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Unit 10: Time Series
(b) To predict the effect of cyclical variations so as to provide guidelines for future Notes
business policies.
10.2.3 Random or Irregular Variations
As the name suggests, these variations do not reveal any regular pattern of movements. These
variations are caused by random factors such as strikes, floods, fire, war, famines, etc. Random
variations is that component of a time series which cannot be explained in terms of any of the
components discussed so far. This component is obtained as a residue after the elimination of
trend, seasonal and cyclical components and hence is often termed as residual component.
Random variations are usually short-term variations but sometimes their effect may be so
intense that the value of trend may get permanently affected.
Self Assessment
Fill in the blanks:
4. .............................. is the general tendency of the data to increase or decrease or stagnate
over a long period of time.
5. The oscillatory movements are termed as ……………….if their period of oscillation is
equal to one year.
6. Random variations are usually ………………variations
10.3 Time Series Forecasting Method
Time series forecasting methods are based on analysis of historical data. They make the
assumption that part patterns in data can be used to forecast future data points. In this unit, we
will discuss two methods: (a) Moving Average Method and (b) Exponential Smoothing.
10.3.1 Method of Moving Average
This method is based on the principle that the total effect of periodic variations at different
points of time in its cycle gets completely neutralised, i.e., SSt = 0 in one year and SCt = 0 in the
period of cyclical variations.
In the method of moving average, successive arithmetic averages are computed from
overlapping groups of successive values of a time series. Each group includes all the observations
in a given time interval, termed as the period of moving average. The next group is obtained by
replacing the oldest value by the next value in the series. The averages of such groups are known
as the moving averages.
The moving average of a group is always shown at the centre of its period. The process of
computing moving averages smoothens out the fluctuations in the time series data. It can be
shown that if the trend is linear and the oscillatory variations are regular, the moving average
with period equal to the period of oscillatory variations would completely eliminate them.
Further, the effect of random variations would get minimised because the average of a number
of observations must lie between the smallest and the largest observation. It should be noted
here that the larger is the period of moving average the more would be the reduction in the
effect of random component but more information is lost at the two ends of data.
When the trend is non-linear, the moving averages would give biased rather than the actual
trend values.
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