I am doing out-of-sample forecasting with ARIMA and derived one model (0,0,1) with auto.arima on a differenced time series. The series is daily observations over the course of 3 years. I would like to derive one more model (it has to be ARIMA) to forecast with to be able to compare the accuracy. I have tried to find alternative models with loops that finds the lowest AIC and BIC with the result of an (0,0,1). Also when plotting the residual there is a small significant correlation at lag 15, but adding that lag will not make a good alternative model.
1.What other ways are there to find tentative forecasting models? It needs a theoretical ground and I am not utilizing machine learning.
2.And when reporting the final model is it praxis to report a differenced model (ex ARIMA (0,0,1) y' = ...., or should one report that it is a ARIMA(0,1,1) with y = ...?