Pruning and Truncating the Mixture R‐Vine Model Using the Mixture Weight

Vine copula mixture models are highly flexible and can handle complex hidden dependencies among variables without restricting the parametric shape of the margins or the type of dependency structure. But it loses flexibility as the number of dimensions increases. That is due to two main reasons. First, both the number of mixture components and the type of copulas (mixture components) need to be estimated. With the various kinds of copulas, each can model a specific type of dependence; the individual choice of each element is challenging. Second, as the dimension increases, the number of parameters to be estimated will grow dramatically, making the truncation of the mixture model a critical step. However, selecting the optimal level of truncation is also not straightforward. Therefore, the selection strategy for truncation or pruning in mixture copula models is a complex step and remains a significant research gap. In this paper, we use the mixture weight as a criterion to determine the truncation level and to prune pairs of variables in the mixture vine copula model. The simulation results and real‐data applications illustrate the performance of the new method. In simulation studies, the proposed method, using the mixture weight, outperforms the traditional model even with small sample sizes. In two of three simulation scenarios, the proposed model correctly identifies the optimal truncation levels. In contrast, the conventional model fails to capture strong dependencies at higher levels of the vine copula models. For the 15‐dimensional R‐vine copula mixture model applied to real data, different selection criteria favor the traditional truncation method over our proposed method. However, the conclusion of our real‐data study aligns with that of existing studies using the same real data, which also support the truncation level we use. Hence, this illustrates that traditional models fail to capture strong dependencies at higher levels of the vine, thereby highlighting the importance of the pruning‐and‐truncation level proposed in this paper.