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Unit 22: Time Series Analysis—Introduction and Components of Time Series

Distinction between Cyclical and Seasonal Variations Notes

The following are the main points of distinction between seasonal and cyclical variations:
(i) Duration of Variations: Cyclical variations have a duration of two to fifteen years, whereas
seasonal variations have a duration of one year only.
(ii) Degree of Accuracy: Cyclical variations cannot be accurately estimated because of lack of their
regularity whereas seasonal variations can be estimated with a high degree of accuracy.
(iii) Regularity: There is no regularity in the periodicity of cyclical variations whereas there is regular
periodicity in seasonal variations.
(iv) Causes of Variations: The main causes of cyclical variations are economic whereas seasonal
variations take place because of weather conditions and customs and traditions.
(v) Activities of Preceding Variations: Cyclical variations depend upon the activities of the
preceding period whereas seasonal variations do not depend on the activities of preceding
period.
Irregular Variation

The last component of a time series is the irregular variation. After eliminating the trend, cyclical,
and seasonal variations from a time series, we have an unpredictable element left in the series. Irregular
variation, generally, occurs over a short interval of time period and follows a random pattern. For
example, a strike in an industrial unit may push down its production and consequently, the sales.
Some other causes for these variations are flood draught, fire, war or other unforeseeable events.
Because of the unpredictability of irregular variation, attempt has not been made to study it
mathematically. However, we can often isolate its causes, although in some situations it is difficult to
identify such causes. But it should be noted that over a period of time, these random fluctuations
tend to counteract each other and thus we may have a time series free of irregular variation.
22.3 An Illustration Involving all Components

As an illustration for studying all the components of a time series, we shall work out a problem
involving all the components. An engineering firm producing farm equipments wants to predict
future sales based on the analysis of its past sales pattern. The sales effected by the firm during the
past five years is given in Table 6.

Table 6: Quarterly Sales of an Engineering Firm during 1975 to 1979
(Rs. in lakhs)
Quarters
Year I II III IV

1975 5.5 5.4 7.2 6.0
1976 4.8 5.6 6.3 5.6
1977 4.0 6.3 7.0 6.5
1978 5.2 6.5 7.5 7.2
1979 6.0 7.0 8.4 7.7

The procedure involved in this study consists of:
1. deseasonalizing the time series,
2. fitting the trend line, and
3. identifying the cyclical variation around the trend line.
The steps involved in deseasonalizing the time series are given in Table 7 and Table 8. These steps
have been already discussed in Seasonal variation.

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