Forecast Error Measures
Scoreboard has templates for many of the common measures used for error analysis.
The scoreboards can display the error values but you can also construct the error values in a favorite view as a Calculated Measure.
Creating a scoreboard from a Formula Template is possible through the right-click option for a scoreboard record. Select from the Select Property column.
M3 DMP will display the Calculation Parameters dialog box with the formula at the bottom of the display. You can copy the formula and make it into a calculated measure in a favorite view, for example, if the scoreboard is not used when opening the favorite view or using the favorite view data manager to copy the values across favorite views.
List of common forecast error measures
This table shows the available forecast methods:
| Measure | Formula |
|---|---|
| Accuracy Signal | AS = ([M1] - [M2]) / ([M1] +
[M2]) Accuracy Signal indicates how close the forecast is to a perfect forecast and whether it is overshooting or undershooting.
Note: AS has the same scale for positive and
negative values.
|
| Mean Absolute Error (MAE) |
This calculates the mean absolute error for demand or calculated forecast. |
| Mean Absolute Percentage Error (MAPE) | This is a common and useful indicator that
shows the relative difference between two measures. Examples include Demand
versus Forecast and Forecast versus Sales. MAPE = Avg(3,Abs(([M1] - [M2]) / [M1])) |
| Mean Error (ME) |
This calculates mean error for demand or calculated forecast. |
| Mean Percentage Error (MPE) |
This calculates mean percentage error for demand or calculated forecast. |
| Mean Square Error (MSE) | MSE = Avg(3,([M1] - [M2])^2) |
| Symmetric MAPE (SMAPE) | Symmetric MAPE (SMAPE)
measures the percentage difference between the forecast and actual demand,
where both values contribute equally to the denominator: SMAPE = |Actual − Forecast| / ((|Actual| + |Forecast|) / 2) A value of 0 means a perfect forecast. A value of 0.05 means the forecast deviates approximately 5% from actual demand. Unlike traditional MAPE, which divides only by the actual value, SMAPE treats over-forecasting and under-forecasting equally. This avoids bias where forecasting 100 when the actual value is 50 (100% error) is penalized differently than forecasting 50 when the actual value is 100 (50% error). With SMAPE, both cases produce the same error. This makes SMAPE particularly suitable for competitive forecast selection, where methods are compared on a fair and balanced basis regardless of whether they tend to forecast above or below actual demand. |
| Theil's U-statistic | Theil's U = Sqr(Sum(3,(([M1][P
+ 1] - [M2][P + 1]) / [M2][P])^2)/Sum(3,(([M2][P + 1] - [M2][P]) /
[M2][P])^2)) This provides a relative comparison and also squares the errors involved so that large errors are given more weight than small errors. Theil's U describes how good a fit two measures are.
|