Hermitian and non-Hermitian covariance estimators for multivariate Gaussian and non-Gaussian assets from random matrix theory
AbstractThe random matrix theory method of planar Gaussian diagrammatic expansion is applied to find the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged cross-covariance estimators, firstly in the form of master equations for the most general multivariate Gaussian system, secondly for seven particular toy models of the true covariance function. For the simplest one of these models, the existing result is shown to be incorrect and the right one is presented, moreover its generalizations are accomplished to the exponentially-weighted moving average estimator as well as two non-Gaussian distributions, Student t and free Levy. The paper revolves around applications to financial complex systems, and the results constitute a sensitive probe of the true correlations present there.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1010.2981.
Date of creation: Oct 2010
Date of revision: May 2012
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-10-23 (All new papers)
- NEP-ECM-2010-10-23 (Econometrics)
- NEP-ETS-2010-10-23 (Econometric Time Series)
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