A New Parametrization of Correlation Matrices. Issue 4 (26th July 2021)

• Record Type: Journal Article
• Authors: Archakov, Ilya; Hansen, Peter Reinhard
• Is Part Of: Econometrica. Volume 89:Issue 4(2021)
• Page Start: 1699
• Page End: 1715
• Publication Date: 2021-07-26
• Subjects: Correlation matrix -- Covariance modeling -- Fisher transformation; Econometrics -- Periodicals; Economics, Mathematical -- Periodicals; Economics -- Periodicals; Économétrie -- Périodiques; Mathématiques économiques -- Périodiques; Économie politique -- Périodiques; 330.05
• DOI: 10.3982/ECTA16910
• Languages: English
• ISSNs: 0012-9682

Abstract

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's Z ‐transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing the unique n × n correlation matrix from any vector in R n ( n − 1 ) / 2 is provided, and we derive its numerical complexity.