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Quantitative Techniques – I

Notes Objectives of Measuring Trend
There are four main objectives of measuring trend of a time series data:
(a) To study past growth or decline of the series. On ignoring the short-term fluctuations,
trend describes the basic growth or decline tendency of the data.
(b) Assuming that the same behaviour would continue in future also, the trend curve
can be projected into future for forecasting.

(c) In order to analyse the influence of other factors, the trend may first be measured
and then eliminated from the observed values.
(d) Trend values of two or more time series can be used for their comparison.

2. Periodic Variations: These variations, also known as oscillatory movements, repeat
themselves after a regular interval of time. This time interval is known as the period of
oscillation. These oscillations are shown in the following figure:
Figure 11.1: Periodic Variations

The oscillatory movements are termed as Seasonal Variations if their period of oscillation
is equal to one year, and as Cyclical Variations if the period is greater than one year.
A time series, where the time interval between successive observations is less than or
equal to one year, may have the effects of both the seasonal and cyclical variations. However,
the seasonal variations are absent if the time interval between successive observations is
greater than one year.
Although the periodic variations are more or less regular, they may not necessarily be
uniformly periodic, i.e., the pattern of their variations in different periods may or may not
be identical in respect of time period and size of periodic variations. For example, if a
cycle is completed in five years then its following cycle may take greater or less than five
years for its completion.

(a) Causes of Seasonal variations: The main causes of seasonal variations are:
(i) Climatic Conditions
(ii) Customs and Traditions

(i) Climatic Conditions: The changes in climatic conditions affect the value of
time series variable and the resulting changes are known as seasonal variations.
For example, the sale of woolen garments is generally at its peak in the month
of November because of the beginning of winter season. Similarly, timely
rainfall may increase agricultural output, prices of agricultural commodities
are lowest during their harvesting season, etc., reflect the effect of climatic
conditions on the value of time series variable.

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