Abstract: The development of copulas resolves the problem of description of dependence patterns,and it is a practicable method to construct multivariate probability distribution function.Because of the difficulty in approximation of mufti-dimensional copula,we study the modeling on dependence patterns of markets firstly with a mufti parametric linear regression framework equipped with the Bernstein polynomial expansion to the mufti-dimensional copula and estimate it with empirical data of Shanghai&Shenzhen Stock Market Comprising Indexes filtered with GARCH.Our result shows that.it is a feasible approach to describing the dependence patterns with the polynomial approximation.

Key words: polynomial copula, bernstein copula, dependence pattern, hebyshev polynomial