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A New Parametrization of Correlation Matrices

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  • Ilya Archakov
  • Peter Reinhard Hansen

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.

Suggested Citation

  • Ilya Archakov & Peter Reinhard Hansen, 2020. "A New Parametrization of Correlation Matrices," Papers 2012.02395, arXiv.org.
    • Handle: RePEc:arx:papers:2012.02395
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