On Generating Correlated Random Variables with a Given Valid or Invalid Correlation Matrix

21 Pages Posted: 3 Aug 2004

Date Written: August 2, 2004


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.

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

JEL Classification: C15, C63, C87, C88

Suggested Citation

Mishra, Sudhanshu K., On Generating Correlated Random Variables with a Given Valid or Invalid Correlation Matrix (August 2, 2004). Available at SSRN: https://ssrn.com/abstract=571601 or http://dx.doi.org/10.2139/ssrn.571601

Sudhanshu K. Mishra (Contact Author)

North-Eastern Hill University (NEHU) ( email )

NEHU Campus
Shillong, 793022
03642550102 (Phone)

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