Normalizing Seasonal Components

In exponential smoothing methods, the m seasonal components are combined with level and trend components to indicate changes to the time series that are caused by seasonal effects. It is sometimes desirable to report the value of these m seasonal components, and then it is important for them to make intuitive sense. For example, in the additive seasonal model ETS(A,A,A), the seasonal components are added to the other components of the model. If one seasonal component is positive, there must be at least one other seasonal component that is negative, and the average of the m seasonal components should be 0. When the average value of the m additive seasonal components at time t is 0, the seasonal components are said to be normalized. Similarly, we say that multiplicative seasonal components are normalized if the average of the m multiplicative seasonal components at time t is 1.

Normalized seasonal components can be used to seasonally adjust the data. To calculate the seasonally adjusted data when the model contains an additive seasonal component, it is necessary to subtract the seasonal component from the data. For a multiplicative seasonal component, the data should be divided by the seasonal component.