A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices
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4 décembre 2020
- 2012.02698
Mots-clés
Economics - Econometrics Quantitative Finance - Computational Finance Statistics - MethodologySujets proches
Matrix algebra Algebra, Matrix Matrixes (Algebra) Cracovians (Mathematics)Citer ce document
Ilya Archakov et al., « A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices », arXiv - économie
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Résumé
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.