Question about my GDP Model

[airdog93]

Greetings of the day!!!

If I build the model for GDP: dlog(gpd_sa) c dlog(pcr_sa) dlog(itr_sa), do the GDP components, namely consumption and investments, need to be lagged, i.e., should the model be written as: dlog(gpd_sa) c dlog(pcr_sa(-1)) dlog(itr_sa(-1)) or is the original form fine?

I noticed that in this model: dlog(gpd_sa) c dlog(pcr_sa) dlog(itr_sa) dlog(gpd_sa(-1)) ar(4) ma(1), the MAPE is minimized when I make forecasts. The sample I have is 2000Q1–2022Q3. The GDP data is quarterly, so if I decide to add GDP lagged by one quarter in the equation, do I need to change the sample to 2000Q2–2022Q3?

I got heteroskedasticity according to the White test. I tried to use HAC, but only ARMA and ML appeared. From what I read online, when I use ARMA, HAC is disabled. To correct for White heteroskedasticity, can I run: arch(1), garch(1), and then stop checking White and ARCH separately, instead relying only on the ARCH-LM test?

Thank you in advance!

Wish you all the best