The Selection And Estimate Of Copulas

In the recent years ,the use of copulas has grown extremely fast and extensive,especially in financial domain. The copula theory provides a new point of view which we study the multivariate distributions, it reduces the choice of the best multivariate distributions into two steps: choose the optimal margins, and then choose the optimal copula. In this article we mostly disscuss how to choose and estimate copula. Considering any distribution function follows uniform distribution on [0,1],we ignore exactly margins and focus on discussing the choice of copula and estimating copula on [0,1]. In this article, the first chapter summarizes the application of copula. The second chapter introduces the copula theory by the numbers and emphasesis on introducing several copulas used in this article and how to create random variables based on copulas. The third chapter discusses several simple methods to choose the right copula family in detail when we know the samples come from which copulas. The fourth chapter gives a double kernel estimate of the copula in a general way and proves its strong consistency. The last chapter simulates the double kernel estimate and tests it byχ2 testing. And the result turns out that the estimate we give in this article is a good approach to copulas.