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GERARS.OUT
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[] Dendrochronology Program Library Run GER Program ARS 18:03 Wed 18 Sep 2024 Page 1
[]
[] P R O G R A M A R S T A N Version 6.05P 32770
------------------------------------------------------------------------------------------------------------------------------------
Title of run:
Data file: GER.rwl
Options specified for this run Selected values
2 Detrending method 1 3 50.0%
4 Special treatment, selected series 0
5 Stabilize variance N 0
Log-transform measurement series N
Normalize detrended series N
6 Indices computed by Division, Subtraction, or
lower Trend in variance D
7 Print plots of 10-year means of series N
8 List values of series N
9 Save individual series in format N
10 Columns in ident indicating tree 1 to 5
11 Tree summaries produced N - format
12 Autoregressive modeling method E
All series used in AR modeling
Force rewhitening of Residual chronology 0 order
13 Chronology computation R Format: C Ident: GER
14 Year-by-year list of chronology Y
==> Time span of data 1836 to 2022 187 years, 62 series, 8058 rings
Mean length of series is 129.97 years.
15 Common interval analysis O
Common interval, Optimum 1885 to 2022 138 years, 37 series, 5106 rings
Common interval adjusted for order of pooled AR model
16 Common interval analysis of red-noise fraction N
17 Number of eigenvectors & amplitudes to save 8
Effect of options selected
First detrending: Neg exponential/Regr
(The asymptote of an exponential curve is allowed to be negative.)
Second detrending: Linear regression
Indices computed as Ratio: Measurement divided by Curve
Autoregressive modeling: Unconstrained
>> ER0102B Span 1845 2022 2 Indices over 3.0
Years: 2020 2021
Values: 3.475 4.366
>> ER0105B Span 1843 2022 1 Indices over 3.0
Years: 1941
Values: 3.215
>> ER0115A Span 1860 2022 2 Indices over 3.0
Years: 1869 1870
Values: 3.334 3.350
>> ER0115B Span 1862 2022 1 Indices over 3.0
Years: 1870
Values: 3.105
>> ER0120A Span 1846 1991 2 Indices over 3.0
Years: 1940 1941
Values: 3.215 3.263
>> ER0129A Span 1855 1981 1 Indices over 3.0
Years: 1929
Values: 3.697
8058 total rings 0 absent rings .0000 %
6 detrended series contain 9 index values over 3.0
STATISTICS of TREE-RING MEASUREMENTS 18:03 Wed 18 Sep 2024 Page 2
------------------------------------------------------------------------------------------------------------------------------------
Mean Std Skew- Kurto- Trend Partial autocorr L-Box
Seq Series Interval Years Mean Median sens dev ness sis var % Ord 1 Ord 2 Ord 3 Prob
--- -------- ---------- ----- ----- ------ ----- ----- ----- ------ ------- ----- ----- ----- -----
1 ER0101A 1842 2022 181 .794 .730 .318 .324 .764 .356 -.0328 .54 .09 .03 .000
2 ER0101B 1872 2022 151 1.011 .960 .392 .510 .452 -.154 .0878 .64 .04 .20 .000
3 ER0102A 1845 2022 178 .507 .465 .404 .307 1.074 1.310 -.0201 .64 .22 .21 .000
4 ER0102B 1845 2022 178 .374 .350 .388 .268 .766 .217 .0192 .72 .36 .19 .000
5 ER0103A 1864 2022 159 .581 .480 .365 .369 .738 -.001 -.0396 .79 .19 .28 .000
6 ER0103B 1864 2022 159 .578 .490 .384 .323 .534 -.576 .0095 .67 .21 .23 .000
7 ER0104A 1842 2022 181 .610 .540 .441 .330 .678 -.155 .0358 .55 .23 .18 .000
8 ER0104B 1836 2022 187 .522 .460 .436 .272 .962 .797 .0040 .44 .16 .08 .000
9 ER0105A 1843 2022 180 .370 .345 .439 .182 .742 .519 .0003 .50 .10 .04 .000
10 ER0105B 1843 2022 180 .425 .375 .381 .225 .759 .529 .0400 .62 .09 .13 .000
11 ER0106A 1838 2022 185 .379 .340 .394 .187 1.014 1.811 -.0460 .53 .23 .32 .000
12 ER0106B 1836 2022 187 .439 .400 .396 .220 .961 1.367 -.0120 .50 .24 .34 .000
13 ER0107A 1865 2022 158 .539 .510 .324 .228 .885 .545 -.0499 .56 .13 .13 .000
14 ER0107B 1866 2022 157 .499 .460 .311 .239 .642 -.225 -.0157 .63 .23 .26 .000
15 ER0108A 1885 2022 138 .717 .655 .390 .347 .817 .206 .0153 .54 .18 .16 .000
16 ER0108B 1885 2022 138 .766 .755 .419 .287 .078 -.633 -.0241 .17 -.01 .08 .000
17 ER0109A 1871 2022 152 .668 .655 .328 .341 .491 -.069 .1137 .69 .24 .22 .000
18 ER0109B 1868 2022 155 .704 .660 .335 .319 .874 .559 .0832 .52 .20 .17 .000
19 ER0110A 1850 2022 173 .512 .470 .296 .208 .935 1.028 -.0245 .48 .15 -.03 .000
20 ER0110B 1843 2022 180 .581 .570 .291 .231 .518 .149 -.0012 .56 -.01 .13 .000
21 ER0111A 1862 2022 161 .690 .670 .312 .279 .664 .630 .0293 .60 .14 .17 .000
22 ER0111B 1854 2022 169 .689 .640 .336 .334 .497 -.485 .0636 .64 .35 .18 .000
23 ER0112A 1843 2022 180 .474 .445 .335 .236 .873 1.033 -.0359 .61 .33 .06 .000
24 ER0112B 1846 2022 177 .493 .470 .346 .250 .655 .129 -.0172 .68 .19 .11 .000
25 ER0113A 1851 2022 172 .522 .460 .432 .309 .833 .043 .0091 .60 .12 .17 .000
26 ER0113B 1854 1991 138 .463 .440 .423 .225 .380 -.414 .0456 .53 .16 .18 .000
27 ER0113B 2000 2022 23 .150 .140 .395 .049 .057 .033 .0016 .01 -.25 -.18 .422
28 ER0114A 1839 2022 184 .500 .435 .360 .247 .997 .639 -.0631 .58 .22 .11 .000
29 ER0114B 1839 2022 184 .439 .410 .344 .196 .807 .965 -.0134 .49 .25 .27 .000
30 ER0115A 1860 2022 163 .451 .380 .455 .295 2.918 14.265 -.0163 .54 -.06 .07 .000
31 ER0115B 1862 2022 161 .474 .380 .444 .370 2.259 9.904 -.0871 .65 .14 .34 .000
32 ER0116A 1849 2022 174 .421 .390 .413 .243 .662 .230 .0540 .62 .29 .02 .000
33 ER0116B 1845 2022 178 .438 .425 .416 .258 .258 -.605 .0924 .69 .23 .11 .000
34 ER0117A 1884 2022 139 .404 .310 .388 .262 .823 -.113 -.0376 .69 .23 .36 .000
35 ER0117B 1882 2022 141 .394 .330 .402 .252 1.276 1.865 -.0244 .63 .19 .21 .000
36 ER0118A 1942 2022 81 .832 .760 .383 .463 .920 .873 -.1594 .64 .06 .11 .000
37 ER0118B 1942 2022 81 .706 .590 .386 .485 1.007 .467 -.1257 .73 .19 -.05 .000
38 ER0119A 1873 2022 150 .457 .340 .400 .333 .835 .207 -.0470 .73 .32 .12 .000
39 ER0119B 1878 1991 114 .318 .300 .448 .179 .920 .611 -.0434 .60 .18 .21 .000
40 ER0119B 2000 2022 23 .187 .200 .303 .056 -.688 -.223 -.0750 .21 -.05 .09 .357
41 ER0120A 1846 1991 146 .513 .470 .428 .315 1.059 .838 -.0659 .67 .16 .19 .000
42 ER0120A 2000 2022 23 .289 .240 .455 .204 3.560 8.091 .4913 .36 -.23 .18 .460
43 ER0120B 1846 2022 177 .417 .350 .423 .310 1.604 2.687 -.0942 .72 .26 .28 .000
44 ER0121A 1931 2022 92 .674 .610 .307 .295 1.183 1.791 -.0634 .58 .03 .02 .000
45 ER0121B 1931 2022 92 .622 .605 .287 .213 .586 .671 -.0726 .49 -.04 .14 .003
46 ER0122A 1938 2022 85 .639 .540 .394 .387 2.391 6.571 -.3506 .58 -.01 .11 .000
47 ER0122B 1938 2022 85 .586 .500 .346 .364 2.343 5.901 -.4149 .64 .03 .23 .000
48 ER0123A 1880 2022 143 .475 .420 .473 .284 1.609 3.568 -.0745 .40 .15 .12 .000
49 ER0123B 1880 2022 143 .524 .470 .400 .272 .843 .241 -.0257 .45 .13 .12 .000
50 ER0124A 1880 1991 112 .389 .390 .486 .203 .769 1.277 .0055 .47 .07 .11 .000
51 ER0124A 2000 2022 23 .252 .250 .336 .085 .360 .039 -.0331 .20 -.09 .18 .442
52 ER0124B 1882 1991 110 .523 .515 .460 .319 1.025 1.468 .0454 .56 .31 .05 .000
53 ER0124B 2000 2022 23 .213 .210 .364 .067 .599 .237 -.0279 .04 -.14 .22 .180
54 ER0125A 1944 2022 79 .699 .610 .372 .369 1.214 1.210 -.1654 .56 .03 .13 .000
55 ER0125B 1944 2022 79 .624 .590 .338 .282 .993 1.366 -.0939 .56 .00 .21 .000
56 ER0126A 1957 2022 66 .763 .715 .261 .331 .848 .687 -.0433 .66 .08 .18 .000
57 ER0126B 1958 2022 65 .828 .770 .269 .330 .668 -.165 -.0688 .60 .06 .20 .000
58 ER0127A 1966 2022 57 1.087 1.010 .333 .457 1.514 2.411 .7260 .38 -.11 -.24 .014
59 ER0127B 1966 2022 57 .878 .850 .297 .308 1.047 1.499 .1399 .33 -.01 .04 .353
60 ER0128A 1962 2022 61 .804 .770 .371 .354 .907 .728 .0244 .39 -.02 -.06 .287
61 ER0128B 1960 2022 63 .602 .560 .323 .235 .875 .383 -.0154 .48 .12 .01 .004
62 ER0129A 1855 1981 127 .413 .390 .404 .230 .865 1.589 .1329 .65 .22 .00 .000
