The seasonal decomposition is a method used in time series analysis to represent a time series as a sum (or, sometimes, a product) of three components – the linear trend, the periodic (seasonal) component, and random residuals.
The seasonal decomposition is useful in analysis of time series affected by factors that change in time in a cyclic (periodical) manner. For example, 10-year temperature records for a particular place include a clear seasonal component – with ups and downs at the same time of the year observed in all 10 years.
The “seasonal” here does not necessarily mean the season of the year. Any periodical component with a known period may be described in this way. For example, the total sales in a supermarket depend on the day of the week. Thus, the periodic component that may be of practical interest has the period 7 days, not a year.
There several methods for seasonal decomposition. Many of them are based on the ARMA model of the time series.
The seasonal decomposition is an essential stage in the seasonal adjustment .