Construction Of A Class Of Copula Function Family And Its Application

Archimedes Copula,as a kind of Copula function family with excellent properties,has been widely used in many fields because of its simple construction,easy calculation and easy application.Copula function can be used to construct multivariable models,such as Copula-ARMA model,Copula-ARCH model,Copula-GARCH model,Copula-SV model and a series of models can be used to describe financial data,analyze the possible relationship between the data,and select the optimal model to capture the correlation and characteristics between financial markets.At present,the research focuses more on the combination of Copula function and GARCH model,whose advantage lies in its ability to accurately capture the characteristics of financial time series.It is precisely because of the characteristics of financial data,such as fluctuation over time,fluctuation aggregation,sharp peak and thick tail,and asymmetry,that the research has more realistic significance.Based on Archimedes Copula function,this paper studies its construction method and uses its construction model to depict financial data.The main work is as follows.(1)Based on the existing methods of constructing the generator of Laplace transform,the method of constructing Archimedean Copula generator is extended to two-dimensional and even multidimensional dimensions.Not only the probability density function can be extended to multidimensional level,but also the non-negative continuous function in the range of real numbers can be extended to multidimensional level.Finally,it is extended to the new method of constructing Archimedean Copula generator with two parameters.(2)The Archimedean Copula-EGARCH hybrid model is constructed to study and analyze the relationship between Shanghai Composite Index and GEM Index and SME Index in China's financial market,as well as the relationship between Shenzhen Index and GEM Index and SME Index.By using the EGARCH-t model to construct the edge distribution of Copula function,it is found that there is leverage between the index returns of GEM,SME and SSE,and the index returns of Shenzhen Stock Exchange,that is,the impact of negative shocks on future fluctuations is greater than the impact of positive shocks.The function with better fitting degree was selected from Archimedean Copula function by the square Euclidean distance method,and then the relationship between them was judged according to the tail dependence.(3)Matlab and Eviews tools are used to model the daily returns of Shanghai Composite Index,Shenzhen Component Index,Growth Enterprise Index and Small and Medium Board Index from June 1 to June 28,2015.Through new build Archimedean Copula-EGARCH model inspection found that the GEM and the SME positively correlated relationship with the Shanghai Composite Index and Shenzhen Component Index,respectively,but when the Shanghai and Shenzhen index fall has bigger impact on SME and GEM,at the same time compared with the Shanghai index relationship,to the end of the GEM,SME and the Shenzhen index with thicker tail relations,namely the Shenzhen's greater influence on the GEM,SME.