A New Parametrization of Correlation Matrices

• 成果类型: Article
• 署名作者: Archakov, Ilya; Hansen, Peter Reinhard
• 署名单位: University of Vienna; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA16910
• 发表日期: 2021
• 页码: 1699-1715
• 关键词: ASYMPTOTIC COVARIANCE-MATRIX; MULTIVARIATE; MODEL; volatility

摘要

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 x n correlation matrix from any vector in Rn(n-1)/2 is provided, and we derive its numerical complexity.