Eigenvalue density of empirical covariance matrix for correlated samples
Abstract
We describe a method to determine the eigenvalue density of empirical covariance matrix in the presence of correlations between samples. This is a straightforward generalization of the method developed earlier by the authors for uncorrelated samples. The method allows for exact determination of the experimental spectrum for a given covariance matrix and given correlations between samples in the limit of large N and N/T=r=const with N being the number of degrees of freedom and T being the number of samples. We discuss the effect of correlations on several examples.
Cite
@article{arxiv.cond-mat/0508451,
title = {Eigenvalue density of empirical covariance matrix for correlated samples},
author = {Z. Burda and J. Jurkiewicz and B. Waclaw},
journal= {arXiv preprint arXiv:cond-mat/0508451},
year = {2008}
}
Comments
12 pages, 5 figures, to appear in Acta Phys. Pol. B (Proceedings of the conference on `Applications of Random Matrix Theory to Economy and Other Complex Systems', May 25-28, 2005, Cracow, Poland