Vine copulas, constructed using bivariate copulas as building blocks, provide a flexible framework for modeling high-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 topological 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. By clarifying the differences between the results and exploring their practical implications, we enhance the precision of truncation selection and contribute to the development of more effective methodologies in vine copula modeling.

翻译：藤Copula以二元Copula为基本构建单元，为高维依赖关系建模提供了灵活框架。然而，这种灵活性伴随着维度增长而迅速增加的复杂性，需要通过适当的截断处理来应对这一挑战。虽然已有研究提出使用Vuong模型选择检验作为确定最优截断水平的方法，但其在藤Copula中的应用仍处于启发式阶段，且仅假设严格非嵌套假设。这一假设与截断藤Copula结构固有的拓扑嵌套特性存在矛盾。本文系统应用Vuong模型选择检验，在嵌套与严格非嵌套假设下区分截断藤Copula的竞争模型。通过厘清检验结果的差异并探讨其实际意义，我们提升了截断选择的精确性，为发展更有效的藤Copula建模方法论作出贡献。