Universal Correlations and Power-Law Tails in Financial Covariance Matrices

Akemann G, Fischmann J, Vivo P (2010)
Physica A 389(13): 2566-2579.

Journal Article | Published | English

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Abstract
Signatures of universality are detected by comparing individual eigenvaluedistributions and level spacings from financial covariance matrices to randommatrix predictions. A chopping procedure is devised in order to produce astatistical ensemble of asset-price covariances from a single instance offinancial data sets. Local results for the smallest eigenvalue and individualspacings are very stable upon reshuffling the time windows and assets. They arein good agreement with the universal Tracy-Widom distribution and Wignersurmise, respectively. This suggests a strong degree of robustness especiallyin the low-lying sector of the spectra, most relevant for portfolio selections.Conversely, the global spectral density of a single covariance matrix as wellas the average over all unfolded nearest-neighbour spacing distributionsdeviate from standard Gaussian random matrix predictions. The data are in fairagreement with a recently introduced generalised random matrix model, withcorrelations showing a power-law decay.
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Akemann G, Fischmann J, Vivo P. Universal Correlations and Power-Law Tails in Financial Covariance Matrices. Physica A. 2010;389(13):2566-2579.
Akemann, G., Fischmann, J., & Vivo, P. (2010). Universal Correlations and Power-Law Tails in Financial Covariance Matrices. Physica A, 389(13), 2566-2579.
Akemann, G., Fischmann, J., and Vivo, P. (2010). Universal Correlations and Power-Law Tails in Financial Covariance Matrices. Physica A 389, 2566-2579.
Akemann, G., Fischmann, J., & Vivo, P., 2010. Universal Correlations and Power-Law Tails in Financial Covariance Matrices. Physica A, 389(13), p 2566-2579.
G. Akemann, J. Fischmann, and P. Vivo, “Universal Correlations and Power-Law Tails in Financial Covariance Matrices”, Physica A, vol. 389, 2010, pp. 2566-2579.
Akemann, G., Fischmann, J., Vivo, P.: Universal Correlations and Power-Law Tails in Financial Covariance Matrices. Physica A. 389, 2566-2579 (2010).
Akemann, Gernot, Fischmann, Jonit, and Vivo, Pierpaolo. “Universal Correlations and Power-Law Tails in Financial Covariance Matrices”. Physica A 389.13 (2010): 2566-2579.
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