Calibrating simplified vine copulas with a noise contrastive estimation approach

Abstract

Vine copulas provide a flexible framework for modeling complex multivariate dependence structures using only bivariate building blocks. Their practical success relies heavily on the simplifying assumption, which restricts conditional pair copulas to be independent of the specific conditioning values. While this assumption greatly facilitates estimation, it may lead to model misspecification in applications with pronounced varying conditional dependence. We propose a novel calibration strategy for simplified vine copula models based on observation-specific correction factors. These factors are derived using noise contrastive estimation (NCE), a supervised learning technique for density estimation that reframes the problem as a binary classification task with an easily sampled noise distribution. Treating the fitted simplified vine copula as the noise model, the NCE approach yields corrected log-likelihood estimates for individual observations, thereby locally adjusting the simplified vine toward the underlying data-generating dependence structure. Simulation studies demonstrate that the proposed calibration provides sensible and effective adjustments, improving model accuracy when the simplifying assumption is violated while remaining neutral when the simplified model is adequate. Two real-data applications further illustrate the practical benefits of the method. The results highlight NCE-based calibration as a promising tool to enhance simplified vine copula models without abandoning their computational tractability.