FC.... "And, (extremely simplistically), the causal relationships have changed over time and will continue to change over time."

Correct and technically - deadly statement = Non-Stationarity
and puts a spanner in the works for most common methods.

In most cases - one has to work with at least temporal stationarity assumption. The problem with that is "then what?"

There are 2 options - at least what I have tried ....

(1) Staged model - try to built a time series model ( you can use your method of choice , although LSTMs are known to beat ARIMAs but its typically not by much , I have stuck to ARIMAs) to handle the time variance and then assume stationarity for the rest.

This one is very flexible but the issue is forward forecast - you dont really know what really is changing on the LT horizons. Really only useful for simulations etc to understand HOW MUCH of a spanner damage it can cause. Additionally if you assume migrating errors - almost all bets are off ( Some people will say GARCH - you can try that - but its all more and more complexity and tons of assumptions - which may or may not hold)

(2) Or incorporate Time variance regressors in the the main model itself. This assumes the time variance itself is a bit stable ( This works for very Short Term types of situations)

NET MSG: Non-Stationarity is a bane - anyone saying its not , well ......