Random correlation matrices generated via partial correlation C-vines

Abstract

The method for generating random $d\times d$ correlation matrices with a partial correlation C-vine is extended so that each correlation can have a distribution that is asymmetric on $(-1,1)$ or on $(0,1)$. With the recursion formulas from the partial correlation C-vine to the correlation matrix, first and second moments can be derived, in the case of the same distribution for each partial correlation in tree $\ell$ of the vine ($1\le \ell <d$). Algorithms and conditions are given so that, after a permutation step, all random correlations have a common mean and second moment. The algorithms can be useful for simulation experiments to generate random correlation matrices that cover the whole space or with the restriction that each correlation is positive.