Models for Decomposition

Classical or traditional decomposition is so called because it's the old, established, standard method for breaking down a time series into its four main components (trend, seasonality, cyclicity, and noise). It takes each value of a variable y and numerically identifies the proportions of that value that each of those four components contributes. There are two ways to describe those proportions.
• On an additive basis, that is, in terms of values that are added to yield the observed y (an ''additive model"):
value of time-series variable = trend + seasonality + cyclicity + noise. .......(1)
• On a multiplicative basis, that is, in terms of values that are multiplied to yield the observed y (a "multiplicative model"): value of time-series variable = trend × seasonality × cyclicity × noise.
As with standardization, it's common to first prepare raw time-series data such that each observation represents a "season" (if the basic measurements weren't made that way). So, for example, if we measure a variable each day but want to define a season as three months, we'd add up the appropriate three months' worth of daily measurements and average them to get a single value that embodies that particular season. Then we'd repeat for subsequent three-month seasons.