There are two different process in which a time series may be deseasonalised. They are : (i) Additive Process and (ii) Multiplicative process. The process to be adopted will depend very much upon the process of analysis of the time series. If in course of analysis of a time series the seasonal var5iations are obtained, or available in absolute form, the additive process of deseasonalisation is to be adopt3ed. On the other hand, if the seasonal variations are obtained, or available in the form of seasonal indices, the multiplicative process of deseasonalisation is to be taken up. The algorithms of these two processes are given here as under:
Additive Process of Deseasonalization.
Under this process, deseasonalisation is made simply by subtracting the seasonal variations from their corresponding observed values, or residual variations of the time series. Symbolically, it may be represented by,
(i) ¯S = (o –t) – S, or ¯S = O – S
(ii) Where, ¯S = the deseasonalised data i.e. (C + 1), or (T + C + 1)
(iii) O = an observed value of a time series.
(iv) T = the trend value i.e. Yc of the above.
S = the seasonal variation of O
(O – T) = the total of short-term variations of the observed value after subtractions of the trend value. In short, it represents the trend eliminated value.
Multiplicative process of Deseasonalisation
Under this process, deseasonalisation is made simply by dividing either the trend eliminated value (O/T), or the original value by its corresponding seasonal effect (SE). Symbolically it can be represented by
¯S = ( O/T) / S.E, or ¯S = O/ SE
Where, ¯S = the deseasonalised value i.e. CI or RCI
O = the original, or observed value
(O/T) × 100 = the trend eliminated value i.e. SCI and
S.E. = Seasonal effect which is obtained by diving the seasonal index by 100 i.e. SE = S.I/ 100