Page 231 - DMGT404 RESEARCH_METHODOLOGY

Unit 10: Time Series

Notes
1
d = [New C.R. for 1st month – 100] for quarterly data
4
1
and d = [New C.R. for 1st month – 100] for monthly data.
12
On the assumption that the trend is linear, d, 2d, 3d, etc., is respectively subtracted from
the 2nd, 3rd, 4th, etc., quarter (or month).

5. Express the adjusted chained relatives as a percentage of their average to obtain seasonal
indices.
6. Make sure that the sum of these indices is 400 for quarterly data and 1200 for monthly data.

Example: Determine the seasonal indices from the following data by the method of link
relatives:
Year 1st Qr 2nd Qr 3rd Qr 4th Qr
1985 26 19 15 10
1986 36 29 23 22
1987 40 25 20 15 :
1988 46 26 20 18
1989 42 28 24 21
Solution:
Calculation Table
Year I II III IV
1985 - 73.1 78.9 66.7
1986 360.0 80.5 79.3 95.7
1987 181.8 62.5 80.0 75.0
1988 306.7 56.5 76.9 90.0
1989 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

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