# 10.2.1 Moving Average Forecast

### Intended learning outcomes: Explain mean and standard deviation in the moving average forecasting technique. Disclose the average age of the observed values. Present an example of determining the forecast value using moving average.

The moving average forecasting technique considers the individual values of a time series as samples from the universe, or parent population, of a sample distribution with constant parameters and performs periodic recalculations according to the principle of the moving average.

Moving average is the arithmetic average of a certain number (n) of the most recent obser­vations. As each new observation is added, the oldest observation is dropped ([APIC16]).

The technique uses the classic repertoire of mathematical statistics, that is, the mean of a sample and, as a measure of dispersion, the standard deviation.

Figure 10.2.1.1 shows the calculation of mean and standard deviation in the moving average forecasting technique. The variables are set according to the definitions in Figure 10.1.3.4. The formulas are independent of k; that is, we interpret the determined parameters as the expected value and dispersion of forecast demands. These remain valid for any periods of time in the future.

Fig. 10.2.1.1      Mean and standard deviation in the moving average forecasting technique.

The average age of the values included in the calculation is shown in Figure 10.2.1.2. Thereby, the age of Nt-i is i for 0 ≤ i ≤ n-1.

Fig. 10.2.1.2      Average age of the observed values.

The larger the value chosen for n, the more exact the mean becomes, but because the moving average reacts more slowly to alterations in demand, so does the forecast; n should be set so that a rapid adaptation to systematic changes is possible, without causing a significant reaction to a purely random variation in demand. See also Section 10.2.3. Figure 10.2.1.3 shows an example of moving average calculation that includes nine periods in the past.

Fig. 10.2.1.3      Example: determining the forecast value using moving average (n = 9).

The calculation formulas and results are valid independent of the underlying consumption distribution, although a particular distribution is assumed for implemen­tation. Forecast calculations often assume a normal distribution as probability distribution. We discuss this assumption in Section 10.5.2.

A probability distribution is a table of numbers, or a mathematical ex­pres­sion, that indicates the frequency with which each event out of a totality of events occurs. The mathematical probability is a number between 0 and 1 that expresses this frequency as a fraction of all occurring events.

The statement in the last column of Figure 10.2.1.3, that the demand value Nt has a 95.4% probability within the confidence interval “forecast value (= mean) ± 2 * forecast error (= standard deviation),” is only valid in a normal distribution.