Environmental Engineering Reference
In-Depth Information
1.0
φ
1
= 0.0
0.5
C
(
t
)
0.0
−
0.5
0
10
20
30
40
50
60
70
t
(a)
1.0
φ
1
= 0.2
0.5
C
(
t
)
0.0
−
0.5
0
10
20
30
40
50
60
70
t
(b)
1.0
φ
1
= 0.4
0.5
C
(
t
)
0.0
−
0.5
0
10
20
30
40
50
60
70
t
(c)
1.0
φ
1
= 0.8
0.5
C
(
t
)
Figure 3.6
Correlograms for four AR[1]
time series. The autocorrelation function
C
(
0.0
) in Equation 3.6 is applied to the four
AR[1] time series shown in Figure 3.5 with
(a)
τ
φ
1
=
0
.
0, (b)
φ
1
=
0
.
2, (c)
φ
1
=
0
.
4,
(d)
70, with
results shown in small circles. Also shown
(dashed line) is the theoretical prediction
for AR[1] time series,
C
(
φ
1
=
0
.
8, for lags 0
≤
τ
≤
−
0.5
0
10
20
30
40
50
60
70
t
τ
=
φ
1
)
(d)
(Equation 3.10).
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