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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?

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  • $\begingroup$ 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). $\endgroup$ – Matthew Gunn Jun 6 '18 at 16:37
  • $\begingroup$ Do I need to difference them and then conduct the VAC? $\endgroup$ – user210797 Jun 6 '18 at 20:21
  • $\begingroup$ You may find these time series notes by John Cochrane useful, particularly the end chapter 11.4. $\endgroup$ – Matthew Gunn Jun 6 '18 at 21:35
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    $\begingroup$ Possible duplicate of 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, this and this, among others. $\endgroup$ – Richard Hardy Jun 7 '18 at 9:54
  • $\begingroup$ 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. $\endgroup$ – user210797 Jun 7 '18 at 14:40