Signal and Noise in a Gaussian Correlation Matrix

Jerzy Jurkiewicz

Marian Smoluchowski Institute of Physics
Jagellonian University

    Using random matrix technique it is possible to determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance (correlation) matrix. Results can be applied in various problems where one experimentally estimates correlations in a system with many degrees of freedom, in particular in quantitative finance and other applications of multivariate statistics.