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))
```

vs

```
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>
```

Thanks.