Yes - many thanks!

Questions:

(1) Just to confirm, if `bootstrap = TRUE`

, would the following be bootstrapping the forecasts of each model, and then averaging each models bootstrap forecasts?

```
auscafe |>
filter(year(date) <= 2018) |>
model(ETS = ETS(turnover),
ARIMA = ARIMA(turnover ~
pdq(d=1) + PDQ(D=1))
) |>
forecast(h = "1 year", bootstrap = TRUE) |>
summarise(
turnover = dist_mixture(
turnover[1], turnover[2],
weights=c(0.5,0.5))
) |>
mutate(.model = "ENSEMBLE") |>
accuracy(
data = auscafe,
measures = list(crps=CRPS, rmse=RMSE)
)
```

And the same question for a Combination?

`mutate(COMB = (ETS + ARIMA)/2)`

The code in the repo plots distributions for Combination and Mixture models, with no transformation and `bootstrap = FALSE`

, as Normals and Mixture of Normals i.e. as "smoothed" distributions.

The models I have used in fable, are:

- ARIMA
- ETS
- ENSEMBLE: ARIMA and ETS

for various series, with transformations:
- none (back-transformed Normal distribution),
- log (back-transformed Log-Normal distribution)
- sqrt (back-transformed Non-Central Chi-squared distribution),

all with `bootstrap = TRUE`

, as a Normal distribution for the residuals may be an unreasonable assumption.

(2) For the single models ARIMA, and ETS, I have used `geom_density`

with `bootstrap = TRUE`

. Correct?

(3) For the ENSEMBLE will `geom_density`

suffice or is there an equivalent `dist_mixture( ?, ?, weights = c(0.5, 0.5)))`

for `geom_density`

? If, not how to plot the forecast distribution for an ENSEMBLE with `bootstrap = TRUE`

?

(4) Also, as per fable: Combination Models, Methodology and Simple Numerical Example - #6 by mitchelloharawild, exactly how are the forecast SE's calculated/aggregated for an ENSEMBLE? I'd very much appreciate a simple numerical example.