Nonparametric Approach to Regression Modeling Based on Copula Functions: Application to Bivariate Models

This paper explores a nonparametric approach to regression modeling based on copula functions, which overcomes the limitations of classical linear models. The study analyzes the advantages of the copula approach, including the ability to model complex nonlinear, asymmetric, and tail dependencies, as well as the separation of dependence structure and marginal distributions. The main classes of copulas (elliptical and Archimedean), their properties, and their application in bivariate models are discussed. Special attention is paid to practical examples of copula applications in economics and finance. The advantages of the approach, such as flexibility and universality, are highlighted, along with its limitations related to computational complexity and data quality requirements.