Multivariate bilateral gamma, copulas, CoSkews and CoKurtosis

Correlation graphs are introduced to delineate the levels observed in data and models for return and squared return correlations. A sample of 2048 representative pairs of equity assets is selected from a possible collection of 381, 501 pairs by quantization. Five copulas are estimated and simulated on these pairs of returns, the Gaussian, t-copula, Clayton, Gumbel and Frank. Additionally, the multivariate bilateral gamma (MBG) model that introduces dependence via common time changes is also fit and simulated. Results of fit statistics on returns, CoSkew and CoKurtosis pairs are reported. The general ordering of the models is MBG, t-copula, followed by the Gaussian, Frank, Gumbel and Clayton copulas.