A demand forecast is not an end product. It is an input to an ordering decision, and that decision is asymmetric: running out costs the lost margin, ordering too much costs the markdown. When those two numbers differ, the optimal order is not the expected demand, and the gap between them is computable exactly.
The mean is the wrong number to forecast
Almost every forecasting tutorial minimises mean squared error, whose optimal prediction is the conditional mean. That is the right target when errors in both directions cost the same. In inventory they never do.
Take a product with a margin of £12 a unit and a markdown loss of £4 on anything unsold. Every unit you fail to stock costs £12 of margin you could have had. Every unit you overstock costs £4. Being short is three times as expensive as being long, so a forecast that is right on average is a policy that is wrong most of the time.
The correction is not a fudge factor bolted onto the forecast. It is a different quantity to forecast: a quantile of the demand distribution rather than its centre. Which quantile is not a matter of taste, and it is the same move as deriving a decision threshold from a cost matrix — the economics decide the operating point, and the model is only asked to produce the number the economics need.
