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 Properties for a scoreboard record. Select Calculation Setup 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.

  • AS = 0: Perfect
  • AS < 0: Undershooting AS = -0.333, means M2 = 2 * M1, and AS= -0.048 means M2 is 10% more than M2
  • AS > 0: Overshooting AS = 0.333, means M1 = 2*M2
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.

dmp_MAE

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.

dmp_ME

Mean Percentage Error (MPE)

This calculates mean percentage error for demand or calculated forecast.

dmp_MPE

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.

  • U = 1: The naïve method is as good as the technique used, for example, taking a copy of the last year's sales or repeating the last demand is as good as a guess.
  • U < 1: The method used is better than a simple naive guess. The smaller Theil's U is, the better (U = 0 is a perfect prediction).
  • U > 1: The method used is worse than simple using a naïve method. The copy of last year's sales gives a better forecast.
Note:  These forecast methods are available for Scoreboards and for Competitive Forecasting.