Page 242 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 11: Analysis of Time Series

Notes
Years I II III IV
2007 102.36 91.99 89.46 98.15
2008 110.21 102.86 103.62 111.02
2009 116.86 99.24 94.92 88.81
2010 103.27 95.40 89.16 102.20
Total 432.70 389.49 377.16 400.18
Average 108.18 97.37 94.29 100.05
I
S . . 108.20 97.40 94.32 100.08
399.89
Note: Grand Average, G 99.97
4
Example: Find seasonal variations by the ratio to trend method, from the following
data:

Year - I Qr II -Qr III -Qr IV -Qr
2006 30 40 36 34
2007 34 52 50 44
2008 40 58 54 48
2009 54 76 68 62
2010 80 92 86 82
Solution:
First we fit a linear trend to the annual totals.

Annual Totals 2
Years X XY X
( )
Y
2006 140 2 280 4
2007 180 1 180 1
2008 200 0 0 0
2009 260 1 260 1
2010 340 2 680 4
Total 1120 0 480 10
1120 480
Now a 224 and b 48.
5 10
The trend equation is Y = 224 + 48X, origin : 1st July 2008, unit of X = 1 year.
224 48
The quarterly trend equation is Y = + X = 56 +3X, origin: 1st July 2008, unit of X = 1
4 16
quarter.
Shifting the origin to III quarter of 2008, we get
1
Y = 56 + 3(X + ) = 57.5 + 3X
2

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