# Should simulation from a student-t copula distribution yield the input correlation matrix

I am using mathematica to simulate random variates from a student-t copula distribution. Assuming that I input in the correlation matrix R, after generating a certain number of random variates, should the correlation matrix formed by my simulations fit to the initial correlation matrix R.

My results have indicated lack of fit, but I am unsure if this is true or if I am simply not generating enough results.

Is there any theory behind this?.

• Are you using Gaussian copula? Are we talking about Pearson correlation? Dec 16 '14 at 22:24
• I am not using the Gaussian copula, but the student T copula. I could easily switch between the 2. And yes, we are talking about the standard Pearson correlation
– Jim
Dec 16 '14 at 22:36
• Copulas convey only and entirely the dependency structure. Correlation matrices convey information about a mix of linear dependence ($E(XY)\lesseqgtr E(X)E(Y)$) and marginal distributions. So probably you have some poor specification of the marginal distributions. Dec 16 '14 at 23:23
• Great insight Horst. What if my specified marginal distributions are known to be correct (say, based on empirical information). What other factors could cause the discrepency between the input correlation matrix and the simulated correlation matrix.
– Jim
Dec 16 '14 at 23:43
• How are you judging that 'lack of fit'? Dec 17 '14 at 1:57