I believe that the optimal cointegration test you should use based on your description of the variables is the ARDL bounds test, since it can be applied when your variables are a mix of stationary and integrated of order 1 variables. Note that you have to make sure that your non stationary variables are I(1) and not I(2) or + before using it !

Good luck

Thanks...

You have to test for the unit roots for the non-stationary variables at first difference to be sure the variables are I(1) and not I(2).

If the unit roots test confirm that your variables are I(1), then you can go ahead and estimate ARDL using both the I(0) and I(1) variables. Also, check for cointegration (i.e. Long run relationship). Additionally, ensure that the speed of adjustment is negative, less than 100% and statistically significant. More so, perform the various diagnostic test (serial correlation, hetroskedasticity, normality, functional form, and stability test using the CUSUM and CUSUM of Squares)

Thanks @Prince

Is ARDL a type of cointegration test? And also does using ARDL mean i cant use OLS ?

since you have a mix of stationary and nonstationary variables, and more importantly, that the dependent variable is nonstationary, you need to make sure that the nonstationary variables are I(1) and not I(2), then you can use ARDL bounds test approach to cointegration.

@Temitope, thank you, after using the ARDL can i then use OLS?

ARDL model is an OLS based model. A dynamic error correction model (ECM) can rather be derived from ARDL through a simple linear transformation.

@Temitope, how do i find the relationship of all my variables. Do i use the normal OLS?

Alpha Emmanuel i am not too sure i understand your question, kindly elaborate.

OLS can be used when all the variables are I(0)

Follow the article I have just attached along with this reply. It is one of my published articles and use The Nonparametric Diks-Panchenko Causality Test.

Kind regards