了与Copula相关的基础理论,引入了藤结构Copula模型.特别地,详细地介绍了以C藤和D藤为代表的藤结构Copula模型.在分解多元函数时,藤为二元Copula的选择提供了一定的依据.利用Pair-Copula构造多元变量的密度函数时,多元数据间复杂的相关性可以通过二元Copula刻画出来.在金融和经济等领域中,对于多元时间序列的分析是一种常见的问题,传统的分析工具是向量自回归(Vector Autoregreesion,简称VAR)模型,但VAR模型仅限于反映序列间线性相关和对称相关性.而接下来介绍的基于D藤定义的Copula自回归(Copula Autoregression,简称COPAR)模型能够更好的刻画多元时间序列间的相关性,尤其是在研究一个时间序列对于另一个时间序列的影响时非常有效,并且给出了相应的Copula矩阵以及拓展到高维的方法.在这个模型的基础上,我们提出了一个基于C藤的新的COPAR模型,该模型也能够拓展到任意维且能够预测未来值.文章的最后利用Copula基础理论来研究美国与亚洲、澳洲和欧洲主要国家股票指数同比变化率,并利用R软件中的函数分析数据关系、选择二元Copula和估计相关Copula参数,得出美国与各国之间股票指数同比变化率的相关关系。
[Abstract]:Copula can construct multivariate distribution flexibly and can be used in more and more fields. The basic theories related to Copula are reviewed and summarized in this paper. In this paper, Copula model of rattan structure is introduced. In particular, the Copula model of rattan structure, represented by C and D vines, is introduced in detail. Rattan provides a basis for the selection of binary Copula. Using Pair-Copula to construct the density function of multivariate variables. The complex correlation between multivariate data can be described by binary Copula. In the fields of finance and economy, the analysis of multivariate time series is a common problem. The traditional analysis tool is vector autoregressive vector autoregressive (VAR) model. But the VAR model is limited to reflect the linear correlation and symmetric correlation between sequences. Then the Copula autoregressive model based on the definition of D-rattan is presented. Copula Autoregression. COPAR) model can better describe the correlation between multivariate time series, especially in the study of the influence of one time series on another time series is very effective. The corresponding Copula matrix and the method to extend to high dimension are given. On the basis of this model, we propose a new COPAR model based on C-tene. The model can also be extended to arbitrary dimensions and can predict future values. Finally, the paper uses Copula basic theory to study the rate of stock index change in major countries of the United States and Asia, Australia and Europe. Using the function in R software to analyze the data relationship, select binary Copula and estimate the relevant Copula parameters, and obtain the correlation relationship between the stock index change rate of the United States and other countries.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F831.51

【参考文献】