Copula Selection via Cross-Validation: A Simulation Study

Abstract

This article presents a methodology for modeling the association between continuous random variables using copula functions. Copulas allow for the separation of the dependence structure from the marginal behavior, offering a flexible approach to model complex relationships between variables. Through simulations for different marginal distributions (normal, log-normal, t-Student, weibull), two families of copulas were evaluated, namely elliptical and Archimedean copulas. Model selection was performed using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), as well as graphical methods (Chi-plot and K-plot). In addition, K-Fold cross-validation was employed to evaluate the performance of the selected models and prevent overfitting. The results suggest that elliptical copulas are more suitable for symmetric data, while Archimedean copulas show a better fit for asymmetric distributions. Cross-validation provided a more accurate estimate of prediction error, enhancing the robustness of the selected models.