Decomposition methods are used to deconstruct a time series signal into several components:
Trend
Seasonal
Cyclic
Noise (random error)
Used when the amount of seasonal variation DOES NOT increase (or decrease) steadily over time.
yt = TRt + SNt + CLt + IRt
yt = observed value of the time series in time period t
TRt = trend component
SNt = seasonal component
CLt = cyclical component
IRt = irregular component (noise, random error)
Used when the amount of seasonal variation DOES increase (or decrease) steadily over time.
As an alternative it may be possible to take the natural log of the time series and use additive decomposition.
yt = TRt x SNt x CLt x IRt
yt = observed value of the time series in time period t
TRt = trend component
SNt = seasonal component
CLt = cyclical component
IRt = irregular component (noise, random error)
See subpage Decomposition - Example 1 (R)
See https://www.otexts.org/fpp/6 which also offers a good overview of decomposition methods.