This is tricky.
prior_posterior_statistics_core.m creates the forecasts.
computes the deciles. In principle, you can easily access the saved forecasts across draws in the metropolis-subfolder in the FILENAME_forc_point*.mat-files.
At the current stage, forecasts are from the DSGE-model, not the VAR. It is on our to-do list, but we haven’t managed to do it yet. See github.com/DynareTeam/dynare/issues/819. A year ago a user started working on it, but it went nowhere as far as I know. But maybe it is helpful: [Writtng a dsgevar_forecast function)