Berlin 2005 – wissenschaftliches Programm
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AKSOE: Physik sozio-ökonomischer Systeme
AKSOE 8: Poster Session
AKSOE 8.20: Poster
Montag, 7. März 2005, 14:00–15:30, Poster TU E
Random Matrix Theory and Robust Covariance Matrix Estimation for Generalized Elliptical Distributions — •Gabriel Frahm1 and Uwe Jaekel2 — 1Center of Advanced European Studies and Research, Financial Engineering, Ludwig-Erhard-Allee 2, 53175 Bonn, Germany — 2C&C Research Laboratories, NEC Europe Ltd., Rathausallee 10, 53757 Sankt Augustin
The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust covariance matrix estimator (the “spectral estimator”) for the new class of “generalized elliptical distributions” is presented. It is shown that the spectral estimator corresponds to an M-estimator proposed by Tyler (1983) in the context of elliptical distributions. Both the generalization of elliptical distributions and robust covariance matrix estimation are motivated by the stylized facts of empirical finance. Further, some elements of Random Matrix Theory (RMT) are presented. RMT can be used for analyzing high-dimensional stochastical systems. It is shown that the fundamental theorem of RMT (the “Marčenko-Pastur law”) fails if the sample covariance matrix is considered as a random matrix in the context of elliptically distributed and heavy tailed data. But substituting the sample covariance matrix by the spectral estimator resolves the problem and the Marčenko-Pastur law remains valid.