Suppose, all variables are I(1), except one. The variables, which are I(1), are also I(2). One variable, which is neither I(0) nor I(1), is I(2). Hence, all the variables are now I(2). All the considered variables have same order of integration. Can we proceed to Johansen cointegration test? Should we consider ARDL model in this case?
to conduct johansen cointegration, all the variables must be integrated at the same order. in your case, one variable is integrated at 2nd order and remaining variables are integrated at 1st order. so, the basic condition is not satisfied.
if a variable is integrated at 1st order, it does not make sense to compute the stationarity at 2nd order. even if we do it, definitely, it will be stationary at the higher orders.
if the particular variables is not so important, you drop the variable or you substitute some other variable which may integrate at 1st order.
further discussion in this regard is most welcome.
The answer to your questions is "NO". You cannot proceed to Johansen cointegration if you have any of your series I(2).
Best wishes,
Atif
There is an I(2) cointegration test by Johansen. Refer to the following papers:
Johansen, S. (1995). "A Statistical Analysis of Cointegration for I(2) Variables". Econometric Theory, 11(1): 25-59.
Johansen, S. (1997). “Likelihood analysis of the I(2) model”. Scandinavian Journal of Statistics, 24:433-62.
Paruolo, P., and Rahbek, A. (1999). “Weak exogeneity in I(2) VAR systems”. Journal of Econometrics, 93: 281-308.
The above approach is built in 'gretl', which is available for free. It's a bit complex but quite easily implemented.
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