62 Series means 130.0 .547 .500 .375 .278 .944 1.302 -.0057 .54 .12 .14 .041
STATISTICS of DETRENDED SERIES 18:03 Wed 18 Sep 2024 Page 3
------------------------------------------------------------------------------------------------------------------------------------
Mean Std Skew- Kurto- Trend Partial autocorr L-Box
Seq Series Interval Years Mean Median sens dev ness sis var % Ord 1 Ord 2 Ord 3 Prob Detrending
--- -------- ---------- ----- ----- ------ ----- ----- ----- ------ ------- ----- ----- ----- ----- ----------
1 ER0101A 1842 2022 181 1.000 .924 .318 .404 .752 .403 -.0553 .54 .09 .03 .000 RegrD/RegrD
2 ER0101B 1872 2022 151 1.000 .943 .392 .492 .480 -.183 .0879 .61 .03 .20 .000 Regr-D/RegrD
3 ER0102A 1845 2022 178 1.000 .929 .404 .431 1.054 1.741 -.0178 .43 .12 .09 .000 Regr-D/RegrD
4 ER0102B 1845 2022 178 1.001 .913 .390 .572 2.211 8.102 .2249 .62 .16 .14 .000 Regr-D/Regr+D
5 ER0103A 1864 2022 159 1.000 1.003 .365 .398 .306 -.314 .1282 .48 .00 .18 .000 NExpD/RegrD
6 ER0103B 1864 2022 159 1.000 .949 .383 .403 .523 .224 .0551 .36 -.01 .13 .000 Regr-D/RegrD
7 ER0104A 1842 2022 181 1.000 .949 .441 .480 .911 1.030 -.0111 .48 .19 .11 .000 Regr-D/RegrD
8 ER0104B 1836 2022 187 1.000 .920 .436 .510 .993 .956 -.0203 .44 .12 .08 .000 RegrD/RegrD
9 ER0105A 1843 2022 180 1.000 .915 .439 .448 .603 .268 .0109 .39 .10 .01 .000 Regr-D/RegrD
10 ER0105B 1843 2022 180 1.000 .912 .380 .496 1.002 1.687 .0131 .55 .10 .13 .000 Regr-D/RegrD
11 ER0106A 1838 2022 185 1.000 .970 .395 .422 .696 .698 .0287 .40 .16 .20 .000 NExpD/RegrD
12 ER0106B 1836 2022 187 1.000 .943 .396 .423 .915 1.821 .0529 .39 .11 .27 .000 Regr-D/RegrD
13 ER0107A 1865 2022 158 1.000 .974 .324 .371 .695 .188 .0247 .45 .08 .06 .000 NExpD/Regr-D
14 ER0107B 1866 2022 157 1.000 .996 .311 .319 .512 1.194 .0016 .30 -.01 .14 .000 NExpD/RegrD
15 ER0108A 1885 2022 138 1.000 .962 .390 .452 .756 .200 -.0599 .50 .16 .14 .000 Regr-D/RegrD
16 ER0108B 1885 2022 138 1.000 1.030 .419 .355 .032 -.349 -.0124 .10 -.07 .03 .005 Regr-D/RegrD
17 ER0109A 1871 2022 152 .999 .935 .328 .457 1.070 1.147 .0952 .64 .23 .22 .000 Regr-D/Regr-D
18 ER0109B 1868 2022 155 1.000 .890 .335 .436 1.038 .875 .0261 .50 .17 .16 .000 Regr-D/RegrD
19 ER0110A 1850 2022 173 1.000 .937 .296 .367 .686 .161 -.0172 .47 .09 -.06 .000 Regr-D/RegrD
20 ER0110B 1843 2022 180 1.000 .971 .291 .380 .580 .488 .0257 .55 -.02 .08 .000 Regr-D/RegrD
21 ER0111A 1862 2022 161 1.000 .989 .312 .380 .875 1.544 .0106 .54 .10 .10 .000 Regr-D/RegrD
22 ER0111B 1854 2022 169 1.000 .965 .336 .455 .680 .145 -.0111 .61 .32 .14 .000 Regr-D/RegrD
23 ER0112A 1843 2022 180 1.000 .931 .335 .416 .714 .616 .0776 .52 .26 .03 .000 NExpD/RegrD
24 ER0112B 1846 2022 177 1.000 .915 .347 .456 1.001 1.276 .1426 .59 .17 .04 .000 NExpD/RegrD
25 ER0113A 1851 2022 172 1.000 .935 .433 .467 1.024 1.906 -.0286 .41 .02 .10 .000 Regr-D/RegrD
26 ER0113B 1854 1991 138 1.000 .927 .423 .431 .677 .610 .1017 .38 .06 .14 .000 Regr-D/RegrD
27 ER0113B 2000 2022 23 1.000 .949 .395 .326 -.009 -.140 -.0828 .00 -.27 -.18 .389 RegrD/RegrD
28 ER0114A 1839 2022 184 1.000 .943 .360 .421 .565 .102 -.0656 .48 .15 .05 .000 Regr-D/RegrD
29 ER0114B 1839 2022 184 1.000 .992 .344 .366 .734 1.036 .0542 .24 .08 .13 .000 NExpD/RegrD
30 ER0115A 1860 2022 163 1.000 .954 .455 .521 1.562 4.223 -.0510 .43 -.05 .01 .000 Regr-D/RegrD
31 ER0115B 1862 2022 161 1.000 .956 .444 .466 1.045 2.246 .1212 .33 .00 .08 .000 NExpD/Regr+D
32 ER0116A 1849 2022 174 .999 .931 .413 .525 1.108 1.520 .0826 .55 .31 .01 .000 Regr-D/Regr-D
33 ER0116B 1845 2022 178 .996 .918 .416 .540 .860 .651 .1435 .62 .26 .07 .000 Regr-D/Regr-D
34 ER0117A 1884 2022 139 1.000 .972 .388 .387 .408 -.209 .1135 .34 .08 .20 .000 NExpD/Regr+D
35 ER0117B 1882 2022 141 1.000 .943 .401 .395 .639 .156 -.0011 .28 .03 .03 .101 Regr-D/RegrD
36 ER0118A 1942 2022 81 1.000 1.011 .383 .385 .061 -.610 .0797 .34 -.10 -.02 .410 NExpD/RegrD
37 ER0118B 1942 2022 81 1.000 1.055 .380 .370 .028 -.255 -.0726 .35 .11 -.10 .339 NExpD/Regr+D
38 ER0119A 1873 2022 150 1.002 .891 .402 .561 1.165 1.422 .3455 .65 .23 .01 .000 NExpD/Regr+D
39 ER0119B 1878 1991 114 1.000 .993 .450 .404 .753 1.332 .0526 .19 -.02 -.01 .103 NExpD/RegrD
40 ER0119B 2000 2022 23 1.000 1.010 .302 .289 -.604 -.018 -.2321 .12 -.12 .11 .423 Regr+D/Regr+D
41 ER0120A 1846 1991 146 1.000 .915 .427 .503 1.592 4.457 .1928 .54 .03 .12 .000 NExpD/Regr-D
42 ER0120A 2000 2022 23 1.000 .811 .449 .561 2.573 4.797 2.0815 .20 -.27 .05 .305 Regr+D/Regr+D
43 ER0120B 1846 2022 177 1.000 .937 .423 .459 .766 .250 .0199 .46 .14 .11 .000 NExpD/Regr-D
44 ER0121A 1931 2022 92 1.000 .950 .307 .384 1.332 2.822 .1158 .44 -.08 -.15 .035 NExpD/RegrD
45 ER0121B 1931 2022 92 1.000 .972 .287 .326 .325 .130 -.0426 .45 -.07 .10 .002 NExpD/RegrD
46 ER0122A 1938 2022 85 1.000 .962 .394 .433 .822 .385 -.0424 .36 -.12 -.04 .445 NExpD/RegrD
47 ER0122B 1938 2022 85 1.000 .892 .346 .425 .839 .537 -.0907 .47 -.07 .19 .002 NExpD/RegrD
48 ER0123A 1880 2022 143 1.000 .918 .473 .482 1.098 1.865 -.0774 .27 .03 .04 .001 NExpD/RegrD
49 ER0123B 1880 2022 143 1.000 .955 .400 .428 .614 .208 -.0835 .32 .06 .07 .000 Regr-D/RegrD
50 ER0124A 1880 1991 112 1.000 .959 .485 .455 .328 -.112 .0581 .36 -.03 .07 .019 Regr-D/RegrD
51 ER0124A 2000 2022 23 1.000 .982 .338 .307 .223 -.043 .1030 .05 -.27 .06 .222 Regr-D/Regr-D
52 ER0124B 1882 1991 110 .999 .962 .460 .456 .759 .805 .0201 .34 .16 -.01 .016 Regr-D/Regr-D
53 ER0124B 2000 2022 23 1.000 1.009 .363 .297 .346 -.492 -.2141 -.05 -.27 .10 .485 Regr-D/Regr-D
54 ER0125A 1944 2022 79 1.000 .963 .373 .362 .467 -.045 -.1040 .26 -.11 -.11 .332 NExpD/RegrD
55 ER0125B 1944 2022 79 1.000 1.021 .338 .316 .212 .069 -.0559 .27 -.13 -.01 .244 Regr-D/RegrD
56 ER0126A 1957 2022 66 1.000 .940 .260 .286 .690 .041 .1211 .32 -.07 .00 .236 NExpD/RegrD
57 ER0126B 1958 2022 65 1.000 .956 .267 .290 .604 -.323 .0684 .30 -.15 .09 .034 Regr-D/RegrD
58 ER0127A 1966 2022 57 1.000 .940 .333 .411 1.326 1.871 .6922 .37 -.11 -.24 .018 Regr+D/RegrD
59 ER0127B 1966 2022 57 1.000 .913 .297 .344 1.166 1.752 .2429 .31 -.03 .00 .492 Regr-D/RegrD
60 ER0128A 1962 2022 61 1.000 .983 .371 .441 1.146 1.819 .0774 .37 -.03 -.07 .234 NExpD/Regr-D
61 ER0128B 1960 2022 63 1.000 .957 .324 .344 1.115 1.711 .2596 .24 .02 -.03 .123 NExpD/RegrD
62 ER0129A 1855 1981 127 .999 .880 .404 .556 1.693 4.349 .2662 .60 .22 -.05 .000 Regr-D/Regr-D
62 Series means 130.0 1.000 .950 .375 .420 .793 1.044 .0802 .39 .04 .06 .081
MULTIVARIATE AUTOREGRESSIVE MODELING, DETRENDED SERIES 18:03 Wed 18 Sep 2024 Page 4
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All series used in pooling
Pooled autocorrelations:
T= 0 1.000 T= -1 .324 T= -2 .149 T= -3 .132 T= -4 .238 T= -5 .116
T= -6 .186 T= -7 .086 T= -8 .154 T= -9 .112 T=-10 .095 T=-11 .143
Yule-Walker estimates of autoregression:
Order T= 0 T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10
1 1.0000 .3238
2 1.0000 .3078 .0492
3 1.0000 .3040 .0251 .0784
4 1.0000 .2891 .0203 .0207 .1901
5 1.0000 .2936 .0208 .0212 .1969 -.0236
6 1.0000 .2970 -.0075 .0181 .1939 -.0658 .1436
7 1.0000 .3030 -.0102 .0263 .1947 -.0661 .1561 -.0422
8 1.0000 .3071 -.0252 .0326 .1761 -.0686 .1571 -.0712 .0956
9 1.0000 .3053 -.0238 .0297 .1773 -.0719 .1565 -.0707 .0899 .0186
10 1.0000 .3055 -.0227 .0288 .1793 -.0728 .1587 -.0703 .0896 .0224 -.0126
Last term in each row above is partial autocorrelation coefficient
Akaike Information Criterion:
AR( 0) AR( 1) AR( 2) AR( 3) AR( 4) AR( 5) AR( 6) AR( 7) AR( 8) AR( 9) AR(10)
1972.503 1953.793 1955.339 1956.185 1951.305 1953.200 1951.305 1952.971 1953.253 1955.189 1957.159
A close scrutiny of the AIC trace is suggested to see if the first-minimum AIC choice is adequate.
