Suggested Solutions to Assignment 4 (Optional) - Trent University

7. The composite index is obtained by calculating the percentage change for each series
relative to the base month and then averaging these percentage changes. The percentage
change from the first to the second month is 10 for indicator A, 15 for indicator B, and
−10 for indicator C. Their simple average (since each indicator is given equal weight)
is 5 percent. Taking the first month as the base period with a composite index of 100,
we obtain the composite index of 105 for the second month.
For the third month, the change of each indicator from the base period is 20 percent, 10
percent, and 10 percent, respectively, with an average of 13.3 percent. Adding this value
to 100 (the base-period value of the composite index), we get the composite index of 113.33
for the third month. These composite indexes are shown in the second column of Table 4.
Since two indicators rise and one falls from the first to the second period, the diffusion index
for the second period is 66.7 percent. On the other hand, since all three indicators rise from
the second to the third month, the diffusion index for the third month is 100 percent. These
diffusion indexes are shown in the third column of Table 4.
Thus, according to the composite and diffusion indexes, the level of economic activity
should improve in future months.
Table 4
Month
Composite
Index
Diffusion
Index
1 100.00 —
2 105.00 66.70
3 113.33 100.00
8. (a) Time series A is a coincident indicator of the index series of cereal sales of the Tasty
Food Company. The reason for this is that series A moves in step or coincidentally
with the time series of the sales index. When the time series of the sales index rises,
series A rises, and when the sales index falls, series A also falls in the same month.
(b) Time series B is a leading indicator of the index of cereal sales. That is, series B
anticipates or leads changes in the direction of the sales index and can, therefore, be
used to forecast changes in the firm's sales index. The lead time is two months.
For example, the decline in the sales index between the third and fourth month is
anticipated and can be forecasted from the decline in the value of time series B from
the first to the second month. Similarly, the rise in the index of cereal sales in the fifth
month can be forecasted by the rise in the value of series B in the third month, and so on.
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