I have to forecast the value-added growth rate of the Italian service sector, and I would like to do that with an ARIMA model with an external regressor. By looking at the dataset at my disposal and the GDP growth rate in the same testing period, I've seen a correlation between the two series.
So, my idea is to analytically verify the correlation (through a cross-correlation function) and then use as an explanatory variable the GDP, for which I also have its projections for the period I am interested in for the forecast.
My doubt is about how much sense this approach has, especially considering that it is more reasonable to think that the causality between GDP and service sector goes the other way around, i.e., the service sector affects GDP and not the contrary.
Also, some references about the discussion on the causality between independent and dependent variables would be more appreciated, thank you in advance.