If AR orders of the first-minimum and the full-minimum are close, a run of ARSTAN
with a constrained AR order equal to the full-minimum AIC choice may be tried.
Selected autoregression order: 1
Autoregression coefficients:
T= -1
.3238
R-squared due to pooled autoregression = 10.48%
Impulse response function weights for AR ( 1) process:
1.0000 .3238 .1048 .0339 .0110 .0036 .0012 .0004 .0001 .0000
.0000 .0000 .0000 .0000 .0000 .0000
UNIVARIATE AUTOREGRESSIVE MODELING 18:03 Wed 18 Sep 2024 Page 5
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Unconstrained AR model for each series
Statistics of RESIDUAL SERIES
Mean Std Skew- Kurto- Trend Partial autocorr L-Box
Seq Series Interval Years Mean Median sens dev ness sis var % Ord 1 Ord 2 Ord 3 Prob
--- -------- ---------- ----- ----- ------ ----- ----- ----- ------ ------- ----- ----- ----- -----
1 ER0101A 1843 2022 180 1.001 .937 .388 .340 .656 .282 -.0413 -.05 .05 -.01 .025
2 ER0101B 1873 2022 150 .997 .970 .450 .389 .455 -.071 .0621 -.02 -.11 .02 .001
3 ER0102A 1847 2022 176 1.000 .989 .476 .386 .640 .487 -.0119 -.01 -.05 .04 .323
4 ER0102B 1850 2022 173 1.011 .960 *459 .417 .971 2.386 .0187 -.01 .03 .07 .423
5 ER0103A 1865 2022 158 1.002 .985 .434 .350 .007 -.148 .0809 .00 -.09 .10 .305
6 ER0103B 1865 2022 158 1.000 .996 .443 .377 .311 .086 .0503 .00 -.05 .06 .379
7 ER0104A 1846 2022 177 .997 .990 .486 .403 .337 .121 -.0350 .02 -.04 -.01 .324
8 ER0104B 1838 2022 185 1.005 .954 .532 .453 .782 1.061 -.0197 -.02 -.08 -.06 .001
9 ER0105A 1845 2022 178 .993 .963 .498 .407 .361 -.250 .0280 -.02 -.04 -.06 .002
10 ER0105B 1844 2022 179 .997 .919 .459 .413 .754 1.078 .0384 -.05 .00 .03 .000
11 ER0106A 1842 2022 181 .999 .978 .419 .368 .509 .884 .0383 .02 -.01 -.03 .134
12 ER0106B 1839 2022 184 1.001 .973 *437 .374 .469 .764 -.0005 -.02 .00 -.02 .483
13 ER0107A 1866 2022 157 1.000 .950 .388 .332 .442 -.176 -.0166 -.03 .03 -.02 .433
14 ER0107B 1867 2022 156 .997 .972 .355 .304 .325 .738 -.0134 .00 -.06 .06 .293
15 ER0108A 1889 2022 134 1.002 .941 .453 .370 .465 .070 -.0116 -.02 -.06 -.03 .232
16 ER0108B 1886 2022 137 .999 1.002 .436 .354 .064 -.418 -.0155 .01 -.07 .01 .006
17 ER0109A 1875 2022 148 .993 .993 .384 .324 .446 .687 -.0280 .02 .00 -.02 .483
18 ER0109B 1872 2022 151 .998 .963 .385 .354 .711 .526 -.0184 .00 -.03 -.04 .006
19 ER0110A 1851 2022 172 .995 .946 .354 .320 .424 .477 -.0521 -.01 .07 -.06 .094
20 ER0110B 1844 2022 179 1.001 .976 .352 .315 .417 1.193 -.0495 .02 -.06 .00 .104
21 ER0111A 1863 2022 160 1.001 .979 .393 .319 .536 .205 .0099 -.06 .01 .02 .049
22 ER0111B 1858 2022 165 1.002 .965 .377 .325 .528 .689 .0091 -.02 -.03 -.03 .396
23 ER0112A 1845 2022 178 .997 .974 .393 .340 .386 .089 .0259 .00 -.03 .05 .385
24 ER0112B 1848 2022 175 .997 .969 .419 .364 .780 1.135 .0575 -.01 -.02 .04 .474
25 ER0113A 1852 2022 171 1.001 .946 .526 .425 .451 .271 -.0179 -.01 -.03 .06 .338
26 ER0113B 1855 1991 137 1.000 .961 .499 .400 .354 .088 .1027 -.02 .00 .08 .329
27 ER0113B 2001 2022 22 1.002 .947 .394 .333 -.042 -.215 -.3795 -.01 -.27 -.20 .265
28 ER0114A 1841 2022 182 1.001 .964 .434 .366 .383 .091 -.0184 .00 -.04 .04 .053
29 ER0114B 1840 2022 183 1.000 .963 .395 .356 .682 .914 .0509 -.02 .04 .09 .142
30 ER0115A 1861 2022 162 .998 .957 *538 .472 1.128 3.723 -.0517 .02 -.04 -.09 .090
31 ER0115B 1863 2022 160 1.001 .989 .497 .439 .987 2.433 .0575 .00 -.03 .03 .455
32 ER0116A 1851 2022 172 .995 .971 *514 .419 .298 .239 .0137 .00 -.04 -.04 .338
33 ER0116B 1847 2022 176 1.000 .962 *488 .407 .509 1.031 .0368 -.02 -.12 -.10 .000
34 ER0117A 1885 2022 138 1.002 .990 .446 .365 .416 -.082 .0415 -.02 .00 .15 .006
35 ER0117B 1883 2022 140 1.001 .943 .450 .380 .520 -.151 -.0161 -.01 .02 .00 .471
36 ER0118A 1943 2022 80 .999 1.007 .427 .363 -.056 -.374 .0731 .05 -.07 -.06 .030
37 ER0118B 1943 2022 80 1.000 1.012 .429 .349 -.093 -.207 -.0944 -.03 .14 -.11 .209
38 ER0119A 1875 2022 148 1.000 .993 .476 .410 .413 .254 .0885 -.01 -.03 -.01 .449
39 ER0119B 1879 1991 113 .998 .994 .477 .398 .647 1.018 .0814 .01 -.02 -.01 .245
40 ER0119B 2001 2022 22 1.022 1.063 .296 .266 -.683 .095 .0934 .01 -.18 .03 .351
41 ER0120A 1847 1991 145 .999 .944 .505 .425 .512 .601 .0903 -.02 -.04 .11 .325
42 ER0120A 2001 2022 22 1.000 .897 .567 .561 2.282 4.822 1.5075 .06 -.27 .08 .396
43 ER0120B 1849 2022 174 .999 .993 .494 .404 .282 -.159 .0160 .00 .00 -.01 .023
44 ER0121A 1932 2022 91 .999 .953 .359 .346 1.322 3.554 .0927 .04 -.01 -.12 .150
45 ER0121B 1932 2022 91 .998 .986 .307 .291 .477 .416 -.0590 .05 -.12 .04 .205
46 ER0122A 1939 2022 84 1.000 .938 .457 .406 .867 .780 .0093 .05 -.09 -.06 .029
47 ER0122B 1939 2022 84 .999 .962 .407 .375 1.036 1.798 -.1028 .04 -.15 .14 .242
48 ER0123A 1881 2022 142 .989 .936 .516 .450 1.194 2.385 -.0535 -.02 -.03 .04 .355
49 ER0123B 1881 2022 142 .997 .931 .467 .405 .735 .394 -.0928 -.02 .03 .03 .296
50 ER0124A 1881 1991 111 .992 .981 .554 .416 .106 -.392 .1303 -.01 -.06 .04 .333
51 ER0124A 2002 2022 21 1.026 .970 .301 .285 .591 .111 -.1101 .01 -.21 -.03 .247
52 ER0124B 1884 1991 108 1.006 1.001 .535 .425 .449 .515 .0318 .00 -.01 -.05 .180
53 ER0124B 2002 2022 21 1.038 1.003 .318 .280 -.064 .207 -.2360 -.08 -.20 -.04 .380
54 ER0125A 1945 2022 78 .999 .975 .414 .351 .337 -.127 -.1641 .04 -.08 -.14 .367
55 ER0125B 1945 2022 78 .997 1.028 .379 .305 .070 -.018 -.0621 .04 -.11 -.06 .434
56 ER0126A 1958 2022 65 .995 .989 .296 .271 .619 .291 .1494 .03 -.07 .00 .224
57 ER0126B 1959 2022 64 .998 .963 .309 .279 .546 -.223 .0760 .05 -.16 .07 .419
58 ER0127A 1967 2022 56 .996 .952 .381 .384 1.239 1.487 .4509 .05 .00 -.15 .491
59 ER0127B 1967 2022 56 .991 .925 .341 .326 1.516 3.486 .1740 .02 -.02 .04 .031
60 ER0128A 1963 2022 60 .992 .954 .436 .410 1.498 3.384 .1613 .01 .00 .00 .020
61 ER0128B 1961 2022 62 1.005 .986 .356 .332 1.151 1.897 .2463 .00 .05 .06 .429
62 ER0129A 1857 1981 125 1.001 .960 .481 .432 1.009 3.505 .1669 .01 -.03 -.16 .047
* Note: If there are any negative values in a series, the decimal point for mean sensitivity is
printed as an asterisk. In such cases mean sensitivity is not strictly correct.
