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https://otexts.com/fpp2/components.html

Time series analysis aids in decomposing a series into parts which can be related to various variations. Time series decomposition was first used by astronomers to calculate planetary orbits. The assumptions for decomposition: A long-term tendency or trend, cyclic movements, a seasonal movement in each year, and residual variations. These variations have been seen as mutually independent from each other thus, indicated by an additive decomposition model. If they depend on each other then, it creates a multiplicative model. In the case, the components are the trend, seasonality, and irregular. The additive model can be used to better understand data observed such as about airline passengers per month for the last ten years. To begin, the trend part of the airline passenger time series is extracted. The computation can be done using moving average. The trend for instance, may move upwards. Next, the time series can be DeTrend by subtracting the trend from time series. Detrended data reinforces seasonal variations of time series (Dagum, 2013). Assume that magnitude is constant. The data points are averaged for each month to find out seasonality. Residual component is what remains after subtracting the trend and season from the time series. Decomposition technique is justified in this example of airline passengers. The time series is composed of a summation of the seasonal variation, trend, and residual, exhibiting additive model. A benefit of decomposition is that it offers a pictorial representation of the data which enhances making a concrete conclusion about the study. It can be used to analyze and comprehend historic time series as well as make forecasts.

Additive model is used when seasonal variation is constant over time. The seasonal variation must have the same magnitude across time to implement additive. On the other hand, multiplicative model is important when seasonal variation rises over time.

The additive model is useful when the seasonal variation is relatively constant over time. The multiplicative model is useful when the seasonal variation increases over time.

The additive decomposition is the most appropriate if the magnitude of the seasonal fluctuations, or the variation around the trend-cycle, does not vary with the level of the time series. When the variation in the seasonal pattern, or the variation around the trend-cycle, appears to be proportional to the level of the time series, then a multiplicative decomposition is more appropriate. Multiplicative decompositions are common with economic time series.

The Figure above shows an additive decomposition of these data. Three components are shown separately in the bottom three panels of. These components can be added together to reconstruct the data shown in the top panel.

Seasonal component changes slowly over time, so that any two consecutive years have similar patterns, but years far apart may have different seasonal patterns. The remainder component shown in the bottom panel is what is left over when the seasonal and trend-cycle components have been subtracted from the data.

 If the purpose is to look for turning points in a series, and interpret any changes in direction, then it is better to use the trend-cycle component rather than the seasonally adjusted data.

Reference

Additive models and multiplicative models – Minitab. (2020). Retrieved 4 March 2020, from 

https://support.minitab.com/en-us/minitab/19/help-and-how-to/modeling-statistics/time-series/supporting-topics/time-series-models/additive-and-multiplicative-models/

Brownlee, J. (2017). How to Decompose Time Series Data into Trend and Seasonality. Retrieved 4 March 2020, from 

How to Decompose Time Series Data into Trend and Seasonality

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Evans, J., & Basu, A. (2013). Statistics, data analysis, and decision modeling. Boston: PearsonBottom of Form

Dagum, E. (2013). Time series modeling and decomposition.

https://www.researchgate.net/publication/307663962_Time_Series_Modelling_and_Decomposition