Second Order Moments

Dear all,

I want to compare the second order moments of the data and the model implied statistics but I am not sure about the method. My understanding is the following:

(1) To get the second order moments (standard deviations or auto-correlation ) of the data, I just calculate them based on the HP filtered data which is just used for estimation.
(2) To get the moments for the model, I should simulate the model at the posterior means and check the standard deviations and auto-correlation.

My questions are:

(1) are there any restrictions or rules for such a simulation? I mean the choices for the number of periods or replications, and how many observations should I drop?
(2) I find that the standard deviations and auto correlation given by the simulation are much different from what I get from the data. I am wondering whether I should do some transformations for these second order moments to get them close to those in the data.

I know this problem is quite basic. If you know the answer, please help…Thanks very much!