Time series and forecasting · insight-0210
Do not average MAPE across series of very different volumes
- Evidence type
- documented fact
- Difficulty
- easy
- Roles
- Data analyst, Data scientist
- Industries
- retail, manufacturing, aviation
Summary: situation, action, reason, boundary
Situation
A portfolio report averages per-series MAPE, and a few slow movers make the whole forecast look broken.
Action
Use a volume-weighted measure such as WAPE or a scaled measure such as MASE for the portfolio, and keep MAPE only for series with consistently large actuals where people find percentages intuitive.
Reason
Percentage errors are infinite or undefined when an actual is zero and unstable near zero, so their unweighted average misrepresents business impact.
Boundary
Retail and spare-parts portfolios, airline routes with seasonal suspensions.
Symptom or risk
Percentage errors explode when actuals are small and are undefined at zero, so an unweighted mean is driven by the least important series.
Exceptions
High-volume series with no near-zero actuals can use MAPE safely.
Trade-offs
Volume weighting means a few large series dominate; show a small-series view too.
Pitfalls
Switching to sMAPE as a fix; it is still unstable near zero and treats over- and under-forecasts asymmetrically.
Lessons and concepts
Claims and their sources
Percentage errors are infinite or undefined if any actual equals zero and take extreme values when actuals are close to zero.
Hyndman and Koehler critique MAPE and sMAPE and recommend scaled errors instead.