The empirical properties of large covariance matrices
AbstractThe salient properties of large empirical covariance and correlation matrices are studied for three datasets of size 54, 55 and 330. The covariance is defined as a simple cross product of the returns, with weights that decay logarithmically slowly. The key general properties of the covariance matrices are the following. The spectrum of the covariance is very static, except for the top three to ten eigenvalues, and decay exponentially fast toward zero. The mean spectrum and spectral density show no particular feature that would separate "meaningful" from "noisy" eigenvalues. The spectrum of the correlation is more static, with three to five eigenvalues that have distinct dynamics. The mean projector of rank k on the leading subspace shows instead that most of the dynamics occur in the eigenvectors, including deep in the spectrum. Together, this implies that the reduction of the covariance to a few leading eigenmodes misses most of the dynamics, and that a covariance estimator correctly evaluates both volatilities and correlations.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 0903.1525.
Date of creation: Mar 2009
Date of revision:
Contact details of provider:
Web page: http://arxiv.org/
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- M. Potters & J. P. Bouchaud & L. Laloux, 2005.
"Financial Applications of Random Matrix Theory: Old Laces and New Pieces,"
- Marc Potters & Jean-Philippe Bouchaud & Laurent Laloux, 2005. "Financial Applications of Random Matrix Theory: Old Laces and New Pieces," Science & Finance (CFM) working paper archive 500058, Science & Finance, Capital Fund Management.
- Gilles Zumbach, 2004. "Volatility processes and volatility forecast with long memory," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 70-86.
- Caporin, M. & McAleer, M.J., 2012.
"Robust Ranking of Multivariate GARCH Models by Problem Dimension,"
Econometric Institute Research Papers
EI2012-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Michael McAleer & Massimiliano Caporin, 2012. "Robust Ranking of Multivariate GARCH Models by Problem Dimension," KIER Working Papers 815, Kyoto University, Institute of Economic Research.
- Massimiliano Caporin & Michael McAleer, 2012. "Robust Ranking of Multivariate GARCH Models by Problem Dimension," Working Papers in Economics 12/06, University of Canterbury, Department of Economics and Finance.
- Massimiliano Caporin & Michael McAleer, 2012. "Robust Ranking of Multivariate GARCH Models by Problem Dimension," Documentos del Instituto Complutense de AnÃ¡lisis EconÃ³mico 2012-06, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, revised Apr 2012.
- Nikolaus Hautsch & Lada M. Kyj & Roel C.A. Oomen, 2009.
"A blocking and regularization approach to high dimensional realized covariance estimation,"
SFB 649 Discussion Papers
SFB649DP2009-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Nikolaus Hautsch & Lada M. Kyj & Roel C. A. Oomen, 2012. "A blocking and regularization approach to high‐dimensional realized covariance estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(4), pages 625-645, 06.
- Hautsch, Nikolaus & Kyj, Lada M. & Hautsch, Nikolaus, 2009. "A blocking and regularization approach to high dimensional realized covariance estimation," CFS Working Paper Series 2009/20, Center for Financial Studies (CFS).
- Romain Allez & Jean-Philippe Bouchaud, 2012. "Eigenvector dynamics: general theory and some applications," Papers 1203.6228, arXiv.org, revised Jul 2012.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.