Mix Copula Model Selection Strategy And Its Application In The Dependence Analysis

In the dependence analysis, the traditional linear dependence coefficient is a rough characterization, it is based on multivariate normal distribution assumption, only can describe linear, symmetrical related structures, while Copula theory is applied to the dependence analysis, we can not only describe dependence from multi-angle in all directions such as quadrant dependent, stochastically increasing and tail dependence, but also make use of split characteristic of the Copula function to construct nonlinear, asymmetric and different tail behavior dependence mode, which will be a more detailed, more accurate measure of the complex multivariate structure. In addition, under strictly increasing transformation Copula function remains invariant, so the dependence measures based on it are not changed, thus Copula theory has been widely applied in the dependence analysis.When solving Copula model, there are completely likelihood function method and two-stage estimation method, regardless of which method we will need likelihood inference, therefore this paper studies some properties of maximum likelihood estimation firstly, and then discusses the solution and evaluation of a Mix Copula model as an example. Aiming at the limitations caused by similarity and great commonality as most of literature select from Archimedes Copula family, this paper proposes a mixed Copula model selection strategy from Copula functions which expands the range of selection and increases the ellipse family as an alternative, that is, combines frequency histogram with AIC value of a single Copula function to determine the Copula functions which form a mixed Copula model, as a result the EM-BFGS algorithm is introduced to solve the model, and finally makes use of goodness of fit test and AIC values for model evaluation.Finally we apply this method to wind power dependence analysis and Shanghai A-share, B-share dependence analysis, comparing with the traditional Mix Copula model which consists of Archimedes Copula family, the Mix Copula model of optimum strategy which is composed of Copula functions selected from ellipse family and Archimedes Copula family has a smaller AIC value and a better fitting effect, thus demonstrates the effectiveness of this method.