*Intended learning outcomes: Present an example of a time series. Explain possible and common demand models.*

Particularly for forecasting based on historical data, statistical techniques are used that are based on a series of observations along the time axis (here see [BoJe15], [IBM73], or [WhMa97]). The following values are fundamental to the determination of stochastic requirements:

A *time series* is the result of measurement of particular quantifiable variables at set observation intervals equal in length.

The *statistical period* or *observation interval* is a time unit, namely, the period of time between two measurements of the time series (e.g., 1 week, 1 month, 1 quarter).

The *forecast interval* is the time unit for which a forecast is prepared ([ASCM22]). This time unit best corresponds to the statistical period.

The *forecast horizon* is the period of time into the future for which a forecast is prepared ([ASCM22]). It is generally a whole number multiple of the statistical period.

As an example, Figure 10.1.3.1 shows the frequency distribution[note 1001] of the observed variable “customer order receipts” during the most recent statistical period as a histogram. [note 1002]

**Fig. 10.1.3.1** Example of a time series.

A *demand model* attempts to represent demand by drawing the curve that shows the least scattering of the measured values.*Curve fitting* is the process performed to obtain that curve, by means of a straight line, polynomial, or another curve.

We assume that the scattering (dispersion) of values is random and, most often, distributed normally. This presupposes that while demand values do indeed have a fluctuating pattern, it is possible to make fairly good approximations. Figure 10.1.3.2 presents some common cases of demand models.

**Fig. 10.1.3.2** Possible and common demand models.

Matching a particular demand model to a particular time series leads to the choice of a forecasting technique. The forecasting technique is thus based on a concept or a model of the course of demand. This concept forms the basis for the perception of regularity or a regular demand*, *and the model is

- Either an
*econometric model*, mostly defined by a set of equations, formulating the interrelation of collected data and variables of the model of the course of the demand as a mathematical regularity, - Or an
*intuitive model*as an expression of the perception of an intuitive regularity.

It is quite possible that for a single time series several models will overlap.

*(Statistical) decomposition* or *time series analysis* is a breakdown of time series data into various components by analysis; for example, into:

- (Long-term) trend component

- Seasonal component

- Nonseasonal, but (medium-term) cyclical component

- Marketing component (advertising, price changes, etc.)

- Random component (nonquantifiable phenomena), e.g., due to *noise*, that is random variation or a random difference between the observed data and the “real” event.

*Continuation in next subsection (10.1.3b).*

## Course section 10.1: Subsections and their intended learning outcomes

##### 10.1 Overview of Demand Planning and Forecasting Techniques

Intended learning outcomes: Produce an overview on the problem of demand planning. Present the subdivision of forecasting techniques. Disclose principles of forecasting techniques with extrapolation of time series and the definition of variables.

##### 10.1.1 The Problem of Demand Planning

Intended learning outcomes: Disclose the difference between human forecasting and IT-supported forecasting techniques with regard to a forecast’s precision. Present a possible demand planning procedure.

##### 10.1.2 Subdivision of Forecasting Techniques

Intended learning outcomes: Explain one possible breakdown of forecasting techniques. Disclose another possible subdivision of forecasting techniques.

##### 10.1.3 Principles of Forecasting Techniques with Extrapolation of Time Series

Intended learning outcomes: Present an example of a time series. Explain possible and common demand models.

##### 10.1.3b Statistical Methods to Determine Mean and Dispersion and Definition of Variables

Intended learning outcomes: Produce an overview on statistical methods to determine mean and dispersion. Identify definitions of variables, each calculated at the end of a statistical period.