Seasonality is the influence of external factors that affect the data cyclically with a predetermined frequency. A time series and cyclic seasonal fluctuations can be represented by models of two main types: a model with additive seasonal components and a model with multiplicative seasonal components.
When a source series shows rather constant periodic deviations in an absolute expression from the mean series level varying in time and based on a predefined period, the seasonal component is additive. An additional δ parameter is added to the exponential smoothing model to reflect this feature. Then in the model
,
where:
. Additive seasonal component.
L. Seasonal period.
Values of the δ parameter may lie in the range 0 to 1. If δ = 0, the seasonal component at the current moment is identical to seasonal component in the corresponding point of the previous seasonal cycle. Thus, the non-varying seasonal component is used to generate a forecasting value one step forward. If δ = 1, the seasonal component at the current moment is equal to the current modeling error. In most cases when the source series includes seasonal component, the optimal value of the parameter δ lies in the range from 0 to 1.
The multiplicative model has the following features: seasonal deviations from the mean level of a source series varying over time change are sufficiently stable relative changes, that is, the change is defined for each point of a seasonal cycle relative to this level. Thus:
,
where:
. Multiplicative seasonal component.
See also:
Library of Methods and Models | Exponential Smoothing | Exponential Smoothing. Growth Models | Best Trial Method