cointegration with different levels of stationary

[ranai]

sorry to add to this mayhem but I am also suffering from the same problem. I've read through the other posts but I can't make sense of most of the detailed ones. I have 5 variables 4 of which are I(2) and one which is I(0).

Firstly can I still use the johansen test or is that only for I(1) and I(0) variables?

Secondly can I still do a Granger Causality test, given that I find cointegration through some other test?

and finally given that I have multi cointegration what can I do to test for cointegrating relationships? Will the ARDL test it correctly, and if so how can I do so on eviews? There isn't a lot of reference material out there on how to tackle multicointegration on eviews so this is my only shot really. I was under the impression I could use Johansen even though I had mixed difference variables and have proceeded on learning and running a VECM with results. My dissertation is unfortunately due soon and I have based and written my empirics on something which basically doesn't work so I am in a flurry trying to fix my cointegration test and still use a VECM if I can.

Would really appreciate the help soon if anyone has the ability to do so. Many thanks

[sid]

Dear All,

This reply is to correct "Hassan" which is also "khnaqvi" suggestion of the Pesaran et al. (2001) bounds testing to cointegration approach within the Autoregressive Distributed Lag (ARDL) framework in handling the I(2) variables. Yes, the bounds testing to cointegration procedure may use to test the presence of long run equilibrium relationship even when the order of integration is mixture. Nevertheless, this definition is imperfect. Strictly speaking, If the explanatory variables are integrated of order two, I(2), and/or the dependent variable is not I(1) process, then the bounds testing approach cannot be used to determine the existence of cointegrating relations as the critical values provided is only for mixture between I(0) and (1) processes. This is well documented in the published articles used the bounds testing approach. In this sense, we still need to test the degree of integration to ensure that the dependent variable is I(1) and none of the explanatory variables is greater than I(1) process.

To find the presence of cointegration for the case of I(2) variables, the concept of multi-cointegration is useful to us. In addition, it is plausible to check the presence of multi-cointegration within the Engle-Granger two step approach and also Johansen cointegration test. You may refer to Enders (2004) Applied Econometrics Time Series, 2nd Edition for more details.

To "mab", do you serious examined the order of integration for each series under consideration? What do I mean is how many conventional unit root tests you have considered? According to Nelson and Plosser (1982) - Journal of Monetary Economics, most of the macroeconomics variables are I(1) process, however Perron (1989) re-examine the dataset used by Nelson and Plosser (1982) and Perron found that some of the variables is I(0). I suggest you to re-investigate the order of integration before proceed to the next step which is multi-cointegration. Is your unit root test result consistent to the earlier studies? If not do you suspect the validity of your result? Therefore, relying on one statistically approach is not a good guidance for a researcher to make a conclusion for his/her research because nothing is perfect and gap or lack always appear.

Anyway, I hope my suggestion and explanation helpful to you all.

Thank you,

Warmest regards,
tcfoon

sorry to ask a stupid question but i have seen many studies using ardl approach with I(0) dependant variable and i am also using stationary dependant . so what should i do now?