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again the Wolfer sunspots series of Table 7.3. And a different way of repre-
senting this time series is shown in Figure 7.1. Let's see then how the data
should be prepared for time series prediction.
160
120
80
40
0
0
10
20
30
40
50
60
70
80
90
100
Time
Figure 7.1.
Wolfer sunspots series (see also Table 7.3).
In time series analysis, the data represent a series of observations taken at
certain intervals, for instance, a year or a day. The idea behind time series
prediction is that past observations determine future ones. This means that,
in practical terms, one is trying to find a prediction model that is a function
of a certain number of past observations. This certain number of past obser-
vations is what is called the embedding dimension
d
in time series analysis.
For the sunspots prediction task of this section, we are going to use
d
= 10.
There is also another important parameter in time series analysis - the delay
time
- that determines how data are processed. A delay time of one means
that the data are processed continuously, whereas higher values of
τ
indicate
that some observations are skipped. For instance, using
d
= 10 and
τ
= 1
(exactly the same settings used in all the experiments of this chapter), the
sunspots series of Table 7.3 gives:
τ
t
-10
t
-9
t
-8
t
-7
t
-6
t
-5
t
-4
t
-3
t
-2
t
-1
t
1.
101
82
66
35
31
7
20
92
154
125
85
2.
82
66
35
31
7
20
92
154
125
85
68
3.
66
35
31
7
20
92
154
125
85
68
38
…
...
89.
55
94
96
77
59
44
47
30
16
7
37
90.
94
96
77
59
44
47
30
16
7
37
74
