What are the downsides of ARIMA models? I recently worked with ARIMA models and realized how common they are in economics and other sciences.
You can find dozens of articles on the Internet that use ARIMA models, but you can find relatively little about the disadvantages of ARIMA models.
What are the main weaknesses of ARIMA models, both methodologically and statistically?
Does anyone have good scientific articles that deal with this topic?

One key downside is that ARIMA models tend not to forecast very well. (I'm sure I will get my share of pushback for that statement. And yes, it is too broad in a sense, but it serves as - I believe - a useful first-order approximation.)
This came as something of a surprise at the earlier forecasting competition, at least to the statisticians who had gone through (or written originally) all the proofs about optimality and similar properties of ARIMA models - though only under the assumption that the true data generating process in fact does follow an ARIMA process, and usually also using asymptotic results.
More information at my answer to Why is non-iid noise so important to traditional time-series approaches?, where I also linked to Rob Hyndman's "Brief history of forecasting competitions" (2020, IJF), which is extremely enlightening reading.
