Transcript Lecture 4

0.0
-0.5
-1.0
x[1:10]
0.5
1.0
Binary iid noise (game payment)
2
4
6
Index
8
10
0.0
-0.5
-1.0
x
0.5
1.0
Binary iid noise (game payment)
0
20
40
60
Index
80
100
0
-5
cumsum(x)
5
Ransom walk on Binary iid noise (game payment)
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20
40
60
Index
80
100
0
-2
-4
x
2
Standard normal iid noise
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200
400
600
Index
800
1000
-1
-2
-3
-4
cumsum(x[1:10])
0
Random walk on standard normal iid noise
2
4
6
Index
8
10
20
10
0
-10
cumsum(x)
30
Random walk on standard normal iid noise
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200
400
600
Index
800
1000
-4
-2
x
0
2
Normal iid noise N(0.05,1)
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2000
4000
6000
8000
10000
Index
-4
-2
x
0
2
Normal iid noise N(0,1)
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2000
4000
6000
Index
8000
10000
300
0
100
cumsum(x)
500
Random walk on normal iid noise N(0.05,1)
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2000
4000
6000
8000
10000
Index
300
100
0
cumsum(x)
500
Random walk on normal iid noise N(0,1)
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2000
4000
6000
Index
8000
10000
0.4
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ACF
0.8
ACF of an IID noise
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400
600
Lag
800
1000
0.4
0.0
ACF
0.8
ACF of an IID noise
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20
40
60
Lag
80
100
0.00
-0.10
ACF
0.10
ACF of an IID noise
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20
40
60
Lag
80
100
1
0
-1
-2
Observations
2
Oscillations+noise
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20
40
60
Time
80
100
0.0 0.5 1.0
-1.0
ACF
ACF of an oscillatory process
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400
600
Lag
800
1000
0.0 0.5 1.0
-1.0
ACF
ACF of an oscillatory process
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20
40
60
Lag
80
100
12
8
4
Observations
16
Oscillations+noise
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20
40
60
Time
80
100
0.00
-0.10
ACF
0.10
ACF of an oscillatory process
0
200
400
600
Lag
800
1000
0.00
-0.10
ACF
0.10
ACF of an oscillatory process
0
20
40
60
Lag
80
100
360
co2
340
320
1960
1970
1980
Time
1990
1960
1970
1980
Time
1990
-1.0
0.0
1.0
Diff residuals
0.4
-0.4 0.0
ACF
0.8
ACF for CO2 (12+1)-differencing
0.0
0.5
1.0
Lag
1.5
2.0
1960
1970
1980
Time
1990
-0.5
0.0
0.5
CDM residuals
0.4
0.0
-0.4
ACF
0.8
ACF for CO2 CDM residuals
0.0
0.5
1.0
Lag
1.5
2.0