Tentative ARIMA models for forecasting

Question

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 = ...?

Answer 1

I just looked at the difficulties you seem to have with your ARIMA(0,0,1) model (or is it ARIMA(0,1,1), since you mention differencing?). I'd strongly suggest you compare your model to some very simple alternatives, which surprisingly often are quite competitive with ARIMA and other more complex methods.

For instance, an overall mean is an ARIMA(0,0,0) with nonconstant mean, and a naive random-walk forecast is ARIMA(1,0,0) with AR(1) coefficient $\phi_1=1$, so both are ARIMA models as you require.