Geoscience Reference
In-Depth Information
17
250
18
20
200
19
150
21
100
16
15
14
8
50
30
12
28
13
26
24
22
20
18
16
6
14
12
11
7
10
5
8
10
4
6
9
4
0.05 Probability level
2
3
2
1
0
0
500 1000 1500
Record length (years BP)
1Random numbers
2 Random numbers
12 Southern Oscillation Index
13 Yellowstone River discharge
14 Palmer Drought Severity Index
(tree rings) USA
15 Beijing speleothem
16 US lake levels (July)
17 Roratonga sea surface temperatures
18 Pacific Decadal Oscillation
19 Scotland speleothem
20 Caribbean sea surface temperatures
21 US tree rings
3 Random numbers
4 Yucatan Lake isotopes (
13
C)
5 Sacramento River discharge
6 Yucatan Lake CaCO
3
7 North Atlantic Oscillation (NAO)
8 New Mexico tree rings
9 Chillagoe speleothem layers
10 Burdekin River discharge
11 White River discharge
Figure 10.3.
Results from the Ljung-box test for serial correlation. (Data from 4, 6,
Hodell
et al
.,
1995
;5,Meko
et al
.,
2001
;7,Cook
et al
.,
2002
;8,Grissino-Mayer,
1996
;
10, Isdale
et al
.,
1998
;11, Cleaveland,
2000
;12, Allan
et al
.,
1996
;Stahle
et al
.,
1998
;
13,Graumlich
et al
.,
2003
;14, Cook,
2000
;15,Tan
et al
.,
2003
;16, Cook
et al
.,
1996
;
17, Linsley
et al
.,
2000
;18, Biondi
et al
.,
2001
;19,Proctor
et al
.,
2000
; 20, Winter
et al
.,
2000
;21, Cook
et al
.,
1996
.)
numbers did not exceed 1.9 despite the substantial length of record (equal to
4000 runs or years if one run equals a year). The curves of the random num-
bers also do not show any substantial increase with increasing length of record
suggesting that they would probably never exceed the critical
Z
score of 1.9.
The Ljung-box test, another statistical test of randomness, was also under-
taken on many of the same long-term hazard and natural event time series. The
Ljung-box test calculates a correlation coefficient for different lags in the time
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