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Statistical rehabilitation of improper correlation matrices


  • A. Frigessi
  • A. Løland
  • A. Pievatolo
  • F. Ruggeri


The simplest way to describe the dependence for a set of financial assets is their correlation matrix. This correlation matrix can be improper when it is specified element-wise. We describe a new method for obtaining a positive definite correlation matrix starting from an improper one. The expert's opinion and trust in each pairwise correlation is described by a beta distribution. Then, by combining these individual distributions, a joint distribution over the space of positive definite correlation matrices is obtained using Cholesky factorization, and its mode constitutes the new proper correlation matrix. The optimization is complemented by a visual representation of the entries that were most affected by the legalization procedure. We also sketch a Bayesian approach to the same problem.

Suggested Citation

  • A. Frigessi & A. Løland & A. Pievatolo & F. Ruggeri, 2011. "Statistical rehabilitation of improper correlation matrices," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1081-1090.
  • Handle: RePEc:taf:quantf:v:11:y:2011:i:7:p:1081-1090
    DOI: 10.1080/14697680903390118

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    Cited by:

    1. Anders Løland & Ragnar Bang Huseby & Nils Lid Hjort & Arnoldo Frigessi, 2013. "Statistical Corrections of Invalid Correlation Matrices," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 807-824, December.


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