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Generating Correlation Matrices Based on the Boundaries of Their Coefficients

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  • Kawee Numpacharoen
  • Amporn Atsawarungruangkit

Abstract

Correlation coefficients among multiple variables are commonly described in the form of matrices. Applications of such correlation matrices can be found in many fields, such as finance, engineering, statistics, and medicine. This article proposes an efficient way to sequentially obtain the theoretical bounds of correlation coefficients together with an algorithm to generate n n correlation matrices using any bounded random variables. Interestingly, the correlation matrices generated by this method using uniform random variables as an example produce more extreme relationships among the variables than other methods, which might be useful for modeling complex biological systems where rare cases are very important.

Suggested Citation

  • Kawee Numpacharoen & Amporn Atsawarungruangkit, 2012. "Generating Correlation Matrices Based on the Boundaries of Their Coefficients," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-7, November.
    • Handle: RePEc:plo:pone00:0048902
    DOI: 10.1371/journal.pone.0048902
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    References listed on IDEAS

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    1. Ledyard Tucker & Raymond Koopman & Robert Linn, 1969. "Evaluation of factor analytic research procedures by means of simulated correlation matrices," Psychometrika, Springer;The Psychometric Society, vol. 34(4), pages 421-459, December.
    2. Joseph Simonian, 2010. "The most simple methodology to create a valid correlation matrix for risk management and option pricing purposes," Applied Economics Letters, Taylor & Francis Journals, vol. 17(18), pages 1767-1768.
    3. Qingna Li & Donghui Li & Houduo Qi, 2010. "Newton’s Method for Computing the Nearest Correlation Matrix with a Simple Upper Bound," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 546-568, December.
    4. Hirschberger, Markus & Qi, Yue & Steuer, Ralph E., 2007. "Randomly generating portfolio-selection covariance matrices with specified distributional characteristics," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1610-1625, March.
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    Cited by:

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    5. Böhm, Walter & Hornik, Kurt, 2014. "Generating random correlation matrices by the simple rejection method: Why it does not work," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 27-30.
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