I would like to understand why the non-seasonal and seasonal parts are multiplied in Seasonal ARIMA models.
To be more specific: when we use the Seasonal ARIMA model we assume a multiplicative model and the ARIMA order is represented as: ARIMA (p,d,q)x(P,D,Q). (https://www.otexts.org/fpp/8/9)
so for e.g the order of SARIMA(1,0,0)x(1,0,0) can be represented mathematically as:
- so why are they multiplied from the first place?
- is there an additive model which can be applied here?
- if there is, why is it not used?
all books of time series analysis that I've checked, just assume that the non-seasonal and seasonal parts should be multiplied, but non have given an explanation why.. I've asked around people who worked with ARIMA but non could help me with that, so I would really appreciate if someone could shed a light on that! a reference would be also very helpful.