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Introduced on day 22

Back-transformation bias

Applying the inverse of a log or Box-Cox transform to a forecast on the transformed scale returns roughly the median of the distribution, not its mean.

In detail

For a log transform with forecast mean m and variance v on the log scale, exp(m) is the median and the mean is about exp(m + v/2). Medians do not add across series while means do, so totals built from unadjusted forecasts are biased low, and more so when the variance is large. Report which one you give.