Automatic ETS from fable package in R does not provide the model with the lowest Information Criteria (AIC, BIC and AICc)

Question

Using the classic shampoo dataset from fpp2 I tried to fit an automatic ets model. This led me to an ETS(A,A,N) framework with aic = 441.0668, bic = 448.9844 and AICc = 443.0668. Nevertheless when using an ETS(A,M,N) model the information criteria metrics are lower (AIC=440.1991, BIC=448.1167, AICc=442.1991), even when the parameter restrict = FALSE (on the automatic ets).

automatic_fit <- ts_train %>%
  model(ETS(value, restrict= FALSE))

report(automatic_fit)

fit_2 <- ts_train %>%
  model(ETS(value ~ error("A") + trend("M"), restrict = FALSE))

report(fit_2)

I know that with the autoarima we have an approximation of the best model since there are to many to check, but I thought that since with ets we have a small number of possibilities we could evaluate all the models. Does anyone knows why we see this results?

Answer 1

By default, the automatic modelling selection done by fable::ETS does not consider multiplicative trend models. The models considered in the selection process are described by the method argument of the model's specials. The default for the trend() special is trend(method = c("N", "A", "Ad")), meaning it will choose the best model between models without trend, with additive trend, and with additive damped trend. To also consider multiplicative trend, you would use trend(method = c("N", "A", "Ad", "M")).