 ## Median Method ### Use

This empirical method, which is used in strategy 36, determines the median of the basic and trend parameters, as well as the seasonal index if applicable.

### Prerequisites

At least 3 seasons of historical data must be available. If the number of periods in a season is 1, the seasonla index is set to 1. There is no seasonal effect. In the case the system needs 3 periods to determine the trend paramter and the basic value.

### Features

No initialization is necessary.

Since this method automatically excludes the influence of outliers, it is not necessary to use further outlier correction. Outlier correction is not available with the median method.

#### Principle of the Median Method

The system determines the difference between the first and second values in the historical data, the second and third, and so on to the end of the data. It then sorts the values in ascending order, for instance Finally it chooses the value that is exactly in the middle of the list, the median value.

### Activities

#### Determination of Trend Paarameter, Seasonal Indices and the Basic Value

The system uses the following procedure to determine the trend parameter, the seasonal indices, and the basic value. It forms groups of data for the first period in the cycle, the second, third and so on. Since

D xy = nT.Sx

The values from the first period in each cycle are used to determine the trend parameter T, as above. The season index for this first period is defined to be 1. The season indices for the other groups can now be calculated by dividing the differences D xy by the trend parameter multiplied by the number of periods in a season. This produces as many estimates of the i th season index as there are groups less one (the first group was used to determine the trend parameter). The median value of each group is the season index for that group. If the number of period in a cycle is 1, there is in effect no seasonal effect and the system only determines the trend parameter and afterwards the basic value. The seasonal index is 1.

Since the historical value is given by:

V = (G – nT).S i

where G is the basic value, T the trend parameter  and Is the seasonal index, and T and Is  are known for all historical values, it is possible to determine G for each historical value.

From this sequence of basic values the system determines the median and uses this as the basic value for the forecast.

F = (G + nT).S i Note that in contrast to normal mathematical conventions, SAP Demand Planning and in general time series forecasting defines the basic value G to be the intercept at the end of the historical data, that is the transition between the historical and forecast periods. This accounts for the change of sign in the two equations above. Similarly the season index starts at this transition. In the historical period the more more a data point is in the past the larger the index. In the forecast period the more a data point is in the future the larger the index.

### Restrictions

As with every forecast model the median method is not suitable for all historical data. You should avoid the following situations:

·        Time series that represent step functions

·        Time series with several data points that have the same value 