Copula Function And Its Application

Nothing can be existed in isolation, so, It is important to analyse therelationships between them. As a tool of multivariate statistic andcorrelation analysis, the Copula function plays an important part incorrelation analysis.For the sake of simplicity, I take bivariate Copula function as anexample and try to do much work of the following aspects in this paper.1. Usually, we can use the maximum likelihood estimation methodand moment estimation method to estimate the Copula function’sparameters. But, Moment estimation in seeking the function ofmultidimensional variables is very difficult, in this paper; I will introducea one-dimensional model to make the complex question simplified.2. Commonly, when we estimate the Copula function’s parameters,we always presuppose the marginal distributions of the Copula functionobey a specified distribution, and then use the maximum likelihoodestimation method to seek parameter values. But in fact, when we use acopula function to solve the financial problems, its marginal distributionsthat we can not be accurately determined in advance. So the usual method for Copula’s parameter estimation is obviously inadequate. For thesereasons, Chapter Ⅲ has used the non-parametric kernel density.3. A single Copula function can only reflect the correlation amongfinancial markets indirectly. If we want to fully understand the relatedstructures among financial markets, it is very necessary to construct amore flexible Copula function——mixed Copula model. Mixed Copulafunction has many excellent properties that a single Copula function doesnot have, and it not only highlights the characteristics of a singlecomponent Copula function，it also covers the mixed characteristics ofthese component Copula functions. The linear combination of Clayton、Gumbel and Frank Copula function is used to construct mixed Copulafunction. The synthesis method based on BMA is easy to make.4. In the United States, the law of government procurement isestablished earlier, so the government procurement’s structure is morereasonable. I analyse the correlation between the GDP and thegovernment spending.Finally, we summarize and analyze the work of this paper, and showthe topic of further study.