Re: How Do I generate correlated random variables without using Cholsesky Decomp


"karvala" <karvala21@xxxxxxxxxxx> wrote in message
news:e4af66$5bf$1@xxxxxxxxxxxxxxxx
Hi karvala,
Thanks for the help. But I run into the same problem again.
mvrnd requires that the correlation matrix be semi positive definite.
Though this is an improvement over cholesky which requires positive
definite correlation matrices, this still means that I cant generate
RVs with arbitrary correlations.

Thanks
Vivek

Yes, because as Simon Durrant correctly says, a correlation matrix must be
positive semi-definite by definition. A proposed correlation matrix that
isn't would not be logically consistent. For example, take the matrix:-

1 -1 -1 -1
-1 1 -1 -1
-1 -1 1 -1
-1 -1 -1 1

This is not positive semidefinite, and cannot be a correlation matrix.
You can easily see this, because if variables 2&3 are completely
negatively correlated, and variables 2&4 are completely negatively
correlated, that would imply that variables 2&4 are perfectly positively
correlated. The matrix, however, claims that these are also completely
negatively correlated, which is not possible. Hence it is not a valid
correlation matrix. In general terms, if any row (or column) sums to a
negative number, it cannot be a correlation matrix. If all rows or
columns obey this condition, you have a positive semidefinite matrix,
hence the requirement.


"that would imply that variables 2&4" sorry, typo: I meant "that would imply
that variables 3&4"


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