For the modeling of covariance matrices, the literature has proposed a variety of methods to enforce the positive (semi) definiteness. In this paper, we propose a method that is based on a novel parametrization of the correlation matrix, specifically the off-diagonal elements of the matrix logarithmic transformed correlations. This parametrization has many attractive properties, a wide range of applications, and may be viewed as a multivariate generalization of Fisher’s Z-transformation of a single correlation.

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docs.google.com/spreadsheets/d/1B5eDfd-p_oFWK5FiVvLebyit0ZQTQ6lkjUzbAFYDhUw/edit#gid=0

Link to paper:
sites.google.com/site/peterreinhardhansen/research-papers/anewparametrizationofcorrelationmatrices