I am trying to understand loss functions when working with sequential (time series) data. Specifically, simple next-step loss functions don’t seem to capture the nuance I would like and are brittle when projecting into the future. Are there some topics/keywords/papers that explore more advanced (expressive?) loss functions in this context?

I am most interested in: predicting higher-levels features of a time series (e.g. variance, confidence bounds) and long term predictions that are more robust. I don’t know how to describe some of the concepts I’m searching for, so some high level discussion or tutorial would also be very helpful. Thanks!