Page 213 - DMGT404 RESEARCH_METHODOLOGY

Unit 10: Time Series

daily b value must be apportioned to each hour. This is accomplished by a further division by Notes
six—the number of trading hours. The result is entered in column (3). Note that the origin of a
time series is always zero. The origin of the time series is always the first period of the season.
In our case this is the 10-11 trading hour. Therefore the first entry in column (3) is always zero to
be followed by the equal (since this is a linear analysis) summed increment of the apportioned
b-value.

Table 10.3: Worksheet for Trend Calculation

Day Code Trading Volume Per Day
x X 1 y x y X 2
7/1 -3 10.85 -32.55 9
7/5 -1 11.22 -11.22 1
7/6 1 14.28 14.28 1
7/7 3 16.19 48.57 9
Total 52.54 19.08 20

S xy
b =
S x 2
19.08
= 0.954
20
and the apportioned b-value is
0.954
= 0.159
6
It is not necessary to calculate the y-intercept (a) in this analysis unless of course, you wish to
combine it with a long-term forecast of daily trading volume. Then, just to review the calculations,
you would find:
S y
a =
n

52.54
=
4
= 13.135
and
y = 13.135 + 0.954 x
c
origin 7/5 and 7/6

x in half trading day units.
In column (4) TS – T = S is performed. Column (4) is already a measure of seasonal variation. But
in order to standardise the answer so that it may be compared with other stock exchange, for
example, it is customary to convert the values in column (4) to a seasonal index. Every index has
a base of 100 and the values above or below the base indicate percentages of above or below
“normal” activity, hence the season. Since the base of column (5) is 100, the mean of the column
should be 100 and the total 600 since there are 6 trading hours. In order to convert the obtained
values of column (4) to index numbers, each of its entries is added to the total mean and then is
divided by the column mean added to total mean and multiplied by 100 yielding the corresponding
entry in column (5). It is customary to show index numbers with one significant digit.

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