My data are consisted of 3 exogenous variables (TFIN, SR, and INF), and 1 endogenous variable (GDP). TFIN and INF are stationary at I(0), GDP is stationary at I(1), and SR is stationary at I(2). I have run Johansen-cointegration test and it shows that data are cointegrated. Then, it is true if I run it through VECM ? Thank you
If the data are truly of different order of integration (truly = this is not due to low power of DF/ADF tests), then it is pointless to perform Johansen analysis.
It will give you random results as it is aimed at I(1) case.
However, in case of I(1) and at least two I(2) variables, you could try multi-cointegration. I(2) variables could cointegrate by 1, so that you could get I(1) combination of I(2) variables which in turn may cointegrate with the remaining I(1) series.
I don't have any experience with such case, but I am aware of the possibility.
One of the most important prerequisite to model estimation is the visualization of the individual variables with the view to understanding the DGP of each variables. Some variables at trend stationary while some have structural breaks at one point or another, some are even seasonal in nature. The visualization might probably suggest the appropriate unit root test and method. ADF and PP are usually affected by sample size and also not robust to structural breaks.A trendy variable probably requires the use of KPSS or DF-GLS. I would suggest you plot your variables to ascertain if there's a marked break in the series which might be a pointer to structural breaks. I(2) variables are somehow rare especially in macroeconomic variables. As noted by Prof @Baranowski, its not possible to use Johansen co integration for series of different order of integration as the assumption only works for series with similar level of integration. You might want to re test the I(2) variable which might probably be an I(1) but due to the weakness of ADF in handling series with structural breaks made it I(2).
This is not the call to test co-integration, because the order of integration is different.
In this case, it is necessary to use the VAR model because there is an integrated series of order 2.
Sure, thank you so much for your answer mr Hamid Muili and Safae Misry
no u cannot use vecm but consider ARDL cos in VECM all variables must be endogenous.
There are misunderstandings in the answers given to this question
I don't know what your variables are so it is difficult to give advice. Does it make sense to include the first difference of your SR variable (which is I(1)) in the analysis? You do need to check in your textbook the meaning of stochastic trends and how cointegration implies that a set of cointegrated variables contain the same stochastic trends. If you include an I(2) variable and it is truly I(2) then it can not explain an I(1) variable.
Dear Firstly I Zara,
Since the order of cointegration of the variables are different, there is no need for cointegration.
To use VECM, all your variables should be endogenous, since they are not then consider ARDL ma.
Regards
Dear Firsty Izzata Bella ;
In your case you need to use Toda and Yamamoto (1995) Augmented Granger Causality. This is the right econometric technique to be used when you have series of I(0), I(1), I(2). Best regards.
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