Impulse Response Functions R: Transitory Shocks for Non-Stationary Data

I am working on generating Impulse Response Functions via the VECM and VAR models, an hence have data that is non-stationary in levels, stationary in first differences and cointegrated. My IRFs generate responses that all do not revert to the zero line in the long run, and shocks do not decay or flatten over time.

A paper by Hoesli et al. (2015) has also generated IRFs via the VECM for similar variables I am using, and hence also has used data that is non-stationary in levels. See IRF graphs attached.

My question is: How has this paper generated responses in their IRFs that all revert to zero in the long run, if the variables used are non-stationary? Would you not expect responses to be permanent in nature where non-stationary data is used?

Like the example paper, I have also deflated index variables and used them in natural log form.

• Do you need the R tag? – Richard Hardy Sep 12 '19 at 16:49
• You're right its not really necessary, removed – James Sep 13 '19 at 0:12