You can see Stock, J. H., and Watson, M. W., 1993, A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems,Econometrica 61,783-820.

Dear Joe,

To the best of my knowledge, we go for Toda-Yamamoto in case of I(2). If you have all I(0), you go for OLS, all I(1) with cointegration go for VECM, all I(1) without cointegration, go for VAR, mix I(0) & I(1), go for ARDL. But for a mix of I(1) and I(2), none of above methods can be used. If you some of the series I(2), if would like to recommend using a different proxy of your variables such as for economic growth we can use gdp growth, gdp growth per capital, gdp current US$, gdp PPP and others. Try using different proxies of variables that are I(2). If, however, you do not have different proxies of your variables, try using transformation of your variables such as log transformation or ratio transformation, then try unit root again.

Best Wishes,

Atif

Muhammed Atif Nawaz is on point

VECM nor VAR can handle the dynamism of I(2) variables

I to recommend for transformation of data log, log difference and ratio as suggested by Muhammad and Ibrahim. Moreover, you can try different combinations of variables in your estimation equation.

I agree with the submissions of both Muhammad, Ibrahim and Vijay, especially on the issue of trying other proxies for the variables with I(2). But, in doing that, examine the appropriateness carefully. If not, go for data transformation either by log or ratio. This again, has to be done with understanding of its operations.

The three variables that are I(0( in first differences can be used I a VECM

If this is meaningful to You . However, the I(2) variables cannot be used.

Best

George K Zestos

In the case of series I [2], the simplest solution is to look at breaking unit root tests. Otherwise, the conversion of series can be considered.