how to determine Time Series Model? Additive Multiplicative? I am new to time series Analysis, and I have noted that there's only two kind of models: Additive or multiplicative.
I want to know if there's other cases where we can find a combination of both.
For example, if We have a Time Series with $S_t$ a complex Seasonality. Then the time serie formula will be like:
$$Y_t=T_t * [S_t(1) * S_t(2) + S_t(3)] + N_t$$
Does this case exist in Time Series Analysis?
 A: Your first sentence is an oversimplification (or incomplete). It is correct that a time series model that has multiple components can have additive or multiplicative interactions between those components; but there are many kinds of models (exponential smoothing, arima, unobserved component, etc.). A given forecast model can be mixed-- additive trend with multiplicative seasonality, or additive errors with multiplicative trend, etc.
Do you have particular data/phenomena in mind? I can imagine something like this:


*

*multiplicative week of year seasonality (not uncommon), where the high points are 10% above average and low points are 10% below

*additive phenomena that could be modeled like seasonality because it's so consistent, eg, customer A always orders 100 units in the first quarter of each year


In the latter case this could be modeled as a regressor rather than as seasonality. Otherwise, thinking about my (limited) knowledge of forecasting implementations I don't know how you would do it. Modeling multiple seasonal frequencies is difficult to find. SAS proc ucm can do it with the BLOCKSEASON statement, that's the only way I've done it and that was for doing seasonality of day of the week and week of the year.