AUTOREGRESSIVE COEFFICIENTS FOR EACH SERIES 18:03 Wed 18 Sep 2024 Page 6
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Variance %
Seq T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 explained
1 .5420 29.97
2 .6160 37.99
3 .3806 .1185 20.44
4 .4308 .1378 .1755 .1639 -.1390 46.88
5 .4775 22.80
6 .3631 13.19
7 .3395 .1089 .0211 .2454 31.18
8 .3848 .1294 21.55
9 .3545 .1076 16.79
10 .5567 31.68
11 .2688 .0712 .1523 .1819 24.44
12 .3141 .0151 .2781 22.98
13 .4506 20.76
14 .3033 9.20
15 .3609 .0740 .0407 .2600 33.87
16 .0997 1.52
17 .3738 .0990 .1128 .2580 51.05
18 .3433 .0864 .0615 .2595 34.90
19 .4751 23.03
20 .5574 31.11
21 .5445 30.41
22 .3161 .1934 .0575 .2726 49.67
23 .3893 .2596 32.62
24 .4922 .1658 36.69
25 .4163 17.38
26 .3806 14.82
27 -.0017 8.12
28 .4105 .1456 24.88
29 .2416 6.37
30 .4296 18.63
31 .3337 11.13
32 .3771 .3136 37.05
33 .4542 .2733 43.97
34 .3418 12.29
35 .2797 7.91
36 .3464 12.86
37 .3500 13.36
38 .4950 .2415 45.96
39 .1922 3.72
40 .1385 3.87
41 .5409 29.33
42 .2068 11.71
43 .3824 .0936 .1096 23.81
44 .4430 20.25
45 .4575 21.49
46 .3652 14.65
47 .4785 23.35
48 .2810 7.99
49 .3290 11.17
50 .3648 13.39
51 .0756 -.3008 10.07
52 .2882 .1588 13.98
53 -.0645 -.3008 9.93
54 .2680 8.46
55 .2762 9.24
56 .3259 11.21
57 .2992 11.02
58 .3736 15.02
59 .3211 10.41
60 .3798 14.49
61 .2488 6.25
62 .4656 .2303 40.08
Average variance explained by autoregression = 20.88%
OUTLIERS in NORMALIZED RESIDUALS (over 3 standard deviations from mean) 18:03 Wed 18 Sep 2024 Page 7
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Seq 1 Years: 1923
Values: 3.33
Seq 3 Years: 1968
Values: 3.41
Seq 4 Years: 2017 2020 2021
Values: 3.44 3.54 3.95
Seq 6 Years: 1941
Values: 3.03
Seq 8 Years: 1894
Values: 3.58
Seq 10 Years: 1935 1941
Values: 3.50 3.60
Seq 11 Years: 1958 1985
Values: 3.64 3.13
Seq 12 Years: 1944 2013
Values: 3.32 -3.02
Seq 14 Years: 1944
Values: 3.35
Seq 17 Years: 1941
Values: 3.50
Seq 18 Years: 1932
Values: 3.14
Seq 20 Years: 1894
Values: 3.84
Seq 21 Years: 1985
Values: 3.06
Seq 22 Years: 1923 1964
Values: 3.28 3.23
Seq 23 Years: 1941
Values: 3.11
Seq 24 Years: 2010 2017
Values: 3.10 3.44
Seq 25 Years: 1940 1941
Values: 3.13 3.08
Seq 26 Years: 1929
Values: 3.30
Seq 29 Years: 1932 2012
Values: 3.60 3.14
Seq 30 Years: 1869
Values: 5.06
Seq 31 Years: 1870 2004
Values: 4.48 3.46
Seq 33 Years: 1964
Values: 3.99
Seq 34 Years: 1923
Values: 3.17
Seq 39 Years: 1958
Values: 3.31
Seq 41 Years: 1940
Values: 3.70
Seq 42 Years: 2017
Values: 3.14
Seq 44 Years: 2017
Values: 4.36
Seq 46 Years: 1943
Values: 3.19
Seq 47 Years: 1943 1997
Values: 3.53 3.04
Seq 48 Years: 1985
Values: 4.38
Seq 49 Years: 1985
Values: 3.07
Seq 58 Years: 1997
Values: 3.04
Seq 59 Years: 1997
Values: 3.95
Seq 60 Years: 2017
Values: 3.76
Seq 61 Years: 2017
Values: 3.34
Seq 62 Years: 1929
Values: 4.76
AUTOREGRESSIVE MODELING, RESIDUAL SERIES 18:03 Wed 18 Sep 2024 Page 8
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Modeling of univariate residual series; AR order constrained not to exceed pooled order selected
All series used in pooling
Pooled autocorrelations:
T= 0 1.000 T= -1 -.089 T= -2 -.099 T= -3 -.051 T= -4 .133 T= -5 -.066
T= -6 .113 T= -7 -.068 T= -8 .068 T= -9 .014 T=-10 -.019 T=-11 .026
Yule-Walker estimates of autoregression:
Order T= 0 T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10
1 1.0000 -.0894
2 1.0000 -.0991 -.1078
3 1.0000 -.1068 -.1149 -.0720
4 1.0000 -.0987 -.1019 -.0600 .1129
5 1.0000 -.0924 -.1053 -.0657 .1074 -.0559
6 1.0000 -.0852 -.1191 -.0572 .1209 -.0440 .1286
7 1.0000 -.0790 -.1212 -.0514 .1181 -.0498 .1244 -.0483
8 1.0000 -.0758 -.1295 -.0481 .1103 -.0464 .1325 -.0430 .0662
9 1.0000 -.0784 -.1278 -.0533 .1122 -.0508 .1344 -.0379 .0692 .0396
10 1.0000 -.0768 -.1249 -.0549 .1177 -.0529 .1390 -.0401 .0640 .0364 -.0411
Last term in each row above is partial autocorrelation coefficient
Akaike Information Criterion:
AR( 0) AR( 1) AR( 2) AR( 3) AR( 4) AR( 5) AR( 6) AR( 7) AR( 8) AR( 9) AR(10)
1923.265 1923.779 1923.618 1924.655 1924.283 1925.703 1924.620 1926.189 1927.376 1929.086 1930.772
Selected autoregression order: 0
Standard Tree-Ring Chronology 18:03 Wed 18 Sep 2024 Page 9
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Tree mask:
Sequence 1 2 3 4 5 6 7 8 9101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960
Radii 1 2 3 4 5 6 7 8 9101112131415161718 1 2 3 4 5 6 7 8 910111213141516171819202122 1 2 3 4 5 6 7 8 91011121314151617181920
Sequence 6162
Radii 2122
GER Standard chronology, no autoregressive modeling
Computed with BIWEIGHT ROBUST MEAN
Title:
All 62 series included in chronology
Ring Index (Year number shown)
Series Iter St dev Coef of --- Two Std Dev band; === Std Err band
Year Index Trees Eff % St err Var Skew Kurt 0 +1 +2 +3
1836 .658 2 2 0 .00 .305 .215 43.64 .000 .000 -------===6===--.---- . .
1837 .516 2 2 0 .00 .407 .288 74.46 .000 .000 --------=====7====---.----- . .
1838 .511 3 2 0 .00 .195 .113 38.71 .000 .000 .-----==8=----- . . .
1839 .933 5 3 0 .00 .370 .165 30.12 .525 7.707 . ---------==9=.=--------- . .
1840 1.067 5 3 0 .00 .038 .017 15.03 -2.171 6.263 . -=0- . .
1841 .762 5 3 0 .00 .086 .038 13.56 -3.977 13.367 . --=1-- . . .
1842 1.425 7 4 4 -1.50 .450 .170 32.03 -2.535 6.721 . --------.---==2===------------ .
1843 1.137 11 5 2 -9.04 .398 .120 33.46 .162 1.488 . -----------==3==---------- . .
1844 .970 11 5 3 82.07 .088 .027 20.29 4.566 11.232 . ---4--- . .
1845 1.496 14 7 4 -11.77 .452 .121 28.88 -1.187 .652 . -------.-----=5==------------- .
1846 .781 17 9 3 -9.21 .263 .064 32.23 .082 .532 . -------=6=--.---- . .
1847 .875 17 9 3 -15.46 .316 .077 33.56 .189 .130 . ---------==7=--------- . .
1848 .728 17 9 2 -11.25 .234 .057 30.26 .781 .357 . ------=8=---.--- . .
1849 1.100 18 9 3 -6.19 .297 .070 26.25 -.093 .836 . --------=9=--------- . .
1850 .992 19 9 3 -4.80 .417 .096 40.34 1.281 .770 . ------------=0.=------------ . .
1851 .874 20 9 4 -2.75 .270 .060 31.83 -.769 1.019 . --------1=-.------ . .
1852 1.129 20 9 3 -2.79 .363 .081 31.65 .176 1.180 . ----------==2=---------- . .
1853 1.110 20 9 3 -2.18 .230 .051 20.63 -.377 1.556 . ------=3=------- . .
