Background: I working on how GDP is affected by CPI, investment,consumption and commodity price. I am working with time-series
Problem: I tried to regress based on log values of all but this resulted in residuals being heteroskedastic and also R-squared was equal 1.0 which I had reservations about (something just didn't feel right). I then decided to change it by regressing log difference of all variables. The results were good with residuals being near perfect homoskedastic as well as stationary though not normally distributed but found some papers that argue normality may not be a problem.
My question is whether it's a good idea to pursue this further? I searched the internet for some answers but found nothing really so any opinions would really be helpful or any links to any research papers that might be useful
I am using Stata to do regression.