Definition
Mean absolute scaled error, or MASE, divides the mean absolute forecast error on an evaluation sample by a naive forecast error scale calculated from training data. For seasonal demand, that scale uses absolute differences between observations one seasonal cycle apart. This produces a unitless measure with an explicit historical reference.
Why It Matters
- A ten-unit forecast miss means something different for a slow accessory and a high-volume staple. Raw unit errors alone can obscure that distinction.
- A Commerce Intelligence OS needs both comparable model evidence and the commercial consequences for each SKU. A scaled score supplies the former, not the complete buying decision.
How It Works
- Fix the SKU, location, demand unit, forecast horizon, and training cutoff. Choose the seasonal lag from the business frequency rather than whichever value improves the score.
- Compute the average absolute lagged difference within training data. For nonseasonal scaling use the previous observation; for seasonal scaling use the selected seasonal lag.
- Divide evaluation mean absolute error by that scale. Record undefined cases when the training scale is zero instead of silently inserting an arbitrary denominator.
- Compare models using identical training scales and evaluation observations. Inspect stockout-censored sales and category-level consequences separately before recommending inventory changes.
Ecommerce Example
Context: Illustrative example: a SKU has training-period seasonal naive error averaging five units. Its new model has evaluation mean absolute error of four units.
Recommended move: MASE is 4 divided by 5, or 0.8. That compares the test error with the historical training benchmark scale.
Why it matters: It does not prove a 20% improvement over a naive model tested on the same future periods. Run that direct comparison separately; these figures are hypothetical.
iKawn Framework
Define
The iKawn framework binds the score to a SKU and planning horizon.
Scale
Preserve the training benchmark and its seasonal lag.
Inspect
Keep undefined scores and availability constraints visible.
Decide
Combine model evidence with margin and inventory consequences under merchant review.
Concise Summary
MASE makes forecast errors comparable through a historical naive scale. Keep that scale fixed, surface zero denominators, and distinguish a historical benchmark from a head-to-head future test.