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Combining permutation tests to rank systemically important banks


In this work we propose the use of a nonparametric procedure to investigate the relationship between the Regulator’s Global Systemically Important Banks (G-SIBs) classification and the equity-based systemic risk measures. The proposed procedure combines several permutation tests to investigate the equality of the multivariate distribution of two groups and assumes only the hypothesis of exchangeability of variables. In our novel approach, the weights used in the combination of tests are obtained using the Particle Swarm Optimization heuristic and quantify the informativeness about the selection. Finally, the p value of the combined test measures the reliability of the result. Empirical results about the selection of G-SIBs show how considering the systematic (\(\beta \)), stress (\(\varDelta \)CoVaR) and connectedness components (in–out connection) of systemic risk cover more than \(70\%\) of weight in all the considered years.

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  1. The analyzed dataset is available on request.

  2. The complete list of included institutions is available upon request.


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We wish to thank the Editor and two anonymous referees for very useful comments and suggestions which have helped to improve and develop the paper further. The authors are also grateful to The System for Scientific Computing of Ca’ Foscari (SCSCF) for computations.

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Correspondence to Claudio Pizzi.

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Frattarolo, L., Parpinel, F. & Pizzi, C. Combining permutation tests to rank systemically important banks. Stat Methods Appl 29, 581–596 (2020).

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  • Systemic risk
  • Global Systemically Important Bank
  • Particle Swarm Optimization
  • Permutation tests