I have a time series that I'm fitting models to, using R.
I have chosen an ARIMA model based on minimising the AIC_C values.
The ETS model (ets()) was chosen based on minimising the model accuracy errors and the rolling forecast accuracy errors (in the latter, I chose the best 3 from the former, and the ets() model was competing against hw() and hw() with multiplicative seasonality, assuming that exponential models are comparable).
Now, I'd like to know which of the two best models is overall best?
How do I compare them?
And generally, if I fit another type of model, is there a "rule of thumb" for comparing the performance of different models with each other?
Edit: The ARIMA model's residuals fail the Shapiro test but pass the Box-Ljung test. The ets() model's residuals pass both tests.