A Comparison of Python Based Copula Parameters Estimation for Archimedean-based Asymmetric Copulas

Abstract

Estimating copula parameters remains a challenge when dealing with multiple correlated variables. Focused studies on the application of uncommon copula functions are also still scarce. Asymmetric dependence is necessary to be taken into account as symmetric dependence may not always be sufficient to model real data dependence. Asymmetric copulas were constructed using the Archimedean family as the basis copula. Linear inversion, random search, and Particle Swarm Optimization (PSO) were used to compare the estimations of copula parameters. Python was used as the main programming software to apply the proposed methods in this paper. From the comparison, linear inversion resulted in 1% of average absolute relative error while PSO and random search resulted in 4% and 19%, respectively. A different result was shown using a real data set. Real data often deal with local extreme values while performing the simulation. PSO was more stable than others when real data were used. It was concluded that PSO is the wisest method for real data cases and asymmetric copula parameter estimation.