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Vine copulas are a sequential cascade of bivariate copulas meant to capture the hierarchical structure in the dependence structure of random variables. How does this relate or differ from the concept of hierarchical copulas?

In Dynamic copula methods in finance, hierarchical copulas are premised on the fact that

The dependence structure of variables of the same group (in a parallel with econometrics, we could call it within dependence) is higher than that of variables of different groups (between dependence).

but no comparison is made between vine and hierarchical copulas, even both seem to capture hierarchical structure.

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