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Time Series :

Time series is statistical data which is recorded or arranged with respect to time, in other words one can say that time series is statistical data which is presented chronologically.

Time series is an important forecasting tool.

Component of time series

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1. Trend Component :

Secular trend or Simply trend we mean the general tendency of data to increase and decrease during a long span of time .

Trend is the general, smooth, long term average tendency . Trend may be linear and nonlinear .

Periodic Changes : In Periodic Changes their are two type of variations

(i). Season variation

(ii) . Cyclic variation

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2 . Seasonal variation :

These variations in a time series are due to the seasonal forces (rhythmic forces) which operate in a regular and perodic manner over a period of less than a year. Thus seasonal variation in time series will be their if the data recorded quarterly , monthly , weekly and so all . The seasonal variation may be attributed becaus eof two causes .

Because of natural forces

Because of man-made convension

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3 . Cyclic variation :

Cyclic variation is the oscillatory movement in a time series with period of oscillation more than one year .

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4 . Irregular Component :

It is also called as random flctuation these fluctuation purly random , unforeseen , unpredictable .Irregular Component are beyond the human control .

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Models of Time Series :

There are two type of models which are generally used for decomposition of time series into its four component . The objective of model is to estimate and the seperate the four type of variations .

(i) Additive modal

(ii) Multiplicated model

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(1) Additive modal : In additive modal the all four component of time series are independent of one another , It means the pattern of change of magnitute of any particular componenet does not affect the other component.

Arithmetically additive modal can be expressed as

Y = T + S + C + R

Where T = trend value S = seasonal variation, C = Cyclic variation and R = Random variation.

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(2) Multiplicative Model: In this model the components of time series are interdependent. Arithmetically the model can be written as:

Y = T x S x C x R

Where T = trend value, S = seasonal variation, C = Cyclic variation and R = Random variation.

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Measurement of Secular Trend

There are four methods to find the same:

(a) Graphical method or Freehand curve method

(b) Method of Semi-Averages

(c) Method of Moving Averages

(d) Method of least Squares or Normal Equations Method

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Measurement of Seasonal variation There are Three methods to find the same:

(a) Simple Average Method

(b) Ratio to Trend Method

(c) Link Relative Method

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