Diffuse filter and forecasting

I am using diffuse_filter in estimation.
After estimation I did these two procedures independent.

  1. I got predictive density using forecasts saved across draws in the metropolis-subfolder in the FILENAME_forc_point*.mat-files. It looks good.

  2. When I retrieve a space-state representation using output after estimation, oo_.dr.ghx, oo_.dr.ghu and M_.Sigma_e and I forecast the state-space model using Monte-Carlo method the density predictive is some explosive. In this forecast I am using ssm function of matlab which use standard Kalman filter (“no diffuse”) to get the initial state means and covariances. So I suspect the explosiveness is dued to using standard filter.

My question is: ¿should I use diffuse filter to compute the initial state means and covariances to initialize forecast (and respectively, should I use diffuse filter to compute forward recursions too)?

Thanks a lot.

I am not sure I understand. If your model has a unit root, you cannot initialize the Kalman filter with the unconditional variances, because they do not exist. So what do you do in this case?