Decomposition (Additive and Multiplicative)

Decomposition is one approach to time-series analysis that isolates four components influencing X’s value over time: trend, cycle, seasonal variations and irregular fluctuations. Trend is the long-term component representing the growth or decline in the time series over an extended period of time (i.e. price inflation or population growth). The cyclical component is an upward and downward change, occurring over a period of two to 10 years or longer (i.e. economic expansions and contractions). The seasonal component is repeated annually, and reflects weather, holidays and/or length of the calendar year (like the seasonal fluxes of retail sales). After the other components have been removed, the irregular component measures the variability of the time series based on unpredictable factors like major weather changes or strikes. In other words, the irregular component accounts for randomness. The goal of decomposition is to extract and take into account each influential factor in a time series and obtain a forecast for each. Then, an overall forecast is achieved by combining the projections for each component. So, rather than having only one defined measurement (time), decomposition justifies X’s value over time, forecasting from specific components within time.