1854 1.347 22 9 2 -9.40 .423 .090 29.81 .638 .315 . --------.---=4=------------- .
1855 .917 23 10 3 -16.94 .347 .072 34.94 .108 -.396 . ----------=5=---------- . .
1856 .424 23 10 3 -8.61 .184 .038 41.47 .411 -.379 ------6=----- . . .
1857 .536 23 10 2 -5.64 .295 .062 53.17 .692 .131 --------=7=------.-- . .
1858 .889 23 10 3 -12.90 .273 .057 29.07 -.420 -.276 . --------=8=------- . .
1859 .608 23 10 3 -8.97 .208 .043 32.94 -.317 -.173 . ------9=------ . .
1860 .693 24 10 3 -10.08 .238 .048 32.70 -.090 -.550 . -------=0----.-- . .
1861 1.093 24 10 2 -7.22 .291 .059 25.67 .320 .314 . --------=1=-------- . .
1862 .794 26 8 3 -4.56 .231 .045 28.36 .215 .532 . ------=2=--.---- . .
1863 .973 26 8 3 5.46 .247 .048 25.73 .715 1.405 . -------=3=------- . .
1864 .530 28 7 3 -7.17 .230 .043 41.20 .724 .439 .------=4=------. . .
1865 .710 29 7 3 -3.99 .201 .037 27.66 .416 .389 . ------=5----.- . .
1866 .760 30 7 3 2.39 .229 .042 29.96 1.082 1.123 . -------=6---.--- . .
1867 .858 30 7 3 -5.35 .238 .044 27.19 -.486 .149 . -------7=-.----- . .
1868 .751 31 8 3 -5.75 .249 .045 32.05 .585 .270 . -------=8---.--- . .
1869 .681 31 8 3 78.12 .251 .045 68.25 4.881 19.349 . --------9=----.-- . .
1870 1.220 31 8 3 71.42 .305 .055 42.48 3.041 7.770 . -------.-=0=--------- . .
1871 .886 32 8 3 -2.18 .254 .045 28.15 .726 .745 . -------=1-.------ . .
1872 .820 33 7 3 -6.73 .262 .046 30.90 .037 .105 . --------=2--.----- . .
1873 1.193 34 8 1 -1.96 .334 .057 27.74 -.033 .667 . --------.-=3=--------- . .
1874 .958 34 8 2 6.83 .311 .053 33.05 .796 1.246 . ---------=4=--------- . .
1875 1.076 34 8 3 -4.58 .317 .054 28.67 .551 .244 . ---------=5=--------- . .
1876 1.033 34 8 3 -7.19 .288 .049 26.85 .179 .100 . --------=6=-------- . .
1877 .912 34 8 3 -4.69 .202 .035 21.58 .482 .262 . ------7=------ . .
1878 .946 35 8 3 2.98 .248 .042 26.31 .684 1.284 . -------=8-------- . .
1879 .935 35 8 3 -7.32 .232 .039 23.69 .673 .266 . -------9=------- . .
1880 1.226 38 9 3 40.47 .246 .040 24.96 1.964 4.241 . -----.-=0=------- . .
1881 1.077 38 9 3 2.15 .235 .038 21.77 .992 .710 . -------=1------- . .
1882 .911 40 11 3 30.84 .234 .037 29.97 2.195 6.467 . ------=2=------- . .
1883 .797 40 11 2 8.59 .199 .031 26.01 .268 1.577 . ------3=--.--- . .
1884 .874 41 10 3 21.76 .228 .036 28.97 .810 2.604 . -------4=-.----- . .
1885 .967 43 9 3 4.56 .208 .032 21.84 .877 1.017 . ------=5------- . .
1886 .605 43 9 2 9.07 .200 .030 34.18 .921 2.181 . ------6=------ . .
1887 .781 43 9 3 -.09 .221 .034 27.96 .835 .644 . ------=7=--.--- . .
1888 1.168 43 9 3 .78 .319 .049 27.50 -.426 .863 . ---------=8=--------- . .
1889 .985 43 9 2 -.56 .253 .039 25.43 .331 .736 . --------9=------- . .
1890 .590 43 9 2 38.08 .171 .026 35.20 1.634 4.028 . ------0----- . . .
1891 1.201 43 9 2 5.36 .318 .049 27.07 .697 1.520 . -------.-=1---------- . .
1892 .802 43 9 2 1.97 .239 .036 29.82 .580 .933 . -------2=--.---- . .
1893 .420 43 9 3 18.89 .162 .025 41.35 1.636 3.624 .-----3=---- . . .
1894 1.249 43 9 2 13.06 .341 .052 28.79 1.367 2.293 . -------.--4=---------- . .
1895 .830 43 9 3 54.33 .187 .029 31.49 3.107 10.515 . -----=5--.--- . .
1896 .564 43 9 3 13.17 .184 .028 34.06 1.326 1.668 . -----=6----- . . .
1897 .746 43 9 3 -4.13 .233 .036 30.16 .784 .279 . -------7=---.--- . .
1898 1.040 43 9 3 -6.08 .256 .039 23.80 .379 -.291 . --------8=------- . .
1899 .526 43 9 3 -8.96 .172 .026 31.17 .475 -.271 . -----=9----- . . .
Series Iter St dev Coef of
Year Index Trees Eff % St err Var Skew Kurt 0 +1 +2 +3
1900 1.023 43 9 2 -7.14 .272 .041 25.68 .018 -.070 . --------=0=-------- . .
1901 1.089 43 9 3 4.75 .278 .042 25.87 .882 1.252 . --------=1=-------- . .
1902 1.572 43 9 2 -7.92 .395 .060 24.17 .080 -.363 . ----.-------=2=----------- .
1903 1.032 43 9 2 7.58 .292 .045 29.14 .918 2.026 . --------=3=-------- . .
1904 1.145 43 9 3 9.31 .255 .039 23.08 .839 1.211 . -------=4-------- . .
1905 .438 43 9 3 -2.50 .123 .019 27.42 .651 .509 . ---=5--- . . .
1906 .758 43 9 2 1.88 .137 .021 18.19 .321 .853 . ----=6---- . .
1907 1.209 43 9 3 12.18 .247 .038 21.52 1.389 2.358 . -----.-=7-------- . .
1908 .936 43 9 3 37.22 .189 .029 24.78 2.129 7.687 . ------8=------ . .
1909 .508 43 9 4 10.14 .177 .027 35.06 1.215 .976 . -----=9----- . . .
1910 .718 43 9 3 -1.39 .184 .028 25.32 .674 .543 . ------0----.- . .
1911 1.219 43 9 3 1.78 .262 .040 21.40 .730 .698 . -----.-=1=------- . .
1912 1.001 43 9 3 17.22 .229 .035 24.68 .972 1.868 . -------=2------- . .
1913 .733 43 9 3 -4.01 .249 .038 33.04 .523 .208 . --------3=---.--- . .
1914 1.398 43 9 1 -6.75 .314 .048 21.68 .213 -.137 . ----.----=4=--------- .
1915 1.051 43 9 3 21.82 .289 .044 30.32 1.731 3.494 . ---------5=--------- . .
1916 1.305 43 9 3 4.27 .272 .042 20.87 .712 .956 . ----.---6=-------- . .
1917 1.101 43 9 3 -6.04 .335 .051 29.53 .147 .015 . ----------=7=---------- . .
1918 1.432 43 9 2 -7.56 .362 .055 24.42 -.153 -.147 . -----.-----8=----------- .
1919 .861 43 9 3 1.38 .316 .048 36.45 1.108 .871 . ----------9=-.------- . .
1920 .818 43 9 1 37.38 .136 .021 20.26 1.696 3.521 . ----=0--.- . .
1921 .398 43 9 3 9.68 .150 .023 38.76 1.184 1.649 .-----1----- . . .
1922 .855 43 9 3 -5.23 .173 .026 19.68 .300 .219 . -----2=-.--- . .
1923 1.341 43 9 4 -13.93 .439 .067 30.34 .513 -.280 . ---------.---=3=------------- .
1924 1.223 43 9 3 13.80 .272 .041 23.36 1.222 1.665 . ------.-=4=-------- . .
1925 1.243 43 9 2 53.87 .242 .037 27.37 2.670 7.833 . ----.--5=------- . .
1926 1.000 43 9 1 -.23 .224 .034 22.25 .465 .816 . -------6=------- . .
1927 1.026 43 9 3 28.77 .291 .044 32.47 1.878 3.916 . --------=7=-------- . .
1928 1.081 43 9 2 -2.18 .311 .047 28.17 .549 .579 . ---------=8=--------- . .
1929 1.624 43 9 3 30.95 .410 .062 29.51 2.102 6.221 . ----.-------=9=------------- .
1930 1.363 43 9 2 9.60 .327 .050 24.90 .937 2.012 . -----.----0=---------- .
1931 1.594 45 9 3 -1.29 .430 .064 26.62 .676 .504 . -----.-------=1=------------- .
1932 1.599 45 9 2 -5.51 .404 .060 24.62 -.011 -.299 . ----.-------=2=------------ .
1933 1.265 45 9 3 -5.37 .351 .052 26.89 .292 .187 . -------.--=3=----------. .
1934 .820 45 9 3 5.46 .191 .028 23.76 .730 1.774 . -----=4--.--- . .
1935 1.505 45 9 3 1.29 .304 .045 20.17 .498 .901 . --.------=5--------- .
1936 .751 45 9 3 -11.64 .245 .037 30.58 .543 -.270 . -------=6---.--- . .
1937 1.258 45 9 3 -7.67 .313 .047 23.84 .550 -.224 . ------.--=7---------- . .
1938 1.093 47 8 3 -9.05 .334 .049 29.16 .335 -.486 . ----------=8=---------- . .
1939 1.487 47 8 3 -4.36 .438 .064 28.78 .215 -.033 . -------.-----=9=------------- .
1940 1.785 47 8 3 -.04 .465 .068 25.84 .778 .783 . ---.----------=0=-------------- .
1941 2.049 47 8 3 -5.99 .572 .083 27.07 .150 -.042 . --.--------------=1==--------------
1942 1.230 49 7 3 5.17 .340 .049 28.26 .286 1.060 . --------.-=2=---------- . .
1943 1.725 49 7 3 -2.96 .345 .049 19.75 -.194 .247 . ----------=3=---------- .
