Mean Absolute Percentage Error (MAPE) Performance Measure

A Mean Absolute Percentage Error (MAPE) Performance Measure is a numeric prediction performance measure based on [math]\displaystyle{ \frac{100}{n}\sum_{t=1}^n \left|\frac{A_t-F_t}{A_t}\right|, }[/math] where A_t is the actual value and F_t is the forecast value.

• Context:
  • It can be appropriate for tasks with actuals that typically greater than zero.
  • It can be an intuitive metric (12.5% average error for task 1 and 17.3% average error on task 2).
  • …
• Example(s):
  • Symmetric MAPE.
  • …
• Counter-Example(s):
  • Median Absolute Percentage Error.
  • RMSE.
• See: Percentage-based Forecasting Performance Measure, Point Estimation Performance Measure, Trend Estimation.

---

---

References

2021

• (Wikipedia, 2021) ⇒ https://en.wikipedia.org/wiki/Mean_absolute_percentage_error Retrieved:2021-8-9.
  • The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting method in statistics. It usually expresses the accuracy as a ratio defined by the formula: : [math]\displaystyle{ \mbox{MAPE} = \frac{100}{n}\sum_{t=1}^n \left|\frac{A_t-F_t}{A_t}\right| }[/math] where A_t is the actual value and F_t is the forecast value. Their difference is divided by the actual value A_t. The absolute value in this ratio is summed for every forecasted point in time and divided by the number of fitted points n.

2017

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Mean_absolute_percentage_error Retrieved:2017-12-9.
  • … Although the concept of MAPE sounds very simple and convincing, it has major drawbacks in practical application
    • It cannot be used if there are zero values (which sometimes happens for example in demand data) because there would be a division by zero.
    • For forecasts which are too low the percentage error cannot exceed 100%, but for forecasts which are too high there is no upper limit to the percentage error.
    • When MAPE is used to compare the accuracy of prediction methods it is biased in that it will systematically select a method whose forecasts are too low. This little-known but serious issue can be overcome by using an accuracy measure based on the ratio of the predicted to actual value (called the Accuracy Ratio), this approach leads to superior statistical properties and leads to predictions which can be interpreted in terms of the geometric mean.

---