At `order=1`

, the solution to your model has a the form of a linear state-space model. This can be used to analytically compute the endogenous moments. See e.g. Hamilton (1994): Time Series Analysis. This is what Dynare does when you request theoretical moments (`periods=0`

). In case of `order=2`

, Dynare provides a second-order accurate approximation to the true second moments based on the linear terms of the second-order solution (see Kim, Kim, Schaumburg and Sims (2008)).

If you specify periods>0, Dynare will instead simulate data series based on the perturbation solution to your model and compute the moments of these simulated series.