# 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.

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 demandand 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.