For a project I am doing I need to simulate the balance sheet of a pension fund. In order to do so I also need to simulate euro inflation. Since my inflation data is non-stationary, I model it using the differenced data. Since this means that the level data of inflation will take on extreme values in the future, I have the following idea:
Since I use a VAR model, I can influence the long-term average of the differenced inflation. I want to set this long-term average such that in the long-run it reaches the 2% ECB target. I do this by calculating the difference between the ECB target and my last observation, and divide it by the total number of timesteps until the 'long-term' is reached. Currently I use 40 years, but this is an arbitrary number.
Now my question is, what is a reasonable number of years to use as 'long-term' in this context?