*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 ([ASCM22]).

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 N_{t-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 N_{t} has a 95.4% probability within the confidence interval “forecast value (= mean) ± 2 * forecast error (= standard deviation),” is only valid in a normal distribution.

## Course section 10.2: Subsections and their intended learning outcomes

##### 10.2 Historically Oriented Techniques for Constant Demand

Intended learning outcomes: Describe the moving average forecast. Explain the first-order exponential smoothing forecast. Differentiate between the moving average forecast and the first-order exponential smoothing forecast.

##### 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.

##### 10.2.2 First-Order Exponential Smoothing Forecast

Intended learning outcomes: Identify the weighted mean as well as exponential demand weighting. Explain first-order exponential smoothing: mean, MAD, and standard deviation. Disclose the average age of the observed values.

##### 10.2.2b The Smoothing Constant α, or Alpha Factor

Intended learning outcomes: Describe how the smoothing constant α determines the weighting of the past. Present an example of first-order exponential smoothing.

##### 10.2.3 Moving Average Forecast versus First-Order Exponential Smoothing Forecast

Intended learning outcomes: Disclose formulas for the relationship between α and n. Present the relationship between α and n in tabular form. Present an example of linear regression.