Page 238 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 11: Analysis of Time Series

11.2 Seasonal Variations Notes

If the time series data are in terms of annual figures, the seasonal variations are absent. These
variations are likely to be present in data recorded on quarterly or monthly or weekly or daily
or hourly basis. As discussed earlier, the seasonal variations are of periodic nature with period
equal to one year. These variations reflect the annual repetitive pattern of the economic or
business activity of any society. The main objectives of measuring seasonal variations are :
1. To understand their pattern.

2. To use them for short-term forecasting or planning.
3. To compare the pattern of seasonal variations of two or more time series in a given period
or of the same series in different periods.

4. To eliminate the seasonal variations from the data. This process is known as
deseasonalisation of data.

11.2.1 Methods of Measuring Seasonal Variations

The measurement of seasonal variation is done by isolating them from other components of a
time series. There are four methods commonly used for the measurement of seasonal variations.
These method are :
1. Method of Simple Averages

2. Ratio to Trend Method
3. Ratio to Moving Average Method
4. Method of Link Relatives
Note: In the discussion of the above methods, we shall often assume a multiplicative model. However,
with suitable modifications, these methods are also applicable to the problems based on additive model.

Method of Simple Averages

This method is used when the time series variable consists of only the seasonal and random
components. The effect of taking average of data corresponding to the same period (say 1st
quarter of each year) is to eliminate the effect of random component and thus, the resulting
averages consist of only seasonal component. These averages are then converted into seasonal
indices, as explained in the following examples.

Example: Assuming that trend and cyclical variations are absent, compute the seasonal
index for each month of the following data of sales (in ‘000) of a company.

Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
2008 46 45 44 46 45 47 46 43 40 40 41 45
2009 45 44 43 46 46 45 47 42 43 42 43 44
2010 42 41 40 44 45 45 46 43 41 40 42 45

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