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 botto ...

1. 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

2. 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 https://machinelearningmastery.com/decompose-time-
series-data-trend-
seasonality/#:~:text=Time%20series%20decomposition%20invol

3. ves%20thinking,time%20series%20analysis%20and%20forecasti
ng.
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_Seri
es_Modelling_and_Decomposition