Compute the Bayesian information criterion (BIC) \(\mathrm{BIC}_\mathbf{C}\) (Chen and Guo, 2019, p. 29), which is computed using mean square error \(\mathrm{MSE}_\mathbf{C}\) as
$$\mathrm{MSE}_\mathbf{C} = \frac{1}{n}\sum_{i=1}^n \bigl(\mathbf{C}_n(u_i,v_i) - \mathbf{C}_{\Theta_m}(u_i, v_i)\bigr)^2\mbox{ and}$$ $$\mathrm{BIC}_\mathbf{C} = m\log(n) + n\log(\mathrm{MSE}_\mathbf{C})\mbox{,}$$
where \(\mathbf{C}_n(u_i,v_i)\) is the empirical copula (empirical joint probability) for the \(i\)th observation, \(\mathbf{C}_{\Theta_m}(u_i, v_i)\) is the fitted copula having \(m\) parameters in \(\Theta\). The \(\mathbf{C}_n(u_i,v_i)\) comes from EMPIRcop. The \(\mathrm{BIC}_\mathbf{C}\) is in effect saying that the best copula will have its joint probabilities plotting on a 1:1 line with the empirical joint probabilities, which is an \(\mathrm{BIC}_\mathbf{C} = -\infty\). From the \(\mathrm{MSE}_\mathbf{C}\) shown above, the root mean square error rmseCOP and Akaike information criterion (AIC) aicCOP can be computed. These goodness-of-fits can assist in deciding on one copula favorability over another, and another goodness-of-fit using the absolute differences between \(\mathbf{C}_n(u,v)\) and \(\mathbf{C}_{\Theta_m}(u, v)\) is found under statTn.
bicCOP(u, v=NULL, cop=NULL, para=NULL, m=NA, ...)The value for \(\mathrm{BIC}_\mathbf{C}\) is returned.
Chen, Lu, and Guo, Shenglian, 2019, Copulas and its application in hydrology and water resources: Springer Nature, Singapore, ISBN 978--981--13--0574--0.
EMPIRcop, aicCOP, rmseCOP