A New Parametrization of Correlation Matrices
Econometrics
2020-12-07 v1 Statistical Finance
Computation
Methodology
Abstract
We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This parametrization can be viewed as a generalization of Fisther's Z-transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing the unique n x n correlation matrix from any d-dimensional vector (with d = n(n-1)/2) is provided, and we derive its numerical complexity.
Cite
@article{arxiv.2012.02395,
title = {A New Parametrization of Correlation Matrices},
author = {Ilya Archakov and Peter Reinhard Hansen},
journal= {arXiv preprint arXiv:2012.02395},
year = {2020}
}