A time series consists of a set of observations arranged in chronological order (either ascending or descending).

**Meaning,
Uses and Basic Components**

**Meaning:**

A time series consists
of a set of observations arranged in chronological order (either ascending or
descending). Time Series has an important objective to identify the variations
and try to eliminate the variations and also helps us to estimate or predict
the future values.

**Why
should we learn Time Series?**

It helps in the analysis
of the past behavior.

It helps in forecasting
and for future plans.

It helps in the
evaluation of current achievements.

It helps in making
comparative studies between one time period and others.

Therefore time series
helps us to study and analyze the time related data which involves in business
fields, economics, industries, etc…

**Components
of Time Series**

There are four types of
components in a time series. They are as follows;

(i) Secular Trend

(ii) Seasonal variations

(iii) Cyclic variations

(iv) Irregular
variations

**(i) Secular Trend**

It is a general tendency
of time series to increase or decrease or stagnates during a long period of
time. An upward tendency is usually observed in population of a country,
production, sales, prices in industries, income of individuals etc., A downward
tendency is observed in deaths, epidemics, prices of electronic gadgets, water
sources, mortality rate etc…. It is not necessarily that the increase or
decrease should be in the same direction throughout the given period of time.

**(ii) Seasonal
Variations**

As the name suggests,
tendency movements are due to nature which repeat themselves periodically in
every seasons. These variations repeat themselves in less than one year time.
It is measured in an interval of time. Seasonal variations may be influenced by
natural force, social customs and traditions. These variations are the results
of such factors which uniformly and regularly rise and fall in the magnitude.
For example, selling of umbrellas’ and raincoat in the rainy season, sales of
cool drinks in summer season, crackers in Deepawali season, purchase of dresses
in a festival season, sugarcane in Pongal season.

**(iii) Cyclic Variations**

These variations are not
necessarily uniformly periodic in nature. That is, they may or may not follow
exactly similar patterns after equal intervals of time. Generally one cyclic
period ranges from 7 to 9 years and there is no hard and fast rule in the
fixation of years for a cyclic period. For example, every business cycle has a
Start- Boom- Depression-Recover, maintenance during booms and depressions,
changes in government monetary policies, changes in interest rates.

**(iv) Irregular
Variations**

These variations do not
have particular pattern and there is no regular period of time of their
occurrences. These are accidently changes which are purely random or
unpredictable. Normally they are short-term variations, but its occurrence
sometimes has its effect so intense that they may give rise to new cyclic or
other movements of variations. For example floods, wars, earthquakes, Tsunami,
strikes, lockouts etc…

**Mathematical
Model for a Time Series**

There are two common
models used for decomposition of a time series into its components, namely
additive and multiplicative model.

**(i) Additive Model:**

This model assumes that
the observed value is the sum of all the four components of time series. (i.e)
Y= T+S+C+I

where Y = Original value , T = Trend Value ,
S = Seasonal component

C = Cyclic component
, I = Irregular component

The additive model
assumes that all the four components operate independently. It also assumes
that the behavior of components is of an additive character.

**(ii) Multiplicative
Model:**

This model assumes that
the observed value is obtained by multiplying the trend(T) by the rates of
other three components. Y = T × S × C × I

where Y = Original value , T = Trend Value ,
S = Seasonal component

C = Cyclic component
, I = Irregular component

This model assumes that
the components due to different causes are not necessarily independent and they
can affect one another. It also assumes that the behavior of components is of a
multiplicative character.

Tags : Applied Statistics , 12th Business Maths and Statistics : Chapter 9 : Applied Statistics

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12th Business Maths and Statistics : Chapter 9 : Applied Statistics : Meaning, Uses and Basic Components of Time Series Analysis | Applied Statistics

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