"Illogical Predictions" in Time Series Models? In class today, we were doing a lab exercise in which we used R to fit a basic ARIMA time series model to predict the rain fall at a daily level. I noticed that during some months where there has not been a lot of rain (e.g. drought), the ARIMA model would make "illogical predictions". For example, the ARIMA model would  predict that the following day will have "negative rainfall", or that the confidence interval would be 1 mm ± 3 mm.
Our prof told us that he wanted us to notice this phenomenon of "illogical predictions" and that this can commonly occur in ARIMA models.
He then mentioned that models like ETS (Exponential Time Smoothing) are less suspectable to producing such "illogical predictions" - but he did not really explain the reasons behind this.
My Question: Is there actually some mathematical reason that proves to us that these kinds of illogical predictions are by definition impossible when using ETS - or is it that sometimes ETS still make these illogical predictions, and that all depends on the specific dataset and the customizations? And are there any such models time series models that are better suited for avoiding these kinds of illogical predictions?
Thanks!

Exponential smoothing predictions are a weighted sum of past observations, but the model explicitly uses an exponentially decreasing weight for past observations.
Since rainfall is always greater or equal to zero, it will be impossible for ETS to smooth historical data into something negative.
Example:
clear
set obs 100
gen t = _n
tsset t
gen y = 100 - 2*t + rnormal(0,15)
replace y = . if y <= 0
tssmooth exponential yhat = y, forecast(20)
tw (scatter y t) (line yhat t)


