Mean forecast error shows the deviation of a forecast from actual demand. This is the mean of the differences per period between a number of period forecasts and the actual demand for the corresponding periods.

Mean forecast error is used as a basis for following up and adjusting forecasts. When it is positive, the forecasts have been low in relation to actual demand and when it is negative, the forecasts have been too high.

**Methods for Calculation**

Mean forecast error can be calculated in three ways, as follows:

**Exponential Smoothing**

ME(i + 1) = ((i) * (D(i) - F(i)) + (1 - ((i)) * ME(i)

**Average Forecast Error**

ME(i + 1) = ((D(i) - F(i)) + ....... + (D(i - (n - 1)) - F(i - (n - 1))) / n

**Explanation**

Base demand and base forecast represent demand and forecast, respectively, for one period adjusted for seasonal variations and the effects of a varying number of workdays per period.

ME(i) | = | Mean forecast error for period (i) |

((i) | = | Smoothing constant for exponential smoothing in period (i) |

D(i) | = | Base demand during period (i) |

F(i) | = | Base forecast for period (i) |

i | = | Period number |

n | = | Number of periods included in calculating the mean |

The two examples below describe each of the calculation methods.

The following data is entered for the product:

Aug. | Sept. | Oct. | Nov. | |

Base demand | 120 | 145 | 138 | 129 |

Base forecast | 136 | 132 | 135 | 133 |

ME for Nov. | 0.5 | |||

(-factor used | 0.3 |

These values for mean forecast error will be calculated for December using the two methods as shown:

**Exponential Smoothing**

ME(Dec.) = 0.3 * (D(Nov.) - F(Nov.)) + (1 - 0.3) * ME(Nov.) = 0.3 * (129 - 133) + 0.7 * -1.5 = 0.3 * - 4 + 0.7 * -0.5 = - 1.55

**Average Forecast Error**

ME(Dec.) = ((D(Nov.) - F(Nov.)) + (D(Oct.) - F(Oct.)) + (D(Sept.) - F(Sept.)) + (D(Aug.) - F(Aug.))) / 4 = (-16 + 13 + 3 - 4) / 4 = -1