A non-stationary VAR is best estimated by a vector error correction model (VECM) should there is at least one cointegrating relation.  In other words, VECM is a dual of VAR under a cointegrated system.  If there is no cointegration, the VAR should be estimated in first difference, or where all variables are stationer. 

A VECM comprises two parts.  The first part is the VAR in first difference.  The second part is the error correction mechanism terms, which represent adjustment process to restore the equilibrium as suggested by the cointegrating relations.  Deviations from the long-run equilibrium would be corrected or pushed back to the equilibrium.  Cointegration itself suggests that co-movement amongst variables would always be established.  The co-movement can be interpreted as a long-run equilibrium condition.  Thus, VECM can be viewed as a VAR with equilibrium restriction.

For technical detail, you may refer to textbooks such as:
Green, W.H (2003), Econometric Analysis (5th edition). Prentice Hall.

Heij, C., de Boer, P., Franses, P.H., Kloek, T, and van Dijk, H.K. (2004), Econometric Methods with Applications in Business and Economics. Oxford University Press.

Hill, R.C., Griffiths, W.E., Lim, G.C. (2011), Principles of Econometrics (4th edition). John Willey and Sons.

Lutkepohl, H. (2005), New Introduction to Multiple Time Series Analysis. Springer.

VECM estimation

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Users can estimate a VECM in i-Regand simply by doing the following steps:

Step 1. Tap on the main menu and select estimate VECM

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Specify endogenous variables, exogenous variables, the number of cointegrating vectors and lag length

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Step 3. Run and see the results

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