1944 1.827 51 8 3 -3.86 .426 .060 22.86 .141 .261 . -.-----------=4=------------ .
1945 1.350 51 8 2 -1.58 .321 .045 23.61 -.114 .469 . -----.---=5=---------. .
1946 .794 51 8 3 -1.55 .213 .030 26.51 .355 .526 . -------6=--.--- . .
1947 1.398 51 8 2 -6.66 .328 .046 22.65 .341 -.069 . -----.----=7=--------- .
1948 1.517 51 8 2 -.84 .392 .055 25.61 .514 .464 . -----.------=8=----------- .
1949 .956 51 8 3 23.94 .359 .050 40.95 1.271 1.868 . -----------=9=---------- . .
Series Iter St dev Coef of
Year Index Trees Eff % St err Var Skew Kurt 0 +1 +2 +3
1950 .442 51 8 3 19.15 .195 .027 46.62 1.274 1.992 ------=0------ . . .
1951 .906 51 8 3 2.07 .339 .047 36.95 .960 .745 . ----------=1=---------- . .
1952 1.186 51 8 3 -3.90 .426 .060 35.08 .274 .403 . -----------.-2=------------- .
1953 1.073 51 8 2 .97 .321 .045 29.82 .626 .694 . ----------=3---------- . .
1954 .513 51 8 3 -3.40 .172 .024 32.72 .558 .191 . -----=4----- . . .
1955 .720 51 8 3 -1.33 .211 .030 28.93 .669 .453 . -------5----.-- . .
1956 1.295 51 8 3 -8.08 .352 .049 26.03 .251 -.182 . -------.--=6=----------. .
1957 1.022 52 8 3 6.53 .302 .042 30.26 .576 1.243 . ---------=7=--------- . .
1958 1.530 53 8 3 -3.08 .385 .053 24.69 .511 .153 . ----.------=8=----------- .
1959 .942 53 8 2 -.98 .251 .034 26.36 .385 .471 . -------=9-------- . .
1960 1.336 54 8 3 28.78 .295 .040 25.23 1.119 1.408 . -----.---=0=-------- . .
1961 .517 54 8 3 4.76 .213 .029 41.35 .980 1.037 .------=1-------. . .
1962 .700 55 8 4 -15.47 .306 .041 40.20 .412 -.562 .---------=2----.---- . .
1963 .903 55 8 3 -7.89 .338 .046 35.84 .257 -.277 . ----------=3=---------- . .
1964 1.491 55 8 3 3.70 .385 .052 26.07 .825 1.165 . -----.------4=------------ .
1965 .923 55 8 2 18.51 .264 .036 31.07 1.386 3.555 . --------5=-------- . .
1966 .835 57 7 3 .83 .270 .036 32.13 .628 .881 . --------=6--.----- . .
1967 .813 57 7 3 -.25 .308 .041 37.47 .461 .556 . ---------=7--.------ . .
1968 1.146 57 7 3 -1.83 .424 .056 36.33 .655 .293 . -------------=8=------------. .
1969 1.218 57 7 4 -1.89 .461 .061 37.02 .571 .455 . ------------.-=9=-------------- .
1970 1.156 57 7 3 4.26 .300 .040 26.40 .282 1.158 . ---------=0=--------- . .
1971 .954 57 7 3 -7.98 .318 .042 32.12 -.032 -.710 . ---------=1---------- . .
1972 .725 57 7 2 2.01 .197 .026 27.67 -.684 .711 . ------2=---.- . .
1973 .984 57 7 3 .74 .204 .027 20.88 -.292 .564 . ------3=------ . .
1974 1.096 57 7 3 -5.42 .291 .039 25.78 .230 .056 . --------=4=-------- . .
1975 .809 57 7 3 4.23 .212 .028 26.68 .113 .933 . ------5=--.--- . .
1976 1.129 57 7 3 -7.82 .314 .042 26.73 .165 -.336 . ---------=6---------- . .
1977 1.013 57 7 3 -7.36 .327 .043 30.85 .488 -.082 . ----------=7---------- . .
1978 .736 57 7 3 -9.55 .295 .039 38.37 -.138 -.346 . ---------8=---.----- . .
1979 1.100 57 7 3 -7.39 .259 .034 22.75 .056 -.123 . --------9=------- . .
1980 1.212 57 7 3 -5.46 .387 .051 30.76 .660 -.088 . ---------.-=0=-----------. .
1981 .856 57 7 3 -8.94 .345 .046 38.70 -.198 -.369 . ----------=1=-.-------- . .
1982 .440 56 7 2 .01 .160 .021 36.11 .449 .657 .-----=2----- . . .
1983 .873 56 7 2 1.64 .213 .028 24.77 -.530 .777 . ------3=-.---- . .
1984 .875 56 7 2 3.68 .224 .030 26.11 -.126 .926 . -------=4-.----- . .
1985 1.303 56 7 3 13.28 .427 .057 34.20 1.233 2.260 . ---------.--=5=------------- .
1986 .907 56 7 3 -4.38 .287 .038 30.71 .596 .007 . --------=6=-------- . .
1987 .510 56 7 3 -1.82 .225 .030 43.18 .774 .249 -------=7-------. . .
1988 .868 56 7 3 16.99 .186 .025 23.59 -.269 2.374 . ------8=-.--- . .
1989 .867 56 7 3 24.78 .219 .029 28.25 .947 2.109 . -------9=-.---- . .
1990 .562 56 7 2 4.10 .156 .021 28.45 -.394 .956 . ----0=---- . . .
1991 .903 56 7 3 -3.62 .205 .027 22.16 .443 .319 . -------1-.----- . .
1992 .333 51 5 2 .11 .165 .023 48.66 .814 .668 ----=2----- . . .
1993 .433 51 5 2 -6.77 .180 .025 40.04 .103 .007 .-----3=----- . . .
1994 .720 51 5 3 -6.79 .201 .028 27.14 -.262 -.167 . ------4----.- . .
1995 .724 51 5 4 2.41 .182 .025 24.99 .798 .765 . ------5----.- . .
1996 .509 51 5 3 7.87 .205 .029 41.28 1.024 1.760 .------=6------ . . .
1997 1.299 51 5 4 -.88 .341 .048 25.57 1.046 .454 . -------.---7=----------. .
1998 .801 51 5 3 -3.87 .273 .038 33.02 .802 .253 . --------8=--.----- . .
1999 1.033 51 5 3 7.25 .229 .032 22.82 1.056 1.982 . -------9=------ . .
2000 .928 56 7 3 -4.51 .411 .055 42.88 .647 -.149 .------------=0=------------ . .
2001 .823 56 7 3 6.05 .263 .035 32.27 .663 1.060 . --------=1--.----- . .
2002 .850 56 7 3 -3.62 .184 .025 21.16 .253 .196 . ------2--.--- . .
2003 .727 56 7 2 11.11 .230 .031 33.22 .364 1.625 . -------3=---.-- . .
2004 1.217 56 7 2 2.20 .333 .045 27.47 .567 1.121 . --------.-=4=---------- . .
2005 1.279 56 7 3 2.19 .284 .038 22.31 .560 1.060 . -----.--=5=-------- . .
2006 .929 56 7 3 .62 .234 .031 24.95 .829 .542 . -------6=------- . .
2007 1.101 56 7 3 -7.08 .254 .034 22.31 .076 -.523 . --------7=------- . .
2008 .921 56 7 3 2.78 .235 .031 25.49 1.057 .655 . -------8=------- . .
2009 .708 56 7 3 -.74 .180 .024 25.13 .552 .401 . -----=9----.- . .
2010 1.266 56 7 4 -2.27 .358 .048 27.34 .886 .169 . --------.--=0=----------. .
2011 1.094 56 7 3 -.73 .297 .040 26.85 .526 .566 . ---------=1=--------- . .
2012 1.052 56 7 3 9.83 .327 .044 32.23 1.031 1.776 . ----------2=---------- . .
2013 .566 56 7 3 -1.67 .179 .024 31.23 .418 .383 . -----=3----- . . .
2014 .593 56 7 3 -7.37 .230 .031 37.41 .071 -.562 . ------=4------- . .
2015 1.092 56 7 3 -.80 .303 .041 27.44 .610 .439 . ---------=5=--------- . .
2016 1.017 56 7 3 16.79 .355 .047 37.26 1.003 1.918 . -----------=6=---------- . .
2017 1.347 56 7 4 -4.53 .613 .082 43.55 .629 .139 .---------------.---=7=------------------- .
2018 1.338 56 7 3 .71 .566 .076 42.02 .501 .625 . -------------.---=8=----------------- .
2019 1.113 56 7 3 -.58 .422 .056 37.45 .591 .530 . ------------=9=-------------. .
2020 .872 56 7 3 61.32 .317 .042 52.79 3.252 11.708 . ----------0=-.-------- . .
2021 .902 56 7 3 71.54 .320 .043 59.85 4.205 19.134 . ---------=1=--------- . .
2022 .528 56 7 3 60.28 .204 .027 55.29 2.949 9.076 .-------2------ . . .
0 +1 +2 +3
Series Iter St dev Coef of Ring Index (Year number shown)
Year Index Trees Eff % St err Var Skew Kurt --- Two Std Dev band; === Std Err band
.022 should be added to each index to adjust chronology mean to 1.0
------------------------------------------------------------------------------------------------------------------------------------
Avge std dev of index means = .280 Avge std error of index means = .04744 Unadjusted mean = .978
Correlation between indices and their standard deviations = .712
Improved indices using robust estimation = 81 Average gain in efficiency over Gaussian estimates = 15.875%
Unimproved indices using robust estimation = 100 Average loss in efficiency over Gaussian estimates = -5.413%
Average error variance of arithmetic means reduced by robust estimation 3.969%
Average error variance reduced by robust estimation in common interval 4.418%
Time span 1836 2022 187 years Mean .978 Median .946 Range .333 2.049 Mean sens .317
Variance .097 Std dev .311 Coef of variation .318 Skewness .447 Kurtosis .367
Autocorrelations, lags 1 to 10: .333 .175 .161 .207 .084 .142 .088 .143 .132 .116
Approx 95 pct confidence limits: .146 .162 .166 .169 .174 .175 .178 .179 .181 .183
Partial autocorrelations: .333 .072 .093 .137 -.042 .103 -.013 .089 .053 .014
Ljung-Box Portmanteau Q 81.6960 DF 25 Prob .0000
Trend in variance (%) = .0142
Residual Chronology from AR Modeling of detrended series 18:03 Wed 18 Sep 2024 Page 10
------------------------------------------------------------------------------------------------------------------------------------
GER Residual chronology without rewhitening
Computed with BIWEIGHT ROBUST MEAN
Title:
All 62 series included in chronology
Ring Index (Year number shown)
Series Iter St dev Coef of --- Two Std Dev band; === Std Err band
Year Index Trees Eff % St err Var Skew Kurt 0 +1 +2 +3
1838 .639 1 1 0 .00 .000 .000 43.64 .000 .000 . 8 . . .
