Hi,

Quantiles (such as the median) are preserved under monotonic transformations. 5.6 Forecasting using transformations | Forecasting: Principles and Practice (3rd ed) (otexts.com) does not explain * why* "the back-transformed point forecast will not be the mean of the forecast distribution", and "will usually be the median of the forecast distribution (assuming that the distribution on the transformed space is symmetric)"?

Also,

*a Taylor Series expansion produces the bias-adjusted back transformed means Forecasting with transformations • fable (tidyverts.org)?*

**why**I'd be grateful for an explanation.

Amarjit