Page 215 - DMGT404 RESEARCH_METHODOLOGY

Unit 10: Time Series

Setting x = 0 as previously explained, Sx3 will also be zero. Notes
Sy = na + cSx 2
2
2
Sx y = aSx + cSx 4
S xy
b =
S x 2
There are direct formulas for a and c as well, but because of the possible compounding of
arithmetic error in manual calculations, it is safer to solve a and c algebraically in this case.

To illustrate the parabolic trend let us forecast earnings per share in dollars for Storage Technology
Corporation for the years 2000 and 2001. Storage Technology manufactures computer data
storage equipment, printers, DVD-ROMS and telecommunication products. The company was
founded in 1969 and after going through a period of explosive growth seems to be moving into
the maturity stage. Data, code and calculations are shown below in the usual worksheet format.
Year Code Earnings
Per Share
4
2
2
x y xy x x y x
1993 -3 0.39 -1.17 9 3.51 81
1994 -2 0.54 -1.08 4 2.16 16
1995 -1 1.13 -1.13 1 1.13 1
1996 0 1.58 0 0 0 1
1997 1 1.72 1.72 1 1.72 1
1998 2 2.50 5.00 4 10.00 16
1999 3 1.84 5.52 9 16.56 81
Total 0 9.70 8.86 28 35.08 196

8.86
Then b =
28
= 0.3164
and solving simultaneously

9.70 = 7a + 28c  4
 38.8 = 28a + 112c

35.08 = 28a + 196c
3.72 = 84c
c = 0.0443

a = 1.2085
Therefore
y = 1.2085 + 0.3164 x – 0.0443x 2
c
origin 1996
x in 1 year units

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