Page 241 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes
Example: Assuming that the trend is linear, calculate seasonal indices by the ratio to
moving average method from the following data:
Quarterly output of coal in 4 years (in thousand tonnes)
Year I II III IV
2007 65 58 56 61
2008 68 63 63 67
2009 70 59 56 52
2010 60 55 51 58
Solution:

By adding the values of all the quarters of a year, we can obtain annual output for each of the four
years. Fit a linear trend to the data and obtain trend values for each quarter.

Year Output X 2 t 1983.5 XY X 2
2007 240 3 720 9
2008 261 1 261 1
2009 237 1 237 1
2010 224 3 672 9
Total 962 0 72 20
962 72
From the above table, we get a 240.5 and b 3.6
4 20
Thus, the trend line is Y = 240.5 - 3.6X, Origin: 1st January 2009, unit of X: 6 months.
240.5 3.6
The quarterly trend equation is given by Y X or Y = 60.13 – 0.45X,
4 8
Origin : 1st January 2009, unit of X : 1 quarter (i.e., 3 months).
Shifting origin to 15th Feb. 2009, we get
1
Y = 60.13 - 0.45(X + ) = 59.9 – 0.45X, origin I-quarter, unit of X = 1 quarter.
2
The table of quarterly values is given by
Year I II III IV
2007 63.50 63.05 62.60 62.15
2008 61.70 61.25 60.80 60.35
2009 59.90 59.45 59.00 58.55
2010 58.10 57.65 57.20 56.75

Y
The table of Ratio to Trend Values, i.e., 100
T

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