The Copula-GARCH model has a wide range of applications in economics and finance. It was first developed to measure the statistical dependency between different markets (with non-Gaussian financial returns) interacting on a global scale. The original paper can be found on the primary author's web page:
The MATLAB Statistics Toolbox contains functions for generating Copula distributions whereas the Econometrics Toolbox contains a function that generates GARCH models. It is not trivial to combine these two models to obtain a Copula-GARCH model. There are implementations for Copula-GARCH models on MATLAB Central. However, they require both the Statistics and Econometrics Toolboxes. The following link contains one such implementation:
