Model selection tests for truncated vine copulas under nested hypotheses

Abstract: Vine copulas, constructed using bivariate copulas as building blocks, provide a flexible framework for modeling multi-dimensional dependencies. However, this flexibility is accompanied by rapidly increasing complexity as dimensionality grows, necessitating appropriate truncation to manage this challenge. While use of Vuong's model selection test has been proposed as a method to determine the optimal truncation level, its application to vine copulas has been heuristic, assuming only strictly non-nested hypotheses. This assumption conflicts with the inherent nesting within truncated vine copula structures. In this paper, we systematically apply Vuong's model selection tests to distinguish competing models of truncated vine copulas under both nested and strictly non-nested hypotheses. Through extensive simulation studies, we characterize the conditions under which the nested hypotheses provide improved discernibility and demonstrate that the strictly non-nested framework can still yield valid distinctions in certain settings. This broader perspective on model comparison contributes to both methodological clarity and practical guidance for vine copula truncation.