I asked a question similar to this. Basically I was wondering if I when getting new observations, do I add them to the existing model or resample the model from scratch. In my case since I can actually observe the data from the new groups, it is best for me to resample from scratch. However, there are cases where you may want to model groups that cannot be observed. In that case you would need to perform some out of model prediction not out of sample prediction.
This is a very helpful tutorial on the matter: Out of model predictions with PyMC - PyMC Labs
The other thing is that since you have temporal data, you may want to consider something that accounts for seasonality or other cycles within the data. This could improve your estimates if what you are modeling has any seasonality.