A New Parametrization of Correlation Matrices
Ilya Archakov, Peter Reinhard Hansen
Econometrica · 2021 · Volume 89 · Issue 4
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 Fisher'sZ-transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing the uniquen×ncorrelation matrix from any vector inis provided, and we derive its numerical complexity.
Keywords
Correlation matrix, Covariance modeling, Fisher transformation
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