The Part Time-varying M-Copula Model Based On Vine Structure

In recent years Pair-Copula model based on Vine structure has been widely used in Multi-Asset Portfolio correlation analysis and prediction.Compared with the multiple copula function,Pair-Copula decompose multivariate distribution function into a series of Pair-Copula modules,which can effectively capture the differences of tail dependence among different risk factors in the Multi-Asset Portfolio,then the dependence structure between the assets can be described more accurately,as well as the model will be more flexible and effective.So the key and difficult points of the Pair-Copula model is to select copula function for each Pair-Copula and estimate its parameters.For a Pair-Copula model based on Vine structure,there are d(d-1)/2Pair-Copula need to be specified.Therefore based on the pair-copula model and combined the characteristic that the dependence structure between the variables will change over time,we proposed time-varying mixed Copula(Time-varying M-Copula)as Pair-Copula in this paper,to avoid error-prone need of Pair-Copula selected and parameter estimation,reducing model risk,making Pair-Copula choice flexible and easy to operate.Meanwhile,based on the existing EM algorithm which is used to solve parameters in M-Copula,in this paper we propose using EM algorithm to solve parameter in time-varying mixed Pair-Copula.Finally,to reduce the complexity of parameters and improve the performance of the model,based on the vine structure the global time-varying mixed Copula(time-varying M-Copula)model is replaced by based on the vine structure the global mixed and part time-varying copula(part time-varying M-Copula)model.In empirical study,by using M-Copula,time-varying M-Copula and part time-varying M-Copula as Pair-Copula to constructed vine model with a given sample data and comparing the value of AIC and BIC,we can find that based on the vine structure part time-varying M-Copula model describes data structure more comprehensive.