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I have seven series with two of them stationary at level; and the other five non-stationary at level.

However, all of them are stationary at first difference. I have the following questions:

(A) Should I still run a cointegration test or can I just proceed with VAR?

(B) Should I use the series at level or at first difference for the VAR?

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  • $\begingroup$ What do you mean by stationary at I(0) or stationary at I(1)? A series can be stationary at level or stationary at first difference, for example. A series can be I(0) or I(1). What you write is nonstandard. $\endgroup$ – Richard Hardy May 9 '18 at 15:30
  • $\begingroup$ Ah yes! Thank you for the correction. I changed the question accordingly. $\endgroup$ – narujapica May 9 '18 at 15:35
  • $\begingroup$ Related question: Cointegration regression for stationary series. $\endgroup$ – Richard Hardy May 10 '18 at 8:51
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By proceeding with a VAR in levels, you would miss a transparent representation of the system due to not having explicit error-correction terms as in a VEC model, but the coefficient estimates should be consistent.

By proceeding with a VAR in first differences, you would have two over-differenced series (with the resulting integrated MA(1) patterns) and missing error-correction terms (omitted variables).

What you should do is build a VEC model with the five cointegrated series and add the two stationary series at levels (both as dependent and independent variables, thus two extra equations and additional lagged terms in each equation corresponding to the two series).

See also "VAR or VECM for a mix of stationary and nonstationary variables".

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