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Do VAR and VEC require no unit-roots? I have three variables where two are difference-stationary (unit roots) and one is trend-stationary (no unit root). The three of them are cointegrated.

Questions:

1) Can I conduct VEC in the presence of unit-roots? 2) If yes, should I difference my variables to make them stationary? 3) Should I be conducting the Johansen test on differenced variables?

user210797
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  • The basic idea of VEC is that if $x$ and $y$ are cointegrated, then a VAR on $\Delta x$ and $\Delta y$ should have an additional term reflecting that $x$ and $y$ can't drift too far apart in levels (because they share the same unit root). – Matthew Gunn Jun 06 '18 at 16:37
  • Do I need to difference them and then conduct the VAC? – user210797 Jun 06 '18 at 20:21
  • You may find these [time series notes by John Cochrane](http://faculty.chicagobooth.edu/john.cochrane/research/papers/time_series_book.pdf) useful, particularly the end chapter 11.4. – Matthew Gunn Jun 06 '18 at 21:35
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    Possible duplicate of [VAR or VECM for a mix of stationary and nonstationary variables](https://stats.stackexchange.com/questions/148994/var-or-vecm-for-a-mix-of-stationary-and-nonstationary-variables). Check out also the linked questions on the right panel of that thread, you will find several closely related ones, e.g [this](https://stats.stackexchange.com/questions/56447/), [this](https://stats.stackexchange.com/questions/193324/) and [this](https://stats.stackexchange.com/questions/194469/), among others. – Richard Hardy Jun 07 '18 at 09:54
  • Thanks everyone for your help! My last question is whether unit roots really matter in VAR/VEC. If some or all of my variables are trend-stationary, can I still use VAR? If they all have unit roots, can I (after differencing)? I ask because it seems that it's not unit roots that matter for VAR, but that the variables are I(0) or I(1) differenced once, i.e. stationary. – user210797 Jun 07 '18 at 14:40

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