Vine truncation

A vine truncated at level retains trees and treats higher-tree dependence as independence.

For a -dimensional model, full depth is  .

model = fit(RVineCopula, U; trunc=2)

or construct an explicit truncated vine directly. An already constructed model can also be structurally reduced:

truncated = truncate(model, 2)
truncation(truncated)

truncate(model, q) returns a new model with the same public vine type, the same variable order, and the first pair-copula trees. It cannot expand a model whose higher trees were not stored.

Truncation is a structural property of the vine and must not be confused with candidate parameter bounds used by automatic family selection. Parameter bounds restrict an optimizer's search space; vine truncation removes higher trees from the model.

Truncation applies uniformly to fitting, density evaluation, Rosenblatt/inverse Rosenblatt transforms, simulation, and the simulation-based numerical CDF, for C-vines, D-vines, and standard general R-vines alike. The omitted trees behave as independence pair-copulas, so a truncated vine and the same vine padded to full depth with independence pair-copulas are the same model.

Automatic data-driven selection of the truncation level is not yet part of the public API.

Tip

Use truncation as a modeling decision, not only as a speed knob. A smaller truncation level can improve interpretability and reduce variance, but it also assumes that omitted higher-tree conditional dependences are negligible.

Level zero

Mathematically, truncation at level zero corresponds to the independence copula. The current public truncate API starts at level one; level-zero support should be added deliberately with matching traversal and fitting semantics.