Integrating GOF Tests and Cross Validation for Copula Model Selection.

Abstract

In dependence modeling, choosing the right copula is crucial, as different copula models can yield distinct interpretations of the relationship between variables. However, real-world applications are often constrained by the limitations of existing copula selection methods, which lack consistency and robustness across datasets. The selection methods in the literature that includes goodness-of-fit (GoF) tests and selection criteria, often yield conflicting results, thereby misrepresenting the dependence structure and leading to misleading conclusions. This study developed an integrated copula selection framework that combines GOF tests with cross-validation techniques. We integrated block-based cross-validation with GoF tests, where data was partitioned into blocks of different sizes. A copula was fitted on the training set, and its performance was validated on the test set using GoF measures. The selection process was repeated across multiple folds, and an aggregation method was applied to determine the most suitable copula. The approach was tested through Monte Carlo simulations and an empirical study was tested on weather variables in Kenya. The findings show that Kendall-based Kolmogorov Smirnov (KendallKS) and Cramrvon Mises (KendallCvM) test statistics integrated with stratified cross-validation, when, perform better when the Benjamini Hochberg (BH) procedure was used for aggregation. The proposed tests successfully identified the true copula and consistently rejected incorrect alternatives, with performance improving as sample size and dependence level increased. The empirical application further demonstrates the methods robustness in real-world settings. These findings demonstrate that the proposed approach enhances the reliability and stability of copula selection.