A Canonical Representation of Block Matrices with Applications to Covariance and 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 Vienna; Copenhagen Business School; Copenhagen Business School
刊物名称：
REVIEW OF ECONOMICS AND STATISTICS
ISSN/ISSBN：
0034-6535
DOI：
10.1162/rest_a_01258
发表日期：
2024-07
页码：
1099-1113
关键词：
摘要：
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 model and regularize large covariance/correlation matrices, test block structures in matrices, and estimate regressions with many variables.
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