1839 1.095 2 2 0 .00 .050 .035 4.27 .000 .000 . -=9=- . .
1840 1.083 3 3 0 .00 .002 .001 5.05 .000 .000 . .0 . .
1841 .841 4 3 0 .00 .048 .024 5.93 1.862 19.768 . --1- . . .
1842 1.721 5 3 0 .00 .160 .071 13.03 1.054 11.491 . . ----=2=---- .
1843 .931 6 4 1 -14.07 .272 .111 27.13 .359 8.747 . -------=3==------- . .
1844 .981 8 5 3 -9.04 .127 .045 12.40 -.214 3.696 . ---=4=--- . .
1845 1.553 10 5 4 -2.21 .326 .103 21.39 -2.234 3.374 . --.------=5==--------- .
1846 .478 11 5 4 70.64 .062 .019 22.61 1.569 4.267 . --6-- . . .
1847 .925 14 8 3 -7.88 .298 .080 31.05 -.180 1.028 . --------=7==-------- . .
1848 .769 15 8 3 -3.10 .196 .051 24.86 .828 1.706 . -----=8=--.-- . .
1849 1.187 16 9 3 -5.54 .238 .060 19.46 .369 1.721 . -----.-9=------- . .
1850 .942 17 9 3 13.45 .337 .082 36.98 1.758 2.850 . ---------==0=--------- . .
1851 .901 19 9 3 37.91 .223 .051 33.25 -2.340 4.078 . ------=1=------ . .
1852 1.206 20 9 3 -1.41 .283 .063 23.21 .535 1.361 . ------.-=2=-------- . .
1853 1.068 20 9 3 14.98 .201 .045 20.63 -.728 2.414 . ------=3------ . .
1854 1.359 20 9 1 -5.69 .324 .073 23.20 .088 1.017 . -----.---=4=---------- .
1855 .740 21 9 3 -11.14 .237 .052 29.81 .714 .583 . -------5=---.--- . .
1856 .422 21 9 3 1.01 .148 .032 35.16 .252 1.622 . ----6=---- . . .
1857 .779 22 10 2 -6.87 .231 .049 28.53 .440 .581 . ------=7=--.--- . .
1858 1.144 23 10 2 -12.21 .176 .037 14.56 -.414 -.279 . -----=8----- . .
1859 .742 23 10 3 -5.28 .134 .028 17.67 -.670 .183 . ----9=---- . .
1860 .897 23 10 3 -.28 .197 .041 22.03 -.732 1.389 . -----=0=----- . .
1861 1.279 24 10 3 -4.77 .219 .045 16.71 .273 .600 . ---.--=1=------ . .
1862 .826 24 10 3 -6.62 .234 .048 27.51 -.287 .612 . -------=2--.---- . .
1863 1.080 26 8 3 8.43 .214 .042 20.46 .959 1.823 . ------=3------- . .
1864 .548 26 8 2 -4.96 .188 .037 33.39 .411 .439 . ------4=----- . . .
1865 .906 28 7 2 .16 .166 .031 18.25 .626 1.119 . ----=5-.--- . .
1866 .907 29 7 3 -7.99 .177 .033 18.64 .591 .616 . -----=6=----- . .
1867 .983 30 7 3 -5.45 .173 .032 17.09 .505 .221 . -----7=----- . .
1868 .873 30 7 3 -7.69 .226 .041 24.74 .504 .213 . -------8=-.----- . .
1869 .823 30 7 3 88.11 .173 .032 54.15 5.599 23.403 . -----=9--.-- . .
1870 1.405 30 7 2 51.45 .280 .051 27.35 2.666 7.220 . ---.----=0=--------. .
1871 .796 30 7 3 7.38 .290 .053 38.18 -.384 1.727 . --------=1=--.------ . .
1872 .867 31 8 3 2.09 .235 .042 27.52 -.359 1.155 . -------2=-.----- . .
1873 1.262 32 7 3 -3.01 .235 .042 18.35 -.094 .512 . ----.--=3------- . .
1874 .889 32 7 1 21.48 .214 .038 26.48 1.361 2.877 . ------=4-.----- . .
1875 1.077 34 8 3 -10.43 .201 .034 17.71 .052 .072 . ------=5------ . .
1876 1.008 34 8 3 -4.32 .246 .042 23.79 .505 .170 . -------=6------- . .
1877 .904 34 8 3 -6.42 .188 .032 20.04 .450 .164 . -----=7-.---- . .
1878 .979 34 8 3 5.91 .220 .038 22.91 1.111 1.468 . -------8=------ . .
1879 .960 35 8 3 2.65 .203 .034 21.26 .972 1.338 . ------=9------ . .
1880 1.242 35 8 3 4.90 .220 .037 18.08 .379 1.002 . ----.--0=------ . .
1881 .967 38 9 3 14.42 .170 .028 18.66 1.336 1.819 . -----1----- . .
1882 .868 38 9 3 52.78 .161 .026 26.07 3.166 11.864 . -----2=-.--- . .
1883 .821 39 10 2 8.90 .186 .030 23.95 -.519 1.697 . -----=3--.--- . .
1884 .959 40 11 2 7.59 .206 .033 22.35 .089 1.351 . ------=4------ . .
1885 1.025 41 10 3 -3.57 .177 .028 16.87 .842 .196 . -----=5------ . .
1886 .620 42 10 2 16.59 .184 .028 32.10 .827 2.880 . -----6=-----. . .
1887 .942 42 10 3 1.45 .202 .031 21.40 1.086 .893 . ------=7------ . .
1888 1.295 42 10 3 2.80 .267 .041 21.03 -.734 1.362 . ----.---8=-------- . .
1889 .933 43 9 2 7.90 .205 .031 22.72 .588 1.591 . ------9=------ . .
1890 .620 43 9 3 -5.15 .170 .026 26.59 .443 .042 . -----0=-----. . .
1891 1.345 43 9 3 -.45 .284 .043 20.94 .729 .707 . ----.---=1=-------- . .
1892 .754 43 9 2 -2.76 .224 .034 29.28 .072 .362 . -------=2---.--- . .
1893 .499 43 9 2 21.08 .144 .022 32.21 .659 3.737 . ----3=---- . . .
1894 1.499 43 9 3 15.61 .289 .044 20.67 1.446 3.018 . --.------4=--------- .
1895 .786 43 9 2 27.29 .232 .035 33.70 1.433 4.540 . -------5=--.---- . .
1896 .633 43 9 2 8.34 .144 .022 23.33 .902 1.285 . ----=6---- . . .
1897 .947 43 9 3 -11.78 .190 .029 18.78 .634 -.308 . -----=7------ . .
1898 1.166 43 9 3 -9.06 .207 .032 17.03 -.087 -.262 . ----.-8=------ . .
1899 .548 43 9 3 3.29 .162 .025 29.87 .495 1.276 . -----9=---- . . .
Series Iter St dev Coef of
Year Index Trees Eff % St err Var Skew Kurt 0 +1 +2 +3
1900 1.219 43 9 3 -.55 .217 .033 17.64 .569 .684 . ----.-=0=------ . .
1901 1.108 43 9 3 33.01 .177 .027 19.07 1.644 3.714 . -----1=----- . .
1902 1.538 43 9 3 -7.04 .309 .047 19.40 .454 -.562 . --.------=2=--------- .
1903 .819 43 9 3 8.99 .244 .037 31.01 .378 1.923 . -------=3--.---- . .
1904 1.060 43 9 3 19.32 .222 .034 22.73 1.553 2.161 . -------4=------- . .
1905 .383 43 9 3 -.36 .122 .019 32.47 -.867 .465 . ---=5---- . . .
1906 .953 43 9 3 -2.24 .168 .026 17.33 .735 .415 . -----=6----- . .
1907 1.334 43 9 3 24.52 .210 .032 17.84 1.903 4.251 . --.---=7------- . .
1908 .888 43 9 3 13.33 .171 .026 20.45 .769 2.147 . -----=8-.--- . .
1909 .553 43 9 3 -4.50 .203 .031 35.21 .790 .299 . ------9=------. . .
1910 .911 43 9 2 -.84 .158 .024 17.28 .258 .615 . -----0-.--- . .
1911 1.365 43 9 2 1.07 .215 .033 15.71 .754 .801 . --.----1=------ . .
1912 .944 43 9 3 14.15 .222 .034 24.91 .930 1.714 . ------=2------- . .
1913 .741 43 9 2 -5.82 .193 .029 25.37 -.243 .020 . ------3=---.-- . .
1914 1.502 43 9 3 -7.26 .221 .034 14.22 .049 -.189 . -------=4-------. .
1915 .912 43 9 3 14.61 .217 .033 25.14 1.270 2.562 . -------5=------ . .
1916 1.280 43 9 3 5.11 .234 .036 18.85 -.185 1.108 . ----.--=6=------ . .
1917 .970 43 9 3 -6.59 .247 .038 24.60 .108 -.353 . -------=7=------- . .
1918 1.342 43 9 2 -5.67 .236 .036 17.06 .196 -.358 . ---.---=8=------- . .
1919 .689 43 9 3 -3.06 .276 .042 39.35 .206 .291 . --------=9----.--- . .
1920 .839 43 9 3 21.68 .143 .022 19.36 -.508 2.629 . -----0--.- . .
1921 .462 43 9 3 14.68 .156 .024 35.63 .813 1.560 . -----1----- . . .
1922 1.082 43 9 2 -4.18 .159 .024 14.44 -.130 .364 . ----=2----- . .
1923 1.454 43 9 4 -12.12 .379 .058 24.38 .507 -.264 . -----.-----=3=----------- .
