I have a large set of relatively simple time series with very similar behaviour, on which I would like to do short-term forecasts. These series are non-aligned, and at one moment in time, only a small fixed number of series is considered. After that, the series are dropped and never become relevant again.
An example to clarify:
At 12:00, three series [A, B, C] are considered, and each is forecasted using an instance of the generic model.
At 12:05, three series [B, C, D] are considered, and each is forecasted with its instance of the generic model. D being a series never seen by the model before. It is a very similar series to the previously seen, and I would expect the model to generalize and provide a reasonable forecast.
I am essentially looking for a model that I could fit on multiple time series and then create instances with data from different series and get forecasts.
What models could suit this problem well? How can I fit/train the model on all the training series evenly to not re-fit just for the last observed series?