Unconstrained Cholesky-based parametrization of correlation matrices

Parameter estimation is relatively complicated for models containing correlation matrices, because the elements of correlation matrices are heavily constrained. We put forward a Cholesky-based parametrization that is easy to implement and allows for unconstrained parameter estimation. To compare the new parametrization with the commonly applied spherical parametrization, we use Monte Carlo simulation in which we estimate multivariate distributions containing Gaussian copulas. We show that the new parametrization performs well, in particular as the dimensionality of the multivariate distribution increases, computing times increase, and non-convergence occurs increasingly often.