Copulas are functional forms that parameterize the joint distribution of random variables based on their stated marginal distributions and a dependence parameter. The approach is based on Sklar’s theorem. Copulas provide a general method for modelling dependence between random variables that may exhibit asymmetric dependence, which is often inadequately captured by measures of linear dependence. Copulas are often generated by using mixtures and convex sums. Although a bivariate distribution is the most commonly encountered specification, higher dimensional joint distributions can also be generated.
KeywordsClayton copula Copulas Cumulative distribution functions GARCH effects Gaussian copula Gumbel copula Marginal distributions Selection models Sklar, A. Sklar’s theorem Tail dependence
JEL ClassificationsC1; C51
- Sklar, A. 1973. Random variables, joint distributions, and copulas. Kybernetica 9: 449–460.Google Scholar
- Sklar, A. 1996. Random variables, distribution functions, and copulas – a personal look backward and forward. In Distributions with fixed marginals and related topics, ed. L. Ruschendorf, B. Schweizer, and M. Taylor. Hayward: Institute of Mathematic Statistics.Google Scholar