The Econometric SocietyEdited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262
Econometrica: Jul, 2021, Volume 89, Issue 4
https://doi.org/10.3982/ECTA16910
p. 1699-1715
Ilya Archakov, Peter Reinhard Hansen
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 is provided, and we derive its numerical complexity.
This zip file contains the replication files for the manuscript.
This is a web appendix with supplementary material for the paper “A New Parametrization of Correlation Matrices” by Archakov and Hansen (2020). Here, we present four sets of results: 1) The finite sample properties of γˆ when C has a Toeplitz structure. 2) The finite sample properties of γˆ when C has general (randomly generated) structure. 3) The Jacobian ∂ρ/∂γ for two correlation matrices. One with a Toeplitz structure, and one based on the empirical correlation matrix for returns on 10 industry portfolios. 4) Software implementations of C(γ), that reconstructs C from γ for Julia, Matlab, Ox, Python, and R.
