Multivariate Vine Copula Regression: Theoretical Foundations and Assumptions
( Pp. 163-169)

This paper develops a theoretical framework for regression analysis within a multivariate vine copula model. In contrast to classical parametric approaches that rely on a fixed functional form of the regression relationship and impose restrictive assumptions on the error structure, the proposed methodology interprets regression as the recovery of the conditional distribution of an endogenous variable given fixed values of exogenous factors. The study focuses on formalizing the procedure for constructing vine copula regression models, including the estimation of marginal distributions, the selection of an appropriate vine structure, and the reconstruction of the joint probability density function. It is shown that regression estimates can be obtained in the form of various functionals of the conditional distribution, such as the conditional mean, mode, and quantiles, which provides a high degree of flexibility and adaptability. The key advantages of the approach are discussed, including robustness to multicollinearity, the absence of normality and linearity assumptions, and stability in the presence of outliers and asymmetric distributions. Particular attention is paid to methodological limitations related to the continuity of marginal distributions and potential nonstationarity of dependencies over time, as well as to possible ways of addressing these issues. The results provide a theoretical foundation for the application of vine copula regression in the analysis and forecasting of complex multivariate dependencies.

Bachaev, U.A. (2026). Multivariate Vine Copula Regression: Theoretical Foundations and Assumptions. Economic Problems and Legal Practice, 22(1), 163-169. DOI: 10.33693/2541-8025-2026-22-1-163-169. EDN: FSLTHF

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multivariate regression, copula functions, vine-copulas, nonparametric regression, conditional distribution..