I'm diving into the field of system identification, black box modeling and forecasting. A lot still has to become clear to me, but one question that came to my mind (and to which the answer might clarify much for me):
I encounter models like AR, MA, ARMA, ARIMA, ARX, VAR and I see some core building blocks in these acronyms:
- V: Vector
- AR: Auto-regressive
- I: Integrated
- MA: Moving average
- X: Exogenous inputs
With these you seem to be able to construct all kinds of models, all the way up to VARIMAX. My question is: Why don't I ever encounter MAX models (Moving Average with Exogenous Inputs)? They should be pretty basic, as they use few building blocks. Is there some reason why this type of model is not very useful or does not make a lot of sense?