Re: Data Simulation from Correlation Matrix

Am 07.12.2006 23:46 schrieb Mike - EMAIL IGNORED:
Can someone indicate where I can find the
mathematics and algorithm needed to generate
a simulated data matrix given a correlation
matrix and a random number generator?
Google led me to programs that will do it,
but no adequate explanation.

Thanks for your help.
Mike.


Correlationmatrix (R) ---> (cholesky-decomposition) --> "loadings"-matrix (L)

loadingsmatrix * randomdata ---> correlated data

Say

L*L' = R

and your randomdata are as rowvectors

f1 ........... data ......
F = f2 ............data ......
f3 ............data ......

where F*F' = I ( Identity-mtrix, all correlations=0)

then
z1 ......... data ........
L * F = Z = z2 ......... data ........
z3 ..........data ........

where
Z * Z' = R

The reason is:

Z * Z' = R

(L*F) * (L*F)' = R
L *F*F' *L' = R
L * I *L' = R

L * L' = R


To get L from a given R, you apply cholesky-decomposition

L = cholesky(R)

Gottfried Helms
.

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