Add artificial/dummy observations (simulated from the underlying DSGE Model) before/above or after/below actual observations

Dear Johannes,
I have estimated a DSGE model, and simulate artificial/dummy observations from the DSGE model, then I plan to combine artificial/observations (size of artificial observations multiply by a scaling factor) with actual observations so as to estimate a DSGE-VAR model, I am wondering that should I put these artificial/dummy observations, which are simulated from the DSGE model and we take a sample size (scaling factor) of artificial observations, before/above or after/below the actual observable variables so as to estimate a DSGE-VAR model?
Thank you very much and look forward to hearing from you.
Best regards,

I am not sure I understand. The idea is usually to factorize the joint likelihood as the product of the likelihood of the two samples. If you want to implement that by by concatenation, you need to be careful due to the lag structure. The lags must not be constructed from a different sample. If you make sure that is the case, the ordering does not matter as the product is commutative.