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Permutation invariant Gaussian matrix models for financial correlation matrices

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  • George Barnes
  • Sanjaye Ramgoolam
  • Michael Stephanou

Abstract

We construct an ensemble of correlation matrices from high-frequency foreign exchange market data, with one matrix for every day for 446 days. The matrices are symmetric and have vanishing diagonal elements after subtracting the identity matrix. For this case, we construct the general permutation invariant Gaussian matrix model, which has 4 parameters characterised using the representation theory of symmetric groups. The permutation invariant polynomial functions of the symmetric, diagonally vanishing matrices have a basis labelled by undirected loop-less graphs. Using the expectation values of the general linear and quadratic permutation invariant functions of the matrices in the dataset, the 4 parameters of the matrix model are determined. The model then predicts the expectation values of the cubic and quartic polynomials. These predictions are compared to the data to give strong evidence for a good overall fit of the permutation invariant Gaussian matrix model. The linear, quadratic, cubic and quartic polynomial functions are then used to define low-dimensional feature vectors for the days associated to the matrices. These vectors, with choices informed by the refined structure of small non-Gaussianities, are found to be effective as a tool for anomaly detection in market states: statistically significant correlations are established between atypical days as defined using these feature vectors, and days with significant economic events as recognized in standard foreign exchange economic calendars. They are also shown to be useful as a tool for ranking pairs of days in terms of their similarity, yielding a strongly statistically significant correlation with a ranking based on a higher dimensional proxy for visual similarity.

Suggested Citation

  • George Barnes & Sanjaye Ramgoolam & Michael Stephanou, 2023. "Permutation invariant Gaussian matrix models for financial correlation matrices," Papers 2306.04569, arXiv.org.
  • Handle: RePEc:arx:papers:2306.04569
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    References listed on IDEAS

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    1. M. Potters & J. P. Bouchaud & L. Laloux, 2005. "Financial Applications of Random Matrix Theory: Old Laces and New Pieces," Papers physics/0507111, arXiv.org.
    2. Aït-Sahalia, Yacine & Fan, Jianqing & Xiu, Dacheng, 2010. "High-Frequency Covariance Estimates With Noisy and Asynchronous Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1504-1517.
    3. Laurent Laloux & Pierre Cizeau & Marc Potters & Jean-Philippe Bouchaud, 2000. "Random Matrix Theory And Financial Correlations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 391-397.
    4. Joël Bun & Jean-Philippe Bouchaud & Marc Potters, 2017. "Cleaning large correlation matrices: tools from random matrix theory," Post-Print hal-01491304, HAL.
    5. Maria Elvira Mancino & Paul Malliavin, 2002. "Fourier series method for measurement of multivariate volatilities," Finance and Stochastics, Springer, vol. 6(1), pages 49-61.
    6. D. Hendricks & T. Gebbie & D. Wilcox, 2016. "Detecting intraday financial market states using temporal clustering," Quantitative Finance, Taylor & Francis Journals, vol. 16(11), pages 1657-1678, November.
    7. Matteo Marsili, 2002. "Dissecting financial markets: Sectors and states," Papers cond-mat/0207156, arXiv.org.
    8. Matteo Marsili, 2002. "Dissecting financial markets: sectors and states," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 297-302.
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