Using Copulas in Statistical Models of Switching Regimes

By a theorem due to Sklar, a multivariate distribution can be represented in terms of its underlying margins by binding them together using a copula function. By exploiting this representation, the “copula approach” to statistical modelling proceeds by specifying distributions for each margin and a copula function. In this paper, a number of families of copula functions are given, with attention focusing on those that fall within the Archimedean class. Members of this class of copulas are rich in various distributional attributes that are desired when modelling. The paper then proceeds by applying the copula approach to construct statistical models for the Roy model of switching regimes. When models are constructed using copulas from the Archimedean class, the resulting expressions for the log-likelihood and score facilitate maximum likelihood estimation. The literature on sample selection models is almost exclusively based on multivariate normal specifications. The copula approach permits modelling based on multivariate non-normality.