VineCopulas.jl

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VineCopulas.jlFlexible vine copula models for Julia

Build, fit, select, evaluate, and simulate C-vines, D-vines, and R-vines on top of Copulas.jl.

Getting started
Manual
API
VineCopulas.jl

C-, D-, and R-vines

Explicit and fitted vine copula models with flexible pair-copula families and truncation support.

Fitting & selection

Pair-family, parameter, rotation, and dependence-structure selection through a unified Julia interface.

Fast vine engines

Fused pair kernels, reusable work buffers, and allocation-conscious C-, D-, and R-vine traversals.

Copulas.jl ecosystem

Built directly on Copulas.jl and the broader Distributions.jl statistical ecosystem.

VineCopulas.jl ​

VineCopulas.jl is a native Julia package for building, fitting, selecting, evaluating, and simulating C-vine, D-vine, and regular-vine copula models on top of Copulas.jl.

The package follows the Distributions.jl/Copulas.jl ecosystem: explicit vine models are copulas, pair copulas come from Copulas.jl, and fitting is exposed through fit.

Vine models are useful when dependence is high-dimensional but can be described through interpretable bivariate building blocks. VineCopulas.jl focuses on the vine layer: structures, pair composition, traversal, simulation, sequential fitting, and structure selection. The mathematics of individual pair-copula families remains the responsibility of Copulas.jl.

What is available ​

  • C-vine, D-vine, and general R-vine models.

  • First-class CVineStructure, DVineStructure, and RVineStructure objects.

  • pdf, logpdf, rand, numerical cdf, Rosenblatt, and inverse Rosenblatt transforms.

  • Pair-copula fitting with family and rotation selection.

  • Sequential fitting for fixed vine structures.

  • Automatic C-vine and D-vine ordering.

  • Dissmann-style R-vine structure selection with maximum spanning trees.

  • AIC, BIC, mBICV, log-likelihood, Kendall-, and Spearman- controls.

  • Truncated vine evaluation, and user-controlled or mBICV-selected fitting truncation.

  • External correctness checks against rvinecopulib and reproducible performance benchmarks.

Current modeling scope

The package currently implements simplified vines. Truncation is user-controlled or selected greedily with trunc=:mbicv for every vine type, and density evaluation, Rosenblatt/inverse Rosenblatt transforms, and simulation all respect it.

Quick example ​

julia
using VineCopulas
using Distributions: fit, logpdf
using Random

rng = MersenneTwister(42)
truth = DVineCopula(
    [1, 2, 3],
    [[GaussianCopula(2, 0.55), ClaytonCopula(2, 1.4)],
     [FrankCopula(2, 2.0)]],
)

U = rand(rng, truth, 300)

fitted = fit(
    DVineCopula,
    U;
    family_set=:default,
    selection_criterion=:bic,
    allow_rotations=true,
)

(order = order(fitted),
 truncation = truncation(fitted),
 loglikelihood = loglikelihood(fitted, U))
(order = (3, 2, 1), truncation = 2, loglikelihood = 133.25928234192196)

Explicit vines are ordinary copulas:

julia
u = [0.2, 0.5, 0.7]
(logdensity = logpdf(truth, u),
 roundtrip_error = maximum(abs.(inverse_rosenblatt(truth, rosenblatt(truth, U)) .- U)))
(logdensity = -0.12694368299308356, roundtrip_error = 7.66053886991358e-15)

Matrices are interpreted as p × n: rows are variables and columns are observations.

Documentation map ​

The site has five conceptual sections plus the home page:

  • Home — this overview, quick example, and citation.

  • Manual — theory, conventions, pair-copula semantics, fitting, transforms, and benchmarks.

  • Bestiary — supported vine structures and pair-copula families.

  • Examples — practical workflows with small, reproducible code.

  • Developer Guide — architecture, contracts, testing, release process, upstream follow-ups, and roadmap.

  • API — public reference, internal non-stable reference, and literature/software references.

The version selector in the documentation provides the development site, the latest stable release, and retained tagged versions.

Citation ​

If you use VineCopulas.jl, please cite the package metadata in CITATION.cff:

bibtex
@software{jimenez_vinecopulas,
  author  = {Santiago Jimenez and contributors},
  title   = {VineCopulas.jl},
  url     = {https://github.com/Santymax98/VineCopulas.jl},
  version = {0.1.2},
  year    = {2026}
}