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Non-parametric cumulants approach for outlier detection of multivariate financial data

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  • Francesco Cesarone
  • Rosella Giacometti
  • Jacopo Maria Ricci

Abstract

In this paper, we propose an outlier detection algorithm for multivariate data based on their projections on the directions that maximize the Cumulant Generating Function (CGF). We prove that CGF is a convex function, and we characterize the CGF maximization problem on the unit n-circle as a concave minimization problem. Then, we show that the CGF maximization approach can be interpreted as an extension of the standard principal component technique. Therefore, for validation and testing, we provide a thorough comparison of our methodology with two other projection-based approaches both on artificial and real-world financial data. Finally, we apply our method as an early detector for financial crises.

Suggested Citation

  • Francesco Cesarone & Rosella Giacometti & Jacopo Maria Ricci, 2023. "Non-parametric cumulants approach for outlier detection of multivariate financial data," Papers 2305.10911, arXiv.org.
    • Handle: RePEc:arx:papers:2305.10911
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/12897 is not listed on IDEAS
    2. Domino, Krzysztof, 2020. "Multivariate cumulants in outlier detection for financial data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    3. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    4. Ané, Thierry & Ureche-Rangau, Loredana & Gambet, Jean-Benoît & Bouverot, Julien, 2008. "Robust outlier detection for Asia-Pacific stock index returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 18(4), pages 326-343, October.
    5. Cesarone, Francesco & Mango, Fabiomassimo & Mottura, Carlo Domenico & Ricci, Jacopo Maria & Tardella, Fabio, 2020. "On the stability of portfolio selection models," Journal of Empirical Finance, Elsevier, vol. 59(C), pages 210-234.
    6. R. Giacometti & G. Torri & S. Paterlini, 2021. "Tail risks in large portfolio selection: penalized quantile and expectile minimum deviation models," Quantitative Finance, Taylor & Francis Journals, vol. 21(2), pages 243-261, February.
    7. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi, 2008. "The centred parametrization for the multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1362-1382, August.
    8. Kondor, Imre & Pafka, Szilard & Nagy, Gabor, 2007. "Noise sensitivity of portfolio selection under various risk measures," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1545-1573, May.
    9. Trendafilov, Nickolay T. & Jolliffe, Ian T., 2006. "Projected gradient approach to the numerical solution of the SCoTLASS," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 242-253, January.
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