A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices
Econometrics
2021-11-16 v2 Computational Finance
Methodology
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.
Keywords
Cite
@article{arxiv.2012.02698,
title = {A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices},
author = {Ilya Archakov and Peter Reinhard Hansen},
journal= {arXiv preprint arXiv:2012.02698},
year = {2021}
}