Variance in 2nd order approximation

[javiergc]

Acording to Dynare Manual, the variable oo_.var is constructed as follows: "After a run of stoch_simul, contains the variance-covariance of the endogenous variables. Contains theoretical variance if the periods option is not present (or an approximation thereof for order=2), and empirical variance otherwise."
I was wondering what is the approximation that Dynare implementes if periods=0 and order=2 in stoch_simul. Could someone please describe how is this is calculated, or simple provide a reference that I can read about it? Thanks!

[jpfeifer]

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)).