In the example in section 13.4 Forecast combinations of FPP3, the simple average of the forecasts from three models (based on ETS, STL-ETS, and ARIMA) models are taken. The comment is made that the "mutate() function... automatically handle[s] the forecast distribution appropriately by taking account of the correlation between the forecast errors of the models that are included."

Does this mean that we don't have to check residual diagnostics if we choose to use the simple average of the ETS, STL-ETS, and ARIMA models? For example, do we need to use the Ljung-Box test to check if the resulting residuals are correlated, or use the residuals plot allow us to check if the residuals have zero mean?

Likewise, I am also wondering whether we need to check residual diagnostics for the automated bagging method discussed in 12.5 Bootstrapping and bagging, as the article doesn't appear to mention this.

^{Referred here by Forecasting: Principles and Practice, by Rob J Hyndman and George Athanasopoulos}