Vine structures

A vine copula decomposes a multivariate copula density into bivariate pair-copula terms organized in trees. VineCopulas.jl implements three structure families.

• C-vine: each tree is organized around a root variable.

• D-vine: each tree follows a path structure.

• R-vine: the general regular-vine representation, including C- and D-vines as special cases.

For a -dimensional untruncated vine, tree contains   pair copulas. The density is the product of those pair-copula densities evaluated at recursively computed conditional arguments.

Use C- or D-vines when their structure is meaningful for the application. Use an R-vine when the dependence graph should be selected more flexibly from the data.

Structure can be inspected independently from the pair-copula array:

st = structure(model)
order(st)
truncation(st)
edges(model)

Use truncate(model, q) to create a new vine with only trees when those trees are already present in model.

Tip

Start with C- or D-vines when the variable order has a scientific meaning. Start with R-vines when the structure itself should be learned from data.

Warning

A vine structure is not a fitted statistical result. Diagnostics such as convergence, selected criterion, and selection trace belong to fitted-result metadata, not to CVineStructure, DVineStructure, or RVineStructure.