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
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Huang \ Yang (2010) `Correlation matrix with block structure and efficient sampling methods', Journal of Computational Finance 14, 81–94 | 0.874 | 9 | 2 | 100% |
| 2 | Cadima, Calheiros \ Preto (2010) `The eigenstructure of block-structured correlation matrices and its implications for principal component analysis', Journal of… | 0.874 | 7 | 2 | 100% |
| 3 | Engle \ Kelly (2012) `Dynamic equicorrelation', Journal of Business & Economic Statistics 30, 212–228 | 0.811 | 4 | 2 | 100% |
| 4 | Roustant \ Deville (2017) `On the validity of parametric block correlation matrices with constant within and between group correlations', arXiv math.ST/17… | 0.644 | 4 | 1 | 100% |
| 5 | Archakov, Hansen \ Lunde (2020) `A multivariate Realized GARCH model', arXiv:2012.02708 [econ.EM] | 0.644 | 2 | 2 | 100% |
| 6 | Ledoit \ Wolf (2004) `Honey, I shrunk the sample covariance matrix', Journal of Portfolio Management 30, 110–119 | 0.644 | 2 | 2 | 100% |
| 7 | Archakov \ Hansen (2021) `Web appendix to "A canonical representation of block matrices with applications to covariance and correlation matrices"', Web A… | 0.405 | 1 | 1 | 100% |
| 8 | Archakov \ Hansen (2021) `A new parametrization of correlation matrices', Econometrica 89, 1699–1715 | 0.405 | 1 | 1 | 100% |
| 9 | Asai \ So (2015) `Long memory and asymmetry for matrix-exponential dynamic correlation processes', Journal of Time Series Econometrics 7, 69–74 | 0.405 | 1 | 1 | 100% |
| 10 | Creal, Koopman \ Lucas (2013) `Generalized autoregressive score models with applications', Journal of Applied Econometrics 28, 777–795 | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 18 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Cluster GARCH | 1.000 | 7 | 4 |
| 2 | Dynamic Factor Correlation Model | 1.000 | 7 | 3 |
| 3 | Characterizing Correlation Matrices that Admit a Clustered Factor Representation | 1.000 | 6 | 3 |
| 4 | A Multivariate Realized GARCH Model | 0.888 | 10 | 4 |
| 5 | Split-Session Cluster GARCH for Overnight and Intraday Returns: The Role of Tail Heterogeneity | 0.737 | 3 | 2 |
| 6 | Convolution-$t$ Distributions | 0.405 | 1 | 1 |
| 7 | A Robust Similarity Estimator | 0.405 | 1 | 1 |
| 8 | Principled Identification of Structural Dynamic Models | 0.000 | 1 | 1 |