Model: Constant Forecast Formulae

From these two points mentioned above, the constant model of exponential smoothing can be derived (see formula (5)). In this case, the formula is used for calculating the basic value. A straight forward derivation produces the basic formula for exponential smoothing (see formula (6)).

To determine the forecast value, you only require the preceding forecast value, the last past consumption value and the so-called smoothing factor, alpha. This smoothing factor is responsible for weighting the most recent consumption values more than the past values so that they have a stronger influence on the forecast.

How quickly the forecast should react to a change in consumption pattern depends on your choice of smoothing factor. If you select 0 for alpha then the new average will be equal to the old one. In this case, the basic value calculated previously remains, that is, the forecast does not react to current consumption data. If you select 1 for the alpha value, the the new average will equal the last consumption value.

The most common values for alpha lie, therefore, between 0.1 and 0.5. An alpha value of 0.5 weights past consumption values as follows:

1st past value : 50%

2nd past value : 25%

3rd past value : 12,5%

4th past value : 6,25%

and so on.

The weightings of past consumption data can be changed by one single parameter. Therefore, it is relatively easy to respond to changes in the time series.

The constant model of first-order exponential smoothing derived above is applicable to time series that do not have trend-like patterns or seasonal-like variations.