Environmental Engineering Reference
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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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