Decomposition is a multicomponent model. It assumes that the time series is composed of four components: trend, seasonality, cyclical components and irregular components. The seasonal component is constant from year to year.
The model is:
Yt = f(Tt,Ct,St,e)
Where,
Yt = Actual value of the time series at time
f = Mathematical function of
T = Trend
C = Cyclical influences
S = Seasonal influences
e = error
Seasonal variations are: ..., 12 months, 4 quarters, 7 days, ...
The risidual component e, error, is not explained by T, C and S.
There are two types of decomposition models:
Y = T + C + S + e, the additive model
Y = T * C * S * e, the multiplicative model