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I have one dependent variable and 5 exogenous variables. I do not wish to make a decision on the order of integration of my dependent variable and 3 of the 6 explanatory variables. I also do not want to decide on cointegration between the variables that are possibly I(1). For the two remaining explanatory variables I am quite sure that they are stationary. It is precisely the coefficient estimates to these two I(0) variables that I am interested in.

My questions: when I regress the dependent variable on my 5 explanatory variables, can I perform inference on the estimated parameters to my two I(0) variables? Can the estimates to I(0) variables be spurious because of (a) the (correct or incorrect) inclusion of I(1) variables, or (b) because of the dependent variable being integrated of order 1?

Thank you trubador for the link. I'll go for the ARDL-option you suggest in the thread you linked to. VAR would not make much sense since all of my explanatory variables can be expected to be exogenous.

I'm still interested to know whether or not regressing an i(1) variable on other, possibly independent, i(1) variables and on i(0) variables produces correct estimates for the coefficients to the i(0) estimates. In "Spurious regressions with stationary series" by Granger, Hyung, and Jeon (1999), I found simulation results claiming that regressing an i(1) variable on a stationary but autocorrelated variable with autoregressive paramater =0.5 yields spurious results in more than 20% of the cases. No spurious results seem to emerge when there is no autocorrelation in the I(0) variable. However, this doesn't answer my question of whether or not the inclusion of i(1) variables (whose coefficients may be spuriously significant) changes this result.