A Copula-Based Regression Framework for Enhanced Prediction under Heteroscedasticity

2026-07-27

AI Summary

This study addresses the limitations of traditional regression methods, which often rely on restrictive assumptions of homoscedasticity and normally distributed residuals, and are prone to retransformation bias when log-transformations are applied. To overcome these issues, the authors propose a Copula-based regression framework that flexibly models the joint distribution of the response and covariates along with their marginal distributions, explicitly capturing heteroscedasticity and asymmetric dependence structures without imposing strong parametric assumptions. This work represents the first systematic application of Copulas to heteroscedastic regression prediction. The proposed method demonstrates substantially improved accuracy: in simulation studies, it achieves an average MAPE of 0.21, outperforming linear and log-linear models by 6%–33% and 24%–57%, respectively; its superior performance is further confirmed on the real-world Wages dataset.

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 approach explicitly accounts for heteroscedasticity without requiring restrictive distributional assumptions. A comprehensive simulation study is conducted under varying dependence levels and heteroscedastic scenarios to compare the performance of the proposed method with usual regression models and log-linear models. 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. Across all simulation settings, the copula-based model reduced prediction errors by approximately 6%-33% relative to the linear model and 24%-57% relative to the log-linear model. A real-data application using the Wages dataset from the ISLR package in R further confirmed these findings, where conventional log-linear models failed to adequately capture heteroscedasticity. In contrast, the proposed copula-based regression framework produced more accurate predictions, demonstrating its effectiveness for modelling heteroscedastic data. Overall, the results demonstrate that copula-based regression represents a viable modelling alternative in the presence of heteroscedasticity and complex dependence structures.

Problem

• heteroscedasticity
• regression
• copula
• variance stabilization
• dependence structure

Innovation

• copula-based regression
• heteroscedasticity
• asymmetric dependence
• variance stabilization
• prediction accuracy