One way of dealing with the problems where trends are
uncertain is to do what is called a moving average.
What you do is to take, say 5, 10, or 12 steps in a time
series. Such a series might be
time
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
value
15
33
44
87
67
72
59
36
21
19
13
27
39
52
63
74
51
49
and the selected steps are the ten from 1 to 10.
Next action is to average the chosen values:
(15+33+44+87+67+72+59+36+21+19) / 10 = 45.3
Now subtract the first data point:
1
15
and add in the next data point in the series:
11
13
or (33+44+87+67+72+59+36+21+19+13).
Average these values (33+44+87+67+72+59+36+21+19+13) / 10 = 45.1
The resulting values, 45.3, 45.1, and so on, form the data points on the moving average graph.
Repeat these actions, as required, to create a ‘moving average’
graph/chart.
A moving average graph is used to iron out errors/variations. It is
particularly useful where there is a regular variation. For instance,
where seasons effect the data during over each twelve month period, as
with monthly sales in a shop.
In summary, there are various ways and reasons to smooth out data:
in cases of regular variation
with data subject to ‘random’ perturbation, such as years of
temperature data
to average out values estimated by different workers.
sums will
set you free is included in
the series of documents about economics and money at abelard.org.