Rotations

Asymmetric positive-dependence families can represent negative association through rotations.

VineCopulas.jl follows the usual 0, 90, 180, and 270 degree convention and represents rotations through Copulas.SurvivalCopula flips.

During automatic selection:

fit(PairCopula, U; allow_rotations=true)

When preselect=true, the empirical dependence sign can remove rotations that cannot match the data. Set preselect=false for exhaustive parity or benchmark campaigns.

Gaussian, Student-t, and Frank already admit both signs in their base parameterization and therefore do not need rotated duplicates in the default search.