This paper firstly summarizes Copula theory and its modeling method systematically. Subsequently, the graph theory is introduced in order to shed some light on modeling multivariable dependence structure which also provides the possibility for the multiple variables grouping decomposition. Finally, the application in multivariable financial series analysis is investigated. In the analysis of the four financial series, not only the bivariate series dependence is studied, but also the dependence structure of four variables is modeled using vines method, so the advantage of vine method of graph theory in multivariable dependence structure modeling can be proved.The key points and main achievements of this work are listed as follow:(1) This paper summarizes Copula theory and its modeling method systematically. It introduces Copula's concept and property, conditional Copula general form, the relevant indexes which are derived by Copula theory and the parameter estimation in Copula modeling.(2) The graph theory is introduced to provide a new way of multivariable dependence structure modeling which also create an algorithm to solve the positive problem when modeling multivariable dependence structure, and studies the decomposition of the multiple joint distributions using vines. Combining Copula theory with vine theory, this paper innovatively constructs a multivariable dependence structure, with the vine's iterative structure layer upon layer. Furthermore, the feasibility of multiple variables grouping decomposition using vines method is discussed. At the same time, the method of parameter estimation in Copula-vine modeling is shown. Besides, relevant information is introduced, which is used for interpreting the vine description of dependence structure.(3) Copula and vine theory are innovatively applied in finance field. The paper chooses the four exchange rate data as sample series. Basic statistics of the sample are calculated firstly, and then GARCH model is constructed. The dependence structure between bivariate series is analyzed using Copula function, and the fitting results of different Copulas are investigated. At last, dependence model of the four variants is constructed using vines, which compares with Gaussian Copula multivariable dependence model. Then the Copula-vine model is improved. The improved model not only chooses different Copulas in the same vine, but also tries to choose different vines, and then compare with the former model by fitting test. The process not only shows the validity of multivariable dependence structure modeling with vines theory, but also shows the agility of vine structure by choosing different Copula function on every layer and changing different vine structure. |