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I am currently trying to estimate a VAR(1) model for some variables including inflation. Lets say the VAR model looks like this: $$ X_t = c + \Pi X_{t-1} + \epsilon_t. $$ In this case we can set long-term targets for our variables by transforming the constant term $c$. For instance, if we have inflation in our $X_t$, and we want it to move to the long-term ECB target of 2%, then we can set the constant term in $c$ corresponding to inflation equal to 2.

Now, in my data inflation is not stationary so I estimate my VAR on the differenced series. I was wondering if it is possible to set the long-term target of inflation in levels equal to 2% in such a model, since $c$ now corresponds to the long-term difference.

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  • $\begingroup$ Yes, I'm sorry for responding this late! I was away for two days $\endgroup$ – Pim Sep 23 '18 at 9:20
  • $\begingroup$ No problem at all :) $\endgroup$ – Richard Hardy Sep 23 '18 at 10:28
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If your time series is nonstationary in the sense that it has a unit root, it will not tend to any fixed value over time. Hence, trying to find such a value would not make sense. You either have to change the assumption from nonstationary to stationary or give up the target.

You could also model the process as nonstationary within some interval but mean-reverting once it breaks out of the interval. That would imply very large inflation or deflation would not persist, perhaps because of central bank interventions, while moderate inflation would be approximately free of interventions and would not tend to a concrete value as long as it remains moderate. In such a case, defining a target could make sense.

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  • $\begingroup$ Ah of course, that makes a lot of sense! How would you go about modelling this mean reversion? The VAR would still be unstable in this mean-reversion time interval right? $\endgroup$ – Pim Sep 23 '18 at 9:21
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    $\begingroup$ This would be modelled with some threhold variables to account for the different behaviour within the "nonstationary" interval and outside of it. Within the nonstationary (opposite of mean-reverting) interval, the VAR would be unstable. $\endgroup$ – Richard Hardy Sep 23 '18 at 10:29

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