Variance Decomposition

Dynare uses standard time series techniques for linear state space models. For forecast error variance decompositions, see Lütkepohl (2005): New Introduction to Multiple Time Series Analysis, Chapter 2.3.3.
For the shock decomposition, A Kalman Filter/Smoother Approach is used. See Durbin/Koopman (2012): Time Series Analysis by State Space Methods or Hamilton (1994)