When do we need to use following ETS models: additive seasonality model, multiplicative seasonality model, additive error model, multiplicative error model? Is there any study available regarding when one is preferred over other?
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$\begingroup$ Perhaps there are some hints in Hyndman et al. "Forecasting with Exponential Smoothing: the State Space Approach" (2008). $\endgroup$– Richard HardyCommented Jun 12, 2022 at 14:03
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From https://otexts.com/fpp3/holt-winters.html regarding multiplicative vs additive seasonality:
There are two variations to this method that differ in the nature of the seasonal component. The additive method is preferred when the seasonal variations are roughly constant through the series, while the multiplicative method is preferred when the seasonal variations are changing proportional to the level of the series.
From https://otexts.com/fpp3/ets-estimation.html:
Three of the combinations of (Error, Trend, Seasonal) can lead to numerical difficulties. Specifically, the models that can cause such instabilities are ETS(A,N,M), ETS(A,A,M), and ETS(A,Ad,M), due to division by values potentially close to zero in the state equations. We normally do not consider these particular combinations when selecting a model.
So additive errors always go with additive seasonality, and multiplicative errors always go with multiplicative seasonality.
answered Jun 13, 2022 at 1:17