Time series and forecasting · insight-0229

Bias-adjust back-transformed forecasts when totals or means matter

Situation
Daily demand is modelled on a log or Box-Cox scale, and the back-transformed daily forecasts are summed into a monthly budget.
Action
Apply a bias adjustment when back-transforming if the forecast feeds sums, averages or revenue; keep the median when the decision needs a typical value.
Reason
A simple back-transform of a forecast made on a transformed scale gives the median of the forecast distribution; bias adjustment gives the mean.
Boundary
Revenue, sales and load forecasts built on log or Box-Cox scales.

Symptom or risk

Back-transformed point forecasts estimate the median, not the mean, so summed forecasts are systematically below expected totals.

If the forecast variance is small, the difference between median and mean is negligible; check its size.

Bias adjustment depends on the variance estimate, so poor variance estimates can over-correct.

Reporting a downward 'bias' in production and blaming the model rather than the back-transform.

Back-transformed point forecasts are usually the median of the forecast distribution; bias adjustment is needed to obtain the mean.
Forecasting: Principles and Practice (3rd edition)
The Box-Cox family is a power transformation with a parameter chosen, for example, by likelihood.
An Analysis of Transformations