Pair-Copula Autoregressive Model And Its Application In The Stock Index

Copula,which can be used to construct multivariate distribution flexibly without restriction of marginal selection,has been applied in various fields.This paper reviews and summarizes the related basic theory of Copula,and introduces the Vine Copula.In particular,C Vine and D Vine are introduced in details.When decomposing the multivariate density function,the Vine provide the basic theory to choose bivariate Copulas.By using the Pair-Copula construct the probability density function of multiple variables,the complicated correlation among multiple data can be modeled easily.The analysis of multivariate time series is a common problem in areas like finance and economics.The classical tools are Vector Autoregression(VAR)models.But the VAR models are limited to linear and symmetry dependence among series.Next,we introduces a Copula Autoregression(COPAR)model which is based on D Vine.This model allows us to model non-linear dependence among multiple time series.It is especially useful to explore the influence of one time series onto another.This model can be extended to arbitrary number of time series and can be easily used to forecast.And on the basis of this model,we define a new COPAR model based on C Vine.This model also can be extended to arbitrary number of time series.The nature of the two models are similar.By the end of the article,we use basic theory of copula to study American,Asia,Australia and Europe's major countries' stock index rate of change,and by using the functions in R software,we could analyze the data,select bivariate copulas and estimate copulas' parameters,then finally get the dependence between American and other countries.