Hi there, I want to generate correlated random numbers in the course of a monte carlo simulation.
I always read that Cholesky Factorization requires positive definite correlation matrices. I can�t see the reason why it shouldn�t work for positive semidefinite matices as well! Any insights? I heard about eigenvalue and singular value decomposition as alternative approaches. As I understand it SVD is only the extension of an eigenvalue decomposition for non squared matrices. Is there any other use for SVD within a monte carlo simulation of correlated random numbers? If the Eigenvalue Decomposition yields negative eigenvalues caused by rounding errors or other inconsistencies what is the best method to proceed in an monte carlo simulation? (any literature references?) Since Cholesky, Eigenvalue and SVD only work for normal random variables because their concept is based on the fact that linear combinations of normal random variables are themselves normally distributed I wonder if there are any other methods to induce correlation (either Pearson, Spearman or Kendall) into a monte carlo simulation? Has maybe anyone heard about Stein�s Algorithm that works with latin hypercube sampling and is able to explain it to somebody like me with a rather non mathematical background? Thanks in advance Khaled . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