1924 1.135 43 9 3 7.32 .222 .034 20.12 1.049 1.407 . ------=4------- . .
1925 1.181 43 9 3 31.63 .209 .032 20.90 2.139 6.197 . ----.-5=------ . .
1926 .850 43 9 2 -7.73 .208 .032 23.55 .238 .021 . -------6=-.---- . .
1927 .961 43 9 3 34.41 .270 .041 33.41 1.481 4.276 . --------=7=-------- . .
1928 1.051 43 9 3 -5.78 .235 .036 21.86 -.387 .086 . -------8=------- . .
1929 1.553 43 9 3 38.22 .280 .043 22.30 2.150 6.268 . -.-------9=-------- .
1930 1.086 43 9 3 -6.88 .239 .036 21.11 .473 .196 . -------=0-------- . .
1931 1.417 43 9 3 -8.89 .361 .055 24.28 .665 -.365 . -----.----=1=----------- .
1932 1.285 45 9 4 8.24 .311 .046 24.76 1.078 1.356 . ------.--=2=--------- . .
1933 .957 45 9 2 -5.09 .220 .033 22.45 .039 -.056 . ------=3------- . .
1934 .643 45 9 3 19.27 .189 .028 32.43 .458 2.954 . -----=4------ . .
1935 1.501 45 9 3 22.45 .229 .034 17.17 .912 3.449 . -------=5-------. .
1936 .537 45 9 3 -6.47 .217 .032 39.05 .157 -.266 .-------6=------. . .
1937 1.291 45 9 3 .83 .240 .036 18.47 1.050 .785 . ----.---7=------- . .
1938 1.010 45 9 3 -2.57 .254 .038 24.84 .140 .357 . -------=8-------- . .
1939 1.393 47 8 3 -7.12 .344 .050 23.76 .399 -.149 . -----.----=9=---------- .
1940 1.560 47 8 2 11.25 .288 .042 19.38 1.110 1.977 . -.-------0=--------- .
1941 1.657 47 8 3 -6.33 .376 .055 21.99 -.024 -.154 . --.--------=1=----------- .
1942 .751 47 8 2 6.81 .214 .031 30.15 -.877 1.186 . ------=2---.-- . .
1943 1.488 49 7 3 .87 .308 .044 20.69 .515 .771 . ---.------3=--------- .
1944 1.480 49 7 3 -1.20 .266 .038 17.81 .589 .382 . -.------4=-------- .
1945 .918 51 8 2 6.01 .271 .038 30.27 .335 1.247 . --------5=-------- . .
1946 .558 51 8 3 6.24 .195 .027 35.99 .257 1.168 . ------6=------. . .
1947 1.387 51 8 3 -1.98 .330 .046 23.49 .382 .361 . -----.----=7---------- .
1948 1.306 51 8 2 11.56 .257 .036 20.65 .917 1.715 . ----.---8=-------- . .
1949 .731 51 8 3 22.14 .240 .034 36.24 1.000 2.447 . -------9=---.--- . .
Series Iter St dev Coef of
Year Index Trees Eff % St err Var Skew Kurt 0 +1 +2 +3
1950 .417 51 8 3 -2.68 .169 .024 40.38 -.504 .265 .-----0=----- . . .
1951 1.083 51 8 3 3.56 .256 .036 23.89 1.144 1.206 . -------=1-------- . .
1952 1.226 51 8 2 -9.51 .314 .044 24.43 .088 -.155 . -------.-=2=--------- . .
1953 1.016 51 8 3 -3.80 .211 .030 20.38 .224 .465 . ------=3------- . .
1954 .500 51 8 2 -2.77 .163 .023 32.29 -.035 .230 . -----4=----- . . .
1955 .888 51 8 2 7.52 .154 .022 17.82 .682 1.484 . ----=5-.--- . .
1956 1.415 51 8 3 -9.20 .264 .037 17.86 .193 -.491 . --.-----6=--------. .
1957 .914 51 8 3 13.19 .244 .034 28.17 1.101 2.018 . --------7=------- . .
1958 1.525 52 8 3 -2.34 .316 .044 20.36 .585 .325 . --.------=8=--------- .
1959 .741 53 8 2 -8.74 .173 .024 22.38 .004 -.689 . -----9=---.- . .
1960 1.352 53 8 3 5.93 .205 .028 15.51 .734 .880 . -.----0=------ . .
1961 .356 54 8 2 13.13 .200 .027 59.00 .738 2.742 ------1=------ . . .
1962 .813 54 8 3 -6.12 .239 .033 28.33 .447 .002 . -------=2--.---- . .
1963 1.031 55 8 3 -5.73 .221 .030 20.83 .122 -.163 . -------3------- . .
1964 1.541 55 8 3 -1.07 .344 .046 22.13 .606 .529 . ---.------=4=---------- .
1965 .770 55 8 2 11.30 .202 .027 27.38 1.121 2.454 . ------=5---.-- . .
1966 .819 55 8 2 -4.78 .191 .026 22.79 -.169 .018 . ------=6--.--- . .
1967 .863 57 7 3 -3.71 .194 .026 21.99 .123 .150 . ------7=-.---- . .
1968 1.191 57 7 3 14.37 .317 .042 28.18 1.261 2.168 . --------.-=8---------- . .
1969 1.159 57 7 4 1.89 .312 .041 26.61 .927 .665 . ---------=9=--------- . .
1970 1.048 57 7 3 -4.29 .266 .035 24.65 .713 .028 . --------0=-------- . .
1971 .877 57 7 3 2.40 .256 .034 30.00 -.789 .692 . --------=1-.------ . .
1972 .704 57 7 2 -3.71 .205 .027 28.47 .319 .105 . ------=2----.- . .
1973 1.068 57 7 2 -2.93 .162 .021 14.86 .476 .150 . -----=3----- . .
1974 1.116 57 7 3 -3.96 .229 .030 19.89 .611 .190 . -------4=------- . .
1975 .779 57 7 2 4.35 .173 .023 22.61 .144 1.132 . ------5---.- . .
1976 1.209 57 7 3 -5.87 .247 .033 19.82 .034 -.118 . -----.-=6-------- . .
1977 .978 57 7 3 -7.09 .263 .035 25.89 .452 -.229 . --------7=-------- . .
1978 .730 57 7 2 1.19 .229 .030 31.63 -.171 .653 . -------8=---.--- . .
1979 1.218 57 7 3 -6.06 .194 .026 15.39 .308 -.009 . ---.--9------ . .
1980 1.192 57 7 3 -2.07 .306 .040 25.04 .976 .275 . -------.-=0--------- . .
1981 .788 57 7 3 -.81 .236 .031 29.97 -.244 .484 . -------1=--.---- . .
1982 .501 56 7 2 17.04 .124 .017 26.66 1.035 2.326 . ---=2--- . . .
1983 1.087 56 7 2 6.63 .191 .025 18.01 .876 1.688 . -----=3------ . .
1984 .958 56 7 2 -2.79 .179 .024 18.44 -.041 .469 . -----=4------ . .
1985 1.380 56 7 3 16.03 .382 .051 29.45 1.417 2.680 . -------.----=5------------ .
1986 .818 56 7 3 -8.38 .191 .026 22.37 .402 -.494 . ------=6--.--- . .
1987 .528 56 7 3 -5.45 .213 .028 38.80 .678 -.038 .------=7-------. . .
1988 1.053 56 7 2 13.09 .164 .022 16.73 -.641 2.815 . -----8=----- . .
1989 .955 56 7 3 20.09 .223 .030 25.75 .623 2.263 . ------=9------- . .
1990 .625 56 7 2 -8.98 .130 .017 19.89 -.005 -.212 . ----0=---- . . .
1991 1.105 56 7 3 2.47 .154 .021 14.06 .581 .749 . -----1=---- . .
1992 .404 51 5 2 24.75 .149 .021 40.92 1.058 2.705 .-----2----- . . .
1993 .716 51 5 2 4.40 .131 .018 18.72 -.294 1.139 . ----3----. . .
1994 .990 51 5 2 -1.33 .141 .020 14.10 .412 .415 . ----4=---- . .
1995 .902 51 5 1 -6.66 .139 .020 14.94 .226 -.140 . -----5-.-- . .
1996 .672 51 5 2 8.54 .165 .023 25.53 .477 1.457 . -----6=----- . .
1997 1.541 51 5 3 3.88 .266 .037 17.39 1.169 .741 . --------7=-------- .
1998 .736 51 5 3 -8.77 .189 .026 24.48 .570 -.403 . ------8=---.- . .
1999 1.128 51 5 3 -4.57 .188 .026 16.23 .432 .010 . -----=9------ . .
2000 .974 51 5 3 -7.84 .332 .047 32.62 .495 -.390 . ----------=0=---------- . .
2001 .862 54 6 2 .62 .200 .027 23.11 .639 .714 . ------1=-.---- . .
2002 .933 56 7 3 -5.41 .178 .024 18.45 .512 -.043 . -----2=----- . .
2003 .805 56 7 2 22.76 .193 .026 26.77 1.049 3.672 . ------3=--.--- . .
2004 1.326 56 7 3 30.61 .224 .030 19.93 1.829 5.998 . --.---=4------- . .
2005 1.229 56 7 3 5.72 .238 .032 19.70 .819 1.031 . ----.--5=------- . .
2006 .862 56 7 2 -1.60 .240 .032 27.50 .230 .315 . -------6=-.----- . .
2007 1.119 56 7 2 -4.62 .195 .026 16.97 .325 .113 . ------7=------ . .
2008 .892 56 7 3 11.56 .189 .025 22.09 1.037 1.176 . -----=8-.---- . .
2009 .734 56 7 2 5.41 .133 .018 18.46 .846 1.046 . ----9=---. . .
2010 1.384 56 7 3 -.60 .296 .040 21.02 .975 .284 . ----.----=0---------. .
2011 1.004 56 7 3 -4.84 .235 .031 22.67 .680 .113 . -------=1------- . .
2012 1.010 56 7 2 37.95 .203 .027 24.68 1.937 5.496 . ------=2------ . .
2013 .578 56 7 3 20.39 .177 .024 35.42 -1.332 2.458 . -----=3----- . . .
2014 .745 56 7 3 -4.87 .187 .025 24.57 .086 -.023 . ------4=---.- . .