Constant Model w. 1st Order Exponential Smoothing

Definition

The principles of first-order exponential smoothing are:

• The older the time series values, the less important they are for the calculation of the forecast.
• The present forecast error is taken into account in subsequent forecasts.

The constant model with first-order exponential smoothing (forecast strategies 11 and 12) can be derived from the above two considerations. A simple transformation gives the basic formula for exponential smoothing (see below).

To calculate the forecast value, the system uses the preceding forecast value, the last historical value, and the alpha smoothing factor. This smoothing factor weights the more recent historical values more than the less recent ones, so that they have a greater influence on the forecast.

How quickly the forecast reacts to a change in pattern depends on the smoothing factor. If you choose 0 for alpha, the new average is equal to the old one and the basic value calculated previously remains; that is, the forecast does not react to current data. If you choose 1 for the alpha value, the new average equals the last value in the time series.

The most common values for alpha lie, therefore, between 0.1 and 0.5. For example, an alpha value of 0.5 weights historical values as follows:

1st historical value: 50%

2nd historical value: 25%

3rd historical value: 12.5%

4th historical value: 6.25%

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