Yes, you can. Multivariate statistic for testing the stationarity of a given variable tests the restriction that the cointegrating vector contains all zeros except for a unity corresponding to the designated variable , conditional on there being one cointegrating vector. For instance, the null hypothesis of a stationary CPI implies that the cointegrating vector is (1 0 0 0)'. You may want to see some of my papers in the International Review of economics and finance journal. I can't tell you which one right now. If I can find time I will report back but regardless the above is how it is done.

Hi Dear, a) Must better if u must have all I(0) Stationary, from my point of view( the time must do not affect the model). If one of u variable has a unit root I(1) make a difference, so you have all variables stationaries.b) Before doing the VAR, you need the right lag( use information criteria according to time series-avoid multicollinearity ).

hi, you can use that. you can also use cointegration test/ bound test within the ARDL framework and if there exist cointegration, you can then estimate the short and long run parameters from the ARDL.

Thank you and good luck.

Please see the document attached.

As others say, the Johansen procedure can be applied to a mixture of I(1) and I(0) variables. But each I(0) variable will generate its own vector, and therefore identifying any long-run relationships among the I(1) variables will be more difficult. In your specific case, if there truly are three I(0) and only one I(1) variable, the Johansen test will tend to indicate three vectors, each merely measuring the mean of one stationary variable. This would not be a very meaningful economic result. Meanwhile, the I(1) variable cannot be related in the long run to the other variables. Looking for cointegration with such data will not be productive. If, however, you are relatively uncertain about the individual integration properties of the four variables, the ARDL technique could be the way to go, although correct specification of the left-hand variable will be very important.

Thank you very much all, however I have seen some papers recommend that, to use Johansen test for cointegration all variables must be I(1); Is this right?

We never know for sure whether the variables have a unit root , I(1) therefore Johansen cannot be used when the variables is a mixture. We are only interested in a linear combination of variables (not the variable itself). Please again see my papers in the International Review of Economics and Finance and Journal of Business and Economic Statistics. Both papers are A+

Following what David O. Cushman (up over) said yes you can perform your analysis using both ARDL and JOH estimators. For the ARDL, you can perform PSS (2001) F-test for cointegration to identify your RHS variable. Therefore, the dependent variable must be assumed to be nonstationary where all variables are 0=

Thank you very much, your answers are really helpful. Be blessed

When series are integrated to different orders, autoregressive distributed lag(ARDL) becomes more appropriate.

I would suggest to use ARDL as its more appropriate, Johansen test is were the variables belong to the same order and the sample size is big enough, while ARDL overcomes the issue and you could apply it whether the variables are I(0) or I(I) but not I(2), you can use it for small samples and there is less problem with the endogeneity as it is free of residual correlation. Further, you should bear in mind that it is useful even if the explanatory variables are endogenous Suleyman Abas

Good information, Adelajda.

No please.

You can used that only when the variables are integrated at first difference (I(0)).

Am sorry, i mean I(1) not I(0)

Inflation will potentially be I(1) around structural breaks. I would consider a unit root test that allows for breaks. If it is I(0) around breaks all variables would be I(0). In this case you do not use the Johansen VECM. Instead you use a VAR although you may need to allow for breaks in the VAR.

ADRL will be the most suitable as the variables are both I(0) and I(1).

No please, but you can used ARDL since the stationarity of your variables are mixture of both I(0) and l(1). However, Johansen cointegration is applicable when all the variables are stationary at I(1).

Thanks prof. Asitha L. Gunasekara