Why is non-iid noise so important to traditional time-series approaches? I've been reading the whitepaper that accompanied Facebook's release of Prophet, it's time-series modeling library. One topic the authors drew attention to was that noise was assumed to be iid; they note, that this assumption goes against the grain for traditional time-series solutions, such as ARIMA. Likewise, their solution doesn't account for autocorrelation or moving averages whatsoever.
In general, the Prophet model accounts for piecewise linear (or logistic growth) trends, seasonality, and holiday effects (where seasonality is captured via a fourier series.)
I'm curious, why are autocorrelation, moving average, and non-iid noise emphasized in traditional time-series approaches, such as ARIMA? Wouldn't it be easier to just use a GLM where seasonal controls (whether that be month, week, etc) could be used to augment the overall linear (or logistic trend)?
https://www.youtube.com/watch?v=OaTAe4W9IfA
https://www.youtube.com/watch?v=fIbgWVMRnis

Even in ARIMA models, the noise is still IID; it's just that the model part has an auto-correlation component, a moving-average component, and a differencing component.  Now, if you were to take data generated by one of these models and then model it with some simpler model (e.g., lacking the auto-correlation component) then the "noise" from the simpler approximation is going to be non-IID due to the fact that it does not take account of a part of the original model.
