The factors that are responsible for bringing about changes in a time series are called the components of time series.

**COMPONENTS OF TIME SERIES**

The factors that are responsible for bringing about changes in a
time series are called the components of time series.

1. Secular trend

2. Seasonal variation

3. Cyclical variation

4. Irregular (random) variation

There are two approaches to the decomposition of time series data

(i) Additive approach

(ii) Multiplicative approach

The above two approaches are used in decomposition, depending on
the nature of relationship among the four components.

The additive approach is used when the four components of a time
series are visualized as independent of one another. Independence implies that
the magnitude and pattern of movement of the components do not affect one
another. Under this assumption the magnitudes of the time series are regarded
as the sum of separate influences of its four components.

*Y *=* T *+* C *+* S *+* R*

where *Y* = magnitude of a time series

*T *= Trend,

*C *=Cyclical component,

*S *=Seasonal component, and

*R *= Random component

In additive approach, the unit of measurements remains the same
for all the four components.

The multiplicative approach is used where the forces giving rise
to the four types of variations are visualized as interdependent. Under this
assumption, the magnitude of the time series is the product of its four
components.

*i.e. Y *=* T *×* C *×* S *×* R*

**Multiplicative**

1. Four components of time series are interdependent

2. Logarithm of components are additive

**Additive**

1. Four components of time series are independent

2. Components are additive

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

12th Statistics : Chapter 7 : Time Series and Forecasting : Components of Time Series |

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