*Intended learning outcomes: Identify the seasonal index S*_{f}. Explain forecasting that considers seasonality. Differentiate between “Additive seasonality” and “Multiplicative seasonality” formulation.

_{f}. Explain forecasting that considers seasonality. Differentiate between “Additive seasonality” and “Multiplicative seasonality” formulation.

Seasonal fluctuations in the demand for specific items are brought about by factors such as weather, holidays, and vacation periods. Restaurants and theaters experience weekly and even daily “seasonal” variations.

The best way to forecast and take seasonality into account is to compare the pattern of demand over multiple years.

We speak of seasonality or a seasonal demand pattern when the following three conditions hold:

1. Growth in demand occurs in the same time frame for every seasonal cycle.

2. Seasonal fluctuations are measurably larger than the random demand fluctuations.

3. A cause that explains demand fluctuations can be found.

Seasonality does not always have a yearly pattern. In the retail trade, particularly in the grocery industry, there is a commonly observed effect at the end of each month when people receive their monthly salary payments.

Figure 10.3.4.1 shows the definition of the *seasonal index*, which is necessary to accommodate seasonal effects. [note 1007]

**Fig. 10.3.4.1** Seasonal index S_{f}.

The term *base series* stands for the succession of the f seasonal indices. Their average value will be 1.0.

Figure 10.3.4.2 shows the two basic models that superimpose the base series upon the trend in demand (that is, without respecting seasonality) for an item in question. *Additive seasonality* refers to an influence independent of the level of sales, whereas *multiplicative seasonality* refers to an influence that increases with the mean of sales.

Figures 10.3.4.3 and 10.3.4.4 provide qualitative examples of demand adjusted for additive and multiplicative seasonality, respectively.

**Fig. 10.3.4.3** “Additive seasonality” formulation.

**Fig. 10.3.4.4** “Multiplicative seasonality” formulation.

Various techniques that account for seasonal influences can be found in the literature. As an example see [GaKe89]. The following is an example of a simplified procedure:

- Calculate the seasonal mean.
- Calculate the trend line from the seasonal means.
- Determine the base series or the succession of seasonal indices as the average deviation of demand from the trend lines for mutually corresponding periods.
- Calculate the forecast value from the trend lines and the seasonality coefficient for the corresponding periods in the seasonal cycle.

## Course section 10.3: Subsections and their intended learning outcomes

##### 10.3 Historically Oriented Techniques with Trend-Shaped Behavior

Intended learning outcomes: Explain the regression analysis forecast and the second-order exponential smoothing forecast. Describe the Trigg and Leach adaptive smoothing technique. Produce an overview on seasonality.

##### 10.3.1 Regression Analysis Forecast

Intended learning outcomes: Explain mean, standard deviation, and forecast error in linear regression.

##### 10.3.2 Second-Order Exponential Smoothing Forecast

Intended learning outcomes: Disclose the determination of trend lines in second-order exponential smoothing. Explain the formulas for calculation of the trend line and forecast error in second-order exponential smoothing. Present an example of determination of forecast value using second-order exponential smoothing.

##### 10.3.3 Trigg and Leach Adaptive Smoothing Technique

Intended learning outcomes: Identify forecast errors and their exponential weighting (mean deviation). Explain the tracking signal following Trigg and Leach. Describe the determination of the smoothing constant in first-order exponential smoothing.

##### 10.3.4 Seasonality Forecast

Intended learning outcomes: Identify the seasonal index Sf. Explain forecasting that considers seasonality. Differentiate between “Additive seasonality” and “Multiplicative seasonality” formulation.