A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices

Ilya Archakov and Peter Hansen

Papers from arXiv.org

Abstract: We obtain a canonical representation for block matrices. The representation facilitates simple computation of the determinant, the matrix inverse, and other powers of a block matrix, as well as the matrix logarithm and the matrix exponential. These results are particularly useful for block covariance and block correlation matrices, where evaluation of the Gaussian log-likelihood and estimation are greatly simplified. We illustrate this with an empirical application using a large panel of daily asset returns. Moreover, the representation paves new ways to regularizing large covariance/correlation matrices, test block structures in matrices, and estimate regressions with many variables.

Date: 2020-12, Revised 2021-11
New Economics Papers: this item is included in nep-ecm
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Journal Article: A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices (2024)
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