Research On Change-point Detection Of Copula Model

The Copula model connects the joint distribution with their marginal distributions,known as the link function.Although it orgins recently,because of its excellent characteristics,Copula quickly gained wide attention and rapidly developed at home and abroad.It has been applicated in the financial,medical,quality engineering and other fields.Especially in the financial market under the influence of internationalization and diversification,Copula model overcame the shortcomings of traditional tools to better describe the correlation characteristics of the nonlinear,asymmetric and tail dependence.The emergence of Copula model for studying the dependency of scholars also provides special contribution,which prompted Copulas' theory development and practical application of the model.From a formal perspective,Copula functions developed from two dimension to multivariate,and static Copula to dynamic Copula.For the original view,Copula function evolved a single Copula model into the mixed Copula model.The research content of Copula consist of model selection,parameter estimation and goodness of fit.From the perspective of research methods,the main method of parameter estimation,non-parametric estimation and Bayesian estimation methods.At present,research on the Copula model is mainly focused on the static Copula model and the parameter method.The dynamic Copula model takes into account the volatility contagion mechanism of financial variables,so the dynamic Copula model can better depict the structure of financial markets between inside and outside.Variable structure Copula and time-varying Copula model are belong to the dynamic Copula model.Empirical likelihood non-parametric method by Owen(1988),due to its excellent properties,is widely used in various disciplines and fields.This paper uses the empirical likelihood method to analysis of change point detection of the variable structure Copula model under certain assumptions and constraints.The asymptotic distribution of the test statistics,which detect change points,and large sample properties are proved.Finally,by a simulation the non-parametric empirical likelihood method in the paper is verified.The main contents of this paper can be summarized the following points.First,we summarize the research status,background and significance of variable structure Copula model,and puts forward the research methods and content of this paper.Second,we base on the empirical likelihood method,construct the corresponding test statistic and prove the asymptotic distribution and large sample properties,last do a stochastic simulation and illustrate the rationality and feasibility of this method.Third,using the empirical likelihood method to detect multiple change points,which exist in the Copula model.The corresponding test statistic is given and the asymptotic distribution and large sample properties also are proved.we also conduct a random simulation and illustrate the validity and feasibility of this method.Fourth,to summarize the paper,put forward the advantages and disadvantages of the paper,and the future research direction of variable structure Copula model is prospected.