1. In an additive time-series model, the seasonal component is estimated as S = Y – (T+C+I) Where S is for Seasonal values Y is for actual data values of the time-series T is for trend values C is for cyclical values I is for irregular values.
2. In a multiplicative time-series model, the seasonal component is expressed in terms of ratio and percentage as Seasonal effect = (T*S*C*I)/( T*C*I)*100 = Y/(T*C*I )*100; However in practice the detrending of time-series is done to arrive at S*C*I . This is done by dividing both sides of Y=T*S*C*I by trend values T so that Y/T =S*C*I.
3. The deseasonalized time-series data will have only trend (T) cyclical(C) and irregular (I) components and is expressed as:
- Multiplicative model : Y/S*100 =( T*S*C*I)/S*100 = (T*C*I)*100.
- Additive model: Y – S = (T+S+C+I) – S = T+C+I
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