The fine structure of spectral properties for random correlation matrices: an application to financial markets
AbstractWe study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data. We challenge this common knowledge by acting on the empirical correlation matrices of two data sets with a filtering procedure which highlights some of the cluster structure they contain, and we analyze the consequences of such filtering on eigenvalue spectra. We show that empirically observed eigenvalue bulks emerge as superpositions of smaller structures, which in turn emerge as a consequence of cross-correlations between stocks. We interpret and corroborate these findings in terms of factor models, and and we compare empirical spectra to those predicted by Random Matrix Theory for such models.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 28964.
Date of creation: 19 Feb 2011
Date of revision:
random matrix theroy; financial econometrics; correlation matrix;
Other versions of this item:
- G. Livan & S. Alfarano & E. Scalas, 2011. "The fine structure of spectral properties for random correlation matrices: an application to financial markets," Papers 1102.4076, arXiv.org.
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
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- Giacomo Livan & Jun-ichi Inoue & Enrico Scalas, 2012. "On the non-stationarity of financial time series: impact on optimal portfolio selection," Papers 1205.0877, arXiv.org, revised Jul 2012.
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- Thomas Bury, 2013. "Predicting trend reversals using market instantaneous state," Papers 1310.8169, arXiv.org, revised Mar 2014.
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