Thoughts: time series modeling with fable and cross validation

I am building a time series model using fable and cross validation to determine the best model definition to use. Is there a risk of modeling



model(ETS(GDP ~ error('A') + trend('A') + season('A')) and other ETS methods

I am asking this because when I perused the mable from **model(ETS(GDP))**, the chosen model was different among some .id. For example, ETS(A, A, A) for id = 1, ETS(A, Ad, A) for id = 2, etc. If this is the case, is it correct to define all the variants of ETS in order to ensure consistency?

Here is a mable I am referring to:

# A mable: 7 x 5
# Key:     .id, LOB [7]
    .id LOB   ETS          ETS_Exponential ARIMA_Exponential     
  <int> <chr> <model>      <model>         <model>               
1     1 LG    <ETS(A,N,N)> <ETS(A,N,N)>    <ARIMA(0,0,1) w/ mean>
2     2 LG    <ETS(M,N,N)> <ETS(A,N,N)>    <ARIMA(0,0,1) w/ mean>
3     3 LG    <ETS(A,N,N)> <ETS(A,N,N)>    <ARIMA(0,0,1) w/ mean>
4     4 LG    <ETS(A,N,N)> <ETS(A,N,N)>    <ARIMA(0,0,1) w/ mean>
5     5 LG    <ETS(A,N,N)> <ETS(M,N,N)>    <ARIMA(0,0,1) w/ mean>
6     6 LG    <ETS(A,N,N)> <ETS(M,N,N)>    <ARIMA(0,0,0) w/ mean>
7     7 LG    <ETS(A,N,N)> <ETS(M,N,N)>    <ARIMA(0,0,0) w/ mean>


Why would you want the models to be the same? For example, if you wanted to compare model parameters for some reason, then you might want to fit the same model to all series. But if you just want good forecasts, you are probably better off having different models for different series -- some will be trended, some will be seasonal, etc., and you probably need to allow for that.

If in doubt, you could try both approaches and see which one gives the best forecasts (assuming that is what your ultimate purpose is here).

Thanks very much for your response.

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