Problem with ets function diagnostic for model with trend and seasonality I have been meaning to fit an exponential smoothing model to a monthly series that looks like the one below:

When I decompose the series it is almost evident that we have seasonality and also there seems to be an exponential trend in the series. Here is the result:

I first used ets function to apply it on my training set and the diagnostic was an ETS model with additive error, but neither seasonality nor trend:
fit2 <- ets(training)
fit2

ETS(A,N,N) 

Call:
 ets(y = training) 

  Smoothing parameters:
    alpha = 0.4596 

  Initial states:
    l = 354.3194 

  sigma:  155.3593

     AIC     AICc      BIC 
365.3796 366.4231 369.2672 

And the Ljung-Box test also looks fine:
fit2 %>% checkresiduals()

    Ljung-Box test

data:  Residuals from ETS(A,N,N)
Q* = 2.235, df = 3, p-value = 0.5251

Model df: 2.   Total lags used: 5

When I plot the forecasts for 4 months ahead, it seems to be a straight line, as the model doesn't capture the dynamics of the series:

Now I have 2 questions:

*

*Do I need to detrend & deseaonalize the times series with lag 1 and lag 12 differencing before applying an ets model on it. Because I heard from Mr. Hyndman on a datacamp tutorial that we just have to plug in the series into ets so, I am a bit confused here. If I use HoltWinter function I will get a different result, but I don't know the difference between these two.

*Do this model seems legitimate and correct? I am not sure why it could not capture the dynamics here but since there is a seamingly polynomial trend here I thought that might lead to ets diagnose the trend to N, but what about seasonality? why it cannot be catpured?

Thank you very much for your advice in advance I really appreciate it.


Do I need to detrend & deseasonalize the times series with lag 1 and lag 12 differencing before applying an ets model on it?

Does your series have a unit root or a seasonal unit root? If not, why would you consider taking lag 1 or lag 12 differences? (Eyeballing your series does not suggest that.) Each would introduce a unit-root moving-average component into your process and increase your error variance (the first would double it, the other I am not sure by how much). In general, removing a deterministic trend and/or non-unit-root seasonality by differencing is not a good idea.
