A0288
Title: Model selection tests for truncated vine copulas under nested hypotheses
Authors: Ichiro Nishi - The Graduate University for Advanced Studies (Japan) [presenting]
Yoshinori Kawasaki - The Institute of Statistical Mathematics (Japan)
Abstract: Vine copulas 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 the 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. Vuong's model selection tests are systematically applied to distinguish competing models of truncated vine copulas under both nested and strictly non-nested hypotheses (Vuong-N and Vuong-SNN tests, respectively). Through extensive simulation studies, the performance of the Vuong-N and Vuong-SNN tests is evaluated using p-values, the number of rejections, and mean empirical KLIC. The results reveal that the relative performance of each test is sensitive to the strength of dependencies within the vine structure. In scenarios with weaker pairwise dependencies, the Vuong-N test produced lower p-values and higher rejection rates, along with improved mean empirical KLIC. Conversely, when the dependencies are stronger, the Vuong-SNN test yielded valid and often superior model distinctions, demonstrating that strictly non-nested testing, despite its heuristic status, remains an informative approach in such settings.
