Maybe it would be better to train an LLM with various tuning methodologies and make a dedicated ARIMA agent. You throw in data, some metadata and requested window of forecast. Out comes parameters for "optimal" conventional model.
i met an associate working for a particular VC and they were really into time series foundational models. I argued the most of the "Why real forecasting problems break the whole frame" as to why they were wasting their time at that time.
she was totally convinced i was wrong because she was discussing investing with some top and well respected researchers that were really pushing this and wanted to make a startup around it.
i was and am still confused as at all the wishful thinking. then again, sometimes the best time to sell an idea is right before you think it is possible.