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Statistical Methods in Economics
Notes One should note at this stage that the first two and the last two quarters do not have
the corresponding moving averages. This step allows us to recover the seasonal
component for the quarters.
The fourth step is to collect all the percentages of actual to moving average values and
to arrange them by quarter. We then calculate the mean for each quarter. These
computations have been shown in Table 4.
7.5
7.0
6.5
SALES 6.0
5.5 ORIGINAL TIME SERIES
FOUR-QUARTER MOVING
5.0
AVERAGE
4.5
I II III IV I II III IV I II III IV I II III IV I II III IV
1974 1975 1976 1977 1978
Figure 8: Moving Average: Smoothening the Original Data in Table 3
Table 4: Computation of Seasonal Index for Data Given in Table 3
Year Quarter I Quarter II Quarter III Quarter lV
1974 — — 96.2 101.3
1975 106.7 95.7 93.1 99.8
1976 108.1 97.2 96.0 102.8
1977 109.7 94.6 93.2 105.1
1978 103.7 91.3 — —
Mean 107.1 94.7 94.6 102.2
Seasonal Index 107.5 95.1 95.0 102.5
The final step is to adjust these quarterly means slightly. One can find out that the sum of the four
quarterly means is 398.5 (from Table 4). However, the base for an index is 100 and therefore the four
quarterly means should total 400 so that their mean is 100. To correct this error, we multiply each of
the quarterly indices in Table 4 by an adjusting constant, the constant being computed by dividing
the desired sum of indices (400) by the actual sum (398.5). In this case, this constant is 1.0038. Thus,
we get the seasonal indices for each of the quarters. This has been given in the last row of Table 4.
There are a few other methods for computing the seasonal index. One of them is the link-relative
method. However, the computation of seasonal indices by this method is slightly complicated. The
steps involved in this method are as follows:
1. Calculate the seasonal link relatives for each seasonal value by the following formula:
Current seasons' value
Link relative = × 100
Previous season's value
2. Calculate the average of the link relatives for each season.
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