Also I believe that RNNs are useful mainly for highly non-linear problems. Non-linearities in a problem such as sales forecasting are best handled through interaction terms or by including non-linear transformations (e.g. logarithm) of existing features into your model.
So you are saying that RNN won't be suited for non-linear sales forecasting?
If you are convinced that there are complex non-linearities that an ARIMA model cannot describe, then I would try to use RNNs to find a pattern in your ARIMA models' residuals and try to augment your ARIMA model with an RNN.
Knowing nothing about his sales process and features, I would assume there are many complex non-linearities (to be possibly leveraged for better predictions). I find this statement bizarre.
But if you can give me an example of a non-linearity in sales forecasting that cannot be fit by a linear model but can by an RNN I'd honestly be really interested in that.
ARIMA models cannot take into consideration special scenarios or even multivariate features (Like location and time). It's good for simple forecasting but when you need more "human like" predictions we are betting on neural networks.
For example we would instinctively know that sales of turkey goes up on Thanksgiving. ARIMA model cannot factor this but RNN/LSTM should be able to (Theoretically speaking).
https://en.wikipedia.org/wiki/Dummy_variable_(statistics) https://en.wikipedia.org/wiki/Interaction_(statistics)
We are looking to replace our Arima models with RNNs and the results so far has been far from satisfactory.
The usecase is: based on sale quantity in past year, predict the sale quantity tomorrow.
Regression does not consider weekdays or weekends or similar bumps and we thought RNN w/LSTM would be well suited for this problem