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On generating correlated random variables with a given valid or invalid Correlation matrix

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Abstract

In simulation we often have to generate correlated random variables by giving a reference intercorrelation matrix, R or Q. The matrix R is positive definite and a valid correlation matrix. The matrix Q may appear to be a correlation matrix but it may be invalid (negative definite). With R(m,m) it is easy to generate X(n,m), but Q(m,m) cannot give real X(n,m). So, Q has to be converted into the near-most R matrix by some procedure. NJ Higham (2002) provides a method to generate R from Q that satisfies the minimum Frobenius norm condition for (Q-R). Ali Al-Subaihi (2004) gives another method, but his method does not produce an optimal R from Q. In this paper we propose an algorithm to produce an optimal R from Q by minimizing the maximum norm of (Q-R). A Computer program (in FORTRAN) also has been provided. Having obtained R from Q, the paper gives an algorithm to obtain X(n,m) from R(m,m). The proposed algorithm is based on factorization of R, yet it is different from the Kaiser Dichman (1962) procedure. A computer program also has been given.

Suggested Citation

  • Mishra, SK, 2004. "On generating correlated random variables with a given valid or invalid Correlation matrix," MPRA Paper 1782, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:1782
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    References listed on IDEAS

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    1. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    2. Pandu Tadikamalla, 1980. "On simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 45(2), pages 273-279, June.
    3. Al-Subaihi, Ali A., 2004. "Simulating Correlated Multivariate Pseudorandom Numbers," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 9(i04).
    4. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    5. Todd Headrick & Shlomo Sawilowsky, 1999. "Simulating correlated multivariate nonnormal distributions: Extending the fleishman power method," Psychometrika, Springer;The Psychometric Society, vol. 64(1), pages 25-35, March.
    6. Montserrat Ferré, 2004. "The Johansen Test and the Transitivity Property," Economics Bulletin, AccessEcon, vol. 3(27), pages 1-7.
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    More about this item

    Keywords

    Positive semidefinite; negative definite; maximum norm; frobenius norm; correlated random variables; intercorrelation matrix; correlation matrix; Monte Carlo experiment; multicollinearity; cointegration; computer program; multivariate analysis; simulation; generation of collinear sample data;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • C82 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Macroeconomic Data; Data Access

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