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

Ilya Archakov, Peter Reinhard Hansen

arXiv 4 Dec 2020 · Econometrics · publishedThe Review of Economics and Statistics (2022) · 5 citations (OpenAlex)

arXiv:2012.02698 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

18
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main-text words

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Huang \ Yang (2010) `Correlation matrix with block structure and efficient sampling methods', Journal of Computational Finance 14, 81–940.87492100%
2Cadima, Calheiros \ Preto (2010) `The eigenstructure of block-structured correlation matrices and its implications for principal component analysis', Journal of…0.87472100%
3Engle \ Kelly (2012) `Dynamic equicorrelation', Journal of Business & Economic Statistics 30, 212–2280.81142100%
4Roustant \ Deville (2017) `On the validity of parametric block correlation matrices with constant within and between group correlations', arXiv math.ST/17…0.64441100%
5Archakov, Hansen \ Lunde (2020) `A multivariate Realized GARCH model', arXiv:2012.02708 [econ.EM]0.64422100%
6Ledoit \ Wolf (2004) `Honey, I shrunk the sample covariance matrix', Journal of Portfolio Management 30, 110–1190.64422100%
7Archakov \ Hansen (2021) `Web appendix to "A canonical representation of block matrices with applications to covariance and correlation matrices"', Web A…0.40511100%
8Archakov \ Hansen (2021) `A new parametrization of correlation matrices', Econometrica 89, 1699–17150.40511100%
9Asai \ So (2015) `Long memory and asymmetry for matrix-exponential dynamic correlation processes', Journal of Time Series Econometrics 7, 69–740.40511100%
10Creal, Koopman \ Lucas (2013) `Generalized autoregressive score models with applications', Journal of Applied Econometrics 28, 777–7950.40511100%

Showing the top 10 of 18 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Cluster GARCH1.00074
2Dynamic Factor Correlation Model1.00073
3Characterizing Correlation Matrices that Admit a Clustered Factor Representation1.00063
4A Multivariate Realized GARCH Model0.888104
5Split-Session Cluster GARCH for Overnight and Intraday Returns: The Role of Tail Heterogeneity0.73732
6Convolution-$t$ Distributions0.40511
7A Robust Similarity Estimator0.40511
8Principled Identification of Structural Dynamic Models0.00011