# Replace a variable I (0) by an I (1 ) to test cointegration

I'm building a VAR to model the relationship between production of the economy and some of its determinants. One of the endogenous variables of the model is inflation as a measure of macroeconomic stability. However, all my variables are I (1) except inflation which is stationary. I want to test cointegration by Johansen test, but I can not because inflation is I (0). It occurred to me that instead of using inflation is I (0), using the CPI (consumer price index) is I (1). Someone had this problem, or something related. Please, I can give his opinion. Thanks for the help

PS: The method Pesaran, Shin and Smith to contrast cointegration in variables of a different order of integration is not an option.

When modelling economic time series it is actually common to use the price index, such as the CPI, $p_{t}$. Then the first difference can be considered as inflation, $\Delta p_{t}$ so using the CPI is in fact more appropriate than using inflation. On another note then there is nothing wrong with modelling $I\left(0\right)$ and $I\left(1\right)$ variables jointly in a CVAR framework. It would just mean that the stationary $I\left(0\right)$ variables could be considered as an equilibrium relationship on their own.
Another thing to note is that often prices are viewed as $I\left(2\right)$ and hence inflation will be $I\left(1\right)$. If this is the case then it is more apropriate to start out with a CVAR $I\left(2\right)$ model but this is not applicable to you since you state that inflation is $I\left(0\right)$.