Page 246 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 11: Analysis of Time Series

Notes
Example: Determine the seasonal indices from the following data by the method of link
relatives:
Year 1st Qr 2nd Qr 3rd Qr 4th Qr
2006 26 19 15 10
2007 36 29 23 22
2008 40 25 20 15
2009 46 26 20 18
2010 42 28 24 21
Solution.
Calculation Table

Year I II III IV
2006 73.1 78.9 66.7
2007 360.0 80.5 79.3 95.7
2008 181.8 62.5 80.0 75.0
2009 306.7 56.5 76.9 90.0
2010 233.3 66.7 85.7 87.5
Total 1081.8 339.3 400.8 414.9
Mean 270.5 67.9 80.2 83.0
C.R. 100.0 67.9 54.5 45.2
C.R.(adjusted) 100.0 62.3 43.3 28.4
S.I. 170.9 106.5 74.0 48.6
The chained relative (C.R.) of the 1st quarter on the basis of C.R. of the 4th quarter
270.5 45.2
122.3 .
100
1
The trend adjustment factor d 122.3 100 5.6
4
Thus, the adjusted C.R. of 1st quarter = 100
and for 2nd = 67.9 – 5.6 = 62.3
for 3rd = 54.5 - 2 5.6 = 43.3
for 4th = 45.2 - 3 5.6 = 28.4
100 62.3 43.3 28.4
The grand average of adjusted C.R., G 58.5
4
Adjusted C.R. 100
The seasonal index of a quarter
G
Merits and Demerits

This method is less complicated than the ratio to moving average and the ratio to trend methods.
However, this method is based upon the assumption of a linear trend which may not always
hold true.

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