Your simulation has two dimensions.There are N=1000 simulations with say T=2000 time periods. Each of the N simulated series will be based on a different parameter draw from the posterior (but sampled with replacement). At the same time, for each n in N, the stochastic shocks for each t in T are drawn randomly from the shock distribution based on the current parameter set. You could in principle fix the random number generator seed to avoid random chatter, but this is not done by default.
Thank you Professor!
That is useful to know when it comes to application .
kind regards