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Generating random correlation matrices based on partial correlations

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  • Joe, Harry

Abstract

A d-dimensional positive definite correlation matrix R=([rho]ij) can be parametrized in terms of the correlations [rho]i,i+1 for i=1,...,d-1, and the partial correlations [rho]iji+1,...j-1 for j-i[greater-or-equal, slanted]2. These parameters can independently take values in the interval (-1,1). Hence we can generate a random positive definite correlation matrix by choosing independent distributions Fij, 1[less-than-or-equals, slant]i

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  • Joe, Harry, 2006. "Generating random correlation matrices based on partial correlations," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2177-2189, November.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:10:p:2177-2189
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    References listed on IDEAS

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    1. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
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    Cited by:

    1. Ng, Chi Tim & Joe, Harry, 2010. "Generating random AR(p) and MA(q) Toeplitz correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1532-1545, July.
    2. Kirschstein, Thomas & Liebscher, Steffen & Becker, Claudia, 2013. "Robust estimation of location and scatter by pruning the minimum spanning tree," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 173-184.
    3. repec:taf:jnlbes:v:34:y:2016:i:3:p:416-434 is not listed on IDEAS
    4. Daniels, M.J. & Pourahmadi, M., 2009. "Modeling covariance matrices via partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2352-2363, November.
    5. Joseph Romano & Azeem Shaikh & Michael Wolf, 2008. "Control of the false discovery rate under dependence using the bootstrap and subsampling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(3), pages 417-442, November.
    6. 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.
    7. 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.
    8. Smith, Michael Stanley, 2015. "Copula modelling of dependence in multivariate time series," International Journal of Forecasting, Elsevier, vol. 31(3), pages 815-833.
    9. Sylvia Gottschalk, 2016. "Entropy and credit risk in highly correlated markets," Papers 1604.07042, arXiv.org.
    10. Kurowicka, Dorota, 2014. "Joint density of correlations in the correlation matrix with chordal sparsity patterns," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 160-170.
    11. Christopher J. Bennett, 2009. "p-Value Adjustments for Asymptotic Control of the Generalized Familywise Error Rate," Vanderbilt University Department of Economics Working Papers 0905, Vanderbilt University Department of Economics.
    12. Madar, Vered, 2015. "Direct formulation to Cholesky decomposition of a general nonsingular correlation matrix," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 142-147.
    13. Lewandowski, Daniel & Kurowicka, Dorota & Joe, Harry, 2009. "Generating random correlation matrices based on vines and extended onion method," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1989-2001, October.
    14. Steffen Liebscher & Thomas Kirschstein, 2015. "Efficiency of the pMST and RDELA location and scatter estimators," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 63-82, January.
    15. Gottschalk, Sylvia, 2017. "Entropy measure of credit risk in highly correlated markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 11-19.
    16. Wang, Y. & Daniels, M.J., 2013. "Bayesian modeling of the dependence in longitudinal data via partial autocorrelations and marginal variances," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 130-140.

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