Cointegration test is used to check long run relationship.if there is presence of Cointegration vector; you can do Vecm; otherwise apply Engle granger test.Vecm is applicable for var models;so is Cointegration.  You can use var model even for 2 variables. 

Thank you mousumi

The Johansen cointegration test helps you find any integration relationship in the long-run between variables. If you find cointegration vector by using your test, you have to apply Vector error correction approach. If you do not find any cointegration vector, then you have permission to use VAR model. Besides, you can use Granger causality test to find any short-run relationship between your variables.

Thank You Ehsan.

What if I use Johansen and didnt apply the VECM but apply the VAR instead? what will happen in this case ?

im little bit confused on the error correction model, I didn't manage to figure the purpose of doing it .. is it for getting the long run relation or the correcting the error to get the short run relation from the long run ?

and what is the difference between regressing the variables with its difference and the error correction model .. it seems the same for me

VAR models can only be used for stationary variables. So the first thing to do is to check if your variables are stationary or not. If they are stationary, then you can apply a VAR on the original data you have. Cointagration will not make any sense here.

If they are not stationary, then you should check if they are cointegrated with the Johansen tests. If they are cointegrated, you should fit a VECM. If they are not cointegrated, you should fit a VAR on the first difference of the variable.

I hope this helps! Good luck with it!

Thank you Severine,

I think yes, it seems it becomes clear now

You can use Johansen estimator to find whether you have one or more cointegrating vectors. Let's say that you have one cointegrating vector, then you can normalize on that vector by multiplying by -1 and save the residuals. 

Then, use the residual as your Ecm term (i.e. Ecm(-1). Now you can run an error-correction model. For instance,  Dy c Ecm(-1) Dy lags Dx{0, 1 } lags and so on.

***D prefix stands for first difference and { 0 1} implies current and one-period lag.

I think that Engel and Granger residual based approach can test for cointegration just as Johansen. The difference between the two  however, is that Johansen tests a system and can report more than one cointegrating vectors while EG tests only a single equation. Also, the precondition in both cases is that the variables must be integrated of order 1. Then like Narjis pointed out,  if there is cointegration,  VECM which is a restricted VAR can be applied otherwise an unrestricted VAR is applied.  the very essence of error correction is to show speed of adjustment to long run shocks and dynamics.  that's my take on the matter

Johansen and Juselius (1990) showed that the rank ( r ) of Π matrix

is equal to the number of cointegrating vectors in the system. If it has full

rank i.e. r = p it is said that there are p cointegrating

relationships and that all variables are I(0). If the rank r = 0 then it implies that the

sequences are unit root processes and there is no cointegration and the appropriate

model is a VAR in the first differences involving no long run element. If the rank

is reduced [1≤ RankΠ ≤ ( p −1) ], even if all the variables are individually I(1), the

level based long run component would be stationary. The appropriate modelling

methodology here is the Vector-Error Correction Model (VECM).

Kalu & Mousumi,

Engle and Granger (EG) method is for 2 variables (bivariate), whereas Joh method is for more than 2 variables. EG cannot detect more than one cointegration and it is impossible to test the validity of hypothesis about the cointegration vector. It also requires 2 step so that errors from step 1 enters step 2 which makes results unreliable.. Moreover, it cointegration tests (e.g. ADF) lacks power. Then there is a problem of normalization with EG. I conclude by saying that EG differs significantly from the Johansen estimator. Further, the very essence of error correction model is to obtain not only the speed of convergence to equilibrium but to make statements concerning the short-run parameters. Also, it provides albeit  an alternative  way to test for cointegration.        

Thank you all 

Mr. Chuck A Arize, I can understand from what you said  that I cannot use Johansen for two variables .. but at the same time engle granger is not reliable if i use it. 

Yes, if you have two variables, you can use Engle and Granger, but you have to determine which variable is going to be the dependent variable. It possible to choose the wrong one. When you use Johansen even for 2 variables, it is possible to identify which variable is the dependent variable. In the Joh case, you can test almost everything. This is not the case with Engle-Granger

Thank you Chuck 

Hey Narjis;

Thank you!!

Thank you Pandelis

Employing OLS regression after the cointegration tests are perfomed and spurious regression rejected is a common mistake. Application of the OLS estimator on nonstationary time series provides biased coefficients, even we don’t expect spurious regression. And the rest was already answered by others above.

@ Please Svatopluk OLS yields unbiased coefficients. The problem is not with the estimated coefficients. They are still consistent and unbiased. The problem is with the t-values.

Good reaction! You are right, the problem is with nonstandard distribution of t... Stock and Watson (1993, Econometrica)

This should help Article A Drunk and Her Dog: An Illustration of Cointegration and Er...

Cheers!