I'm finding myself confused and unable to find good answers to what seems to be a simple question:

I have (monthly) time series data on the prices of several products (for example call them: y x z). The model I wish to fit is:
y_t = a + bx_t + cz_t + e_t

The question is: do I need to test for stationarity just for y or also for x and z?
if the explanatory variables should be stationarity, is there someway to conduct a test for stationarity of all terms at once, or is stationarity of each variable separately, sufficient to establish stationarity of the model i wish to estimate?

And how do I go about doing these tests in stata? there are a lot of stationarity tests in stata, but they are restricted to testing one variable only - and I'm not sure that's appropriate.