Michael Stanley Smith, Lin Deng
arXiv 17 Sep 2026 · Statistics — Methodology
arXiv:2609.19547 · PDF · Extracted main text
Multivariate longitudinal data may exhibit non-Gaussian margins, nonlinear dynamics, and response vectors with composition that varies across waves. To account for these features, we introduce a vector drawable vine (VD-vine) copula that extends conventional drawable vine copulas from scalar to vector-valued nodes. Here, the response vector at each wave forms a multivariate marginal, and serial dependence is captured through a sequence of linking vector copulas. We establish that the VD-vine is itself a vector copula and reduces to a conventional drawable vine for scalar nodes. Recursive forward and backward conditional transports are derived that enable efficient likelihood evaluation and predictive simulation, with parsimonious reductions under finite-order Markov and stationary restrictions. Unconstrained parameterizations for Gaussian and FGM linking vector copulas, flexible multivariate marginals, and Bayesian variational inference provide a practical implementation. Simulations show improved predictive accuracy when the marginals are asymmetric and serial dependence is multivariate, with little loss under a correctly specified Gaussian panel vector autoregression. In an eight-wave Australian panel of 1,093 individuals with varying response vectors, the full VD-vine delivers the best cross-validated distributional forecasts among the models considered, establishing the benefit of capturing asymmetry and nonlinear dependence.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Fan, Yanqin and Henry, Marc (2023) Vector copulas | 1.000 | 9 | 3 | 100% |
| 2 | Aas, Kjersti and Czado, Claudia and Frigessi, Arnoldo and Bakken, He… (2009) Pair-copula constructions of multiple dependence | 1.000 | 6 | 3 | 100% |
| 3 | Smith, Michael and Min, Aleksey and Almeida, Carlos and Czado, Claudia (2010) Modeling longitudinal data using a pair-copula decomposition of serial dependence self | 1.000 | 5 | 3 | 100% |
| 4 | Grace B. Yu and Mohsen Joshanloo and M. Joseph Sirgy (2025) A Longitudinal Multilevel Analysis of the Reciprocal Associations Between Work-Life Conflict and Subjective Wellbeing | 0.874 | 5 | 2 | 100% |
| 5 | Harry Joe (1996) Families of m-Variate Distributions with Given Margins and m(m-1)/2 Bivariate Dependence Parameters | 0.843 | 3 | 3 | 100% |
| 6 | Zhang, Qi and Li, Bing and Xue, Lingzhou (2026) A Copula Graphical Model for Multi-Attribute Data Using Optimal Transport | 0.843 | 3 | 3 | 100% |
| 7 | Claudia Czado (2019) Analyzing Dependent Data with Vine Copulas: A Practical Guide with R | 0.737 | 3 | 2 | 100% |
| 8 | Norman L. Johnson and Samuel Kotz (1975) On Some Generalized Farlie–Gumbel–Morgenstern Distributions | 0.644 | 2 | 2 | 100% |
| 9 | Nagler, Thomas and Krüger, Daniel and Min, Aleksey (2022) Stationary Vine Copula Models for Multivariate Time Series | 0.644 | 2 | 2 | 100% |
| 10 | Genest, Christian and Quesada Molina, JJ and Rodr\'iguez Lallena, JA (1995) De l'impossibilité de construire des lois à marges multidimensionnelles données à partir de copules | 0.644 | 2 | 2 | 100% |
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