I have built a SARIMA model for forecasting monthly income data in python using the pmdarima library. It gives a confidence interval for each monthly prediction. I want to combine the data til the end of the year to get a yearly prediction and confidence interval which is simple assuming data within the same 12 month period is independant and follows a normal distribution.
If all non-seasonal variables of the SARIMA are zero for example SARIMA(0,0,0)(1,1,0), does this imply each prediction within the same 12 month period is independent?
For example would the prediction for March 2020 be independant of the prediction for February 2020?
If not why is this so when all non seasonal variables are zero?