Iteratively generating synthetic time series using saved residuals as forcing variables

I have run a 6 variable VAR(1) with a 7th variable which is exogenous and saved the residuals as well as the coefficient estimates. I then drew a sample of these residuals with replacement and would like to use this sample of residuals with the coefficient estimates that I saved in the first step to create synthetic time series for the 6 variables of interest.

How can I implement this last step? I thought of using "predict" to generate linear predictions for each of the variables as follows:

predict allsher_d_pred, equation(#1)
predict rr1m_d_pred, equation(#2)
predict djiba3mma_d_pred, equation(#3)
predict djiba3m_d_pred, equation(#4)
predict allshlogdp_d_pred, equation(#5)
predict spread_d_pred, equation(#6)

and then using "generate" as follows:

gen allser_d_syn = allsher_d_pred + res1


where res1 is the synthetic series of residuals created using the saved residuals of the first equation of the VAR.

However I do not think this does what I want. I think this just takes the linear prediction and adds or subtracts the residual with the same index from the synthetic series. Am I mistaken?

What I would like to do instead is start by determining the second value for the first variable in the VAR (which I named allsher) using the first value of the 6 variables in the var weighted by the corresponding VAR coefficient estimates saved in the first step and adding the residual indexed 2 (corresponding to the second period).

I would like to do this for all 6 variables and then use these synthetic values and the residuals indexed 3 (corresponding to the third period) to determine the 3rd value for the six variables and so on..

How may I do this efficiently?

Any help would be much appreciated!