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A New Method for Generating Random Correlation Matrices

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  • Ilya Archakov
  • Peter Reinhard Hansen
  • Yiyao Luo

Abstract

We propose a new method for generating random correlation matrices that makes it simple to control both location and dispersion. The method is based on a vector parameterization, gamma = g(C), which maps any distribution on R^d, d = n(n-1)/2 to a distribution on the space of non-singular nxn correlation matrices. Correlation matrices with certain properties, such as being well-conditioned, having block structures, and having strictly positive elements, are simple to generate. We compare the new method with existing methods.

Suggested Citation

  • Ilya Archakov & Peter Reinhard Hansen & Yiyao Luo, 2022. "A New Method for Generating Random Correlation Matrices," Papers 2210.08147, arXiv.org.
    • Handle: RePEc:arx:papers:2210.08147
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    1. Pourahmadi, Mohsen & Wang, Xiao, 2015. "Distribution of random correlation matrices: Hyperspherical parameterization of the Cholesky factor," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 5-12.
    2. Ilya Archakov & Peter Reinhard Hansen, 2021. "A New Parametrization of Correlation Matrices," Econometrica, Econometric Society, vol. 89(4), pages 1699-1715, July.
    3. Michele Caivano & Andrew Harvey, 2014. "Time-series models with an EGB2 conditional distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 558-571, November.
    4. Joe, Harry, 2006. "Generating random correlation matrices based on partial correlations," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2177-2189, November.
    5. Barndorff-Nielsen, O. & Schou, G., 1973. "On the parametrization of autoregressive models by partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 3(4), pages 408-419, December.
    6. Linton, Oliver & McCrorie, J. Roderick, 1995. "Differentiation of an Exponential Matrix Function," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1182-1185, October.
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    2. Chen Tong & Peter Reinhard Hansen & Ilya Archakov, 2026. "Cluster GARCH," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 44(1), pages 148-161, January.
      • Chen Tong & Peter Reinhard Hansen & Ilya Archakov, 2024. "Cluster GARCH," Papers 2406.06860, arXiv.org.
    3. Archakov, Ilya & Hansen, Peter Reinhard & Lunde, Asger, 2026. "A multivariate realized GARCH model," Journal of Econometrics, Elsevier, vol. 254(PA).
    4. Joe, Harry & Kurowicka, Dorota, 2026. "Random correlation matrices generated via partial correlation C-vines," Journal of Multivariate Analysis, Elsevier, vol. 211(C).
    5. Chen, Han & Fei, Yijie & Yu, Jun, 2025. "Multivariate stochastic volatility models based on generalized Fisher transformation," Journal of Econometrics, Elsevier, vol. 251(C).
    6. Han Chen & Yijie Fei & Jun Yu, 2026. "Multivariate Stochastic Volatility Model with Block Correlations," Working Papers 202638, University of Macau, Faculty of Business Administration.
    7. Ilya Archakov & Peter Reinhard Hansen, 2026. "The Generalized Fisher Transformation: Finite-Sample Properties and Inference," Papers 2606.13864, arXiv.org.

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