If more historical values are available than are required for the system needs initialize the model, an ex-post forecast is carried out automatically as follows:

• The historical values are divided into two groups: the first group with the older values is used for initialization; the more recent values in the second group are used to carry out an ex-post forecast (see the figure below).

• The basic value, the trend value, the seasonal index, and the mean absolute deviation (MAD) are modified in every ex-post period. These values are used to calculate the forecast results in the future.

• The error total is calculated using the ex-post forecast results. The error total allows you to assess the accuracy of the chosen forecast model.