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AGSOE: Arbeitsgruppe Physik sozio-ökonomischer Systeme

AGSOE 4: Financial Markets and Risk Management III

AGSOE 4.5: Vortrag

Montag, 23. März 2009, 15:45–16:00, BAR 205

A numerical analysis of eigenvalues and eigenvectors of covariance matrices — •Daniel Fulger^1,2, Enrico Scalas¹, Giulia Iori³, Mauro Politi², and Guido Germano² — ¹Amedeo Avogadro University of East Piedmont, Alessandria, Italy — ²Philipps-Universität Marburg, Germany — ³City University, London, UK

Covariance matrices are related to similarity and dissimilarity matrices, which are often used as a starting point for classification purposes through clustering. We present numerical analyses of the eigenvalues and eigenvectors of covariance matrices built from independent or from correlated random variables for the cases Q > 1 or Q < 1, where Q = T/N is the ratio of observations T to the number of random variables N. The former case, where there are more observations than variables, is common in physics and in finance, while the latter occurs typically for biological problems such as microarray analysis. We discuss how to compute covariance matrices from synchronous or asynchronous data, we compare the numerical eigenvalue spectra of independent or free independent random variables with analytical results of classical or free random matrix theory, and present several case studies with groups of correlated random variables in a noisy sea of independent random variables.