A Copula-Based Regression Framework for Enhanced Prediction under Heteroscedasticity

Abstract

Classical regression approaches, including ordinary least squares, rely on strong assumptions such as constant variance and normality of residuals, which are often violated in real-world data. Although log-transformation is commonly used to stabilise variance, it may introduce re-transformation bias and fail to address heteroscedasticity and asymmetric dependence structures adequately. To overcome these limitations, this study proposes a copula-based regression framework for modelling data in the presence of heteroscedastic error structures. The proposed copula-based regression framework separates marginal distributions of the response and explanatory variables from their dependence structure, allowing flexible modelling of different tail-dependent relationships. The proposed approach explicitly accounts for heteroscedasticity without requiring restrictive distributional assumptions. A comprehensive simulation study and two real-world applications were considered under heteroscedastic scenarios to compare the performance of the proposed method with existing methods. The simulation results demonstrated that the proposed copula-based model consistently outperformed conventional approaches, achieving an average mean absolute percentage error of 0.21, compared with 0.27 and 0.36 for the linear and log-linear models, respectively. In the first application, which exhibited clear heteroscedasticity, the copula-based model achieved the lowest MAPE, although the overall differences between the copula-based and GAMLSS models were not substantial. In Application 2, all models achieved low predictive performance, as there was a moderate linear relationship between the response and predictor variables. Overall, the findings indicate that no single model consistently dominates across all settings, while copula-based regression provides a flexible and competitive alternative for heteroscedastic data.