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13204656768)9;:=<-8>@?A:=<CBD<FEHG0I0JLKMJ0:)?ONBQPRTSKFUV464MP
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204)XAYMP
1Z8[V\]B24MP
1'WM8[V\]B
204MP
3
4
series
5
6
7
White Noise
0
20
40
60
80
100
time
White Nosie
0.0
Partial ACF
0.4
−0.1
0.2
0.0
−0.2
−0.2
ACF
0.6
0.1
0.8
1.0
0.2
White Noise
0
5
10
15
20
5
Lag
10
^
Lag
15
20
132FUO56768)9;:=<-8>@?A:=<CBD<FEHG0I0JLKMJ0:)?ONB@8_90KM[`B@4>aAY]R
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5
3
4
series
6
7
AR(2): yt=5+0.25yt−1+0.125yt−2+εt
0
20
40
60
80
100
time
AR(2): yt=5+0.25yt−1+0.125yt−2+εt
0.0
0.1
Partial ACF
0.4
−0.2
−0.2
0.0
−0.1
0.2
ACF
0.6
0.2
0.8
0.3
1.0
AR(2): yt=5+0.25yt−1+0.125yt−2+εt
0
5
10
15
20
5
Lag
10
15
20
Lag
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1
−2
−1
0
series
2
3
4
MA(2): yt=2+0.1εt−1+0.2εt−2+εt
0
20
40
60
80
100
time
MA(2): yt=2+0.1εt−1+0.2εt−2+εt
0.0
Partial ACF
0.4
−0.2
−0.2
0.0
−0.1
0.2
ACF
0.6
0.1
0.8
0.2
1.0
MA(2): yt=2+0.1εt−1+0.2εt−2+εt
0
5
10
15
20
5
Lag
10
15
20
Lag
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−2
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series
1
2
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0
20
40
60
80
100
time
x3
Series
x3
0.0
−0.3
−0.2
−0.2
0.0
−0.1
0.2
ACF
Partial ACF
0.4
0.1
0.6
0.2
0.8
0.3
1.0
Series
0
5
10
15
20
5
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10
15
20
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5
10
series
15
20
Random Walk of Order 1
0
20
40
60
80
100
time
Random Walk
0.2
0.4
Partial ACF
0.4
0.0
0.2
0.0
−0.2
−0.2
ACF
0.6
0.6
0.8
0.8
1.0
Random Walk
0
5
10
15
20
5
Lag
10
Ÿ
Lag
15
20
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0
−6
−4
−2
series
2
4
6
ARIMA(1,1,1): yt=1.25yt−1+0.5εt−1+εt
0
20
40
60
80
100
time
x5
Series
x5
−0.5
−0.5
0.0
0.0
ACF
Partial ACF
0.5
0.5
1.0
Series
0
5
10
15
20
5
Lag
10
¡
Lag
15
20