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In this paper, we propose an outlier detection algorithm for multivariatedata based on their projections on the directions that maximize the CumulantGenerating Function (CGF). We prove that CGF is a convex function, and wecharacterize the CGF maximization problem on the unit n-circle as a concaveminimization problem. Then, we show that the CGF maximization approach can beinterpreted as an extension of the standard principal component technique.Therefore, for validation and testing, we provide a thorough comparison of ourmethodology with two other projection-based approaches both on artificial andreal-world financial data. Finally, we apply our method as an early detectorfor financial crises.

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