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PURARS.OUT
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[] Dendrochronology Program Library Run PUR Program ARS 11:41 Tue 08 Oct 2024 Page 1
[]
[] P R O G R A M A R S T A N Version 6.05P 32790
------------------------------------------------------------------------------------------------------------------------------------
Title of run:
Data file: PUR.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: PUR
14 Year-by-year list of chronology Y
==> Time span of data 1811 to 2021 211 years, 26 series, 3481 rings
Mean length of series is 133.88 years.
15 Common interval analysis O
Common interval, Optimum 1898 to 2021 124 years, 18 series, 2232 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
>> pub07x Span 1882 2021 2 Indices over 3.0
Years: 1922 1924
Values: 3.217 3.222
>> pub20x Span 1850 2021 2 Indices over 3.0
Years: 1922 1938
Values: 3.001 3.135
>> pub21x Span 1892 2021 2 Indices over 3.0
Years: 1923 2015
Values: 3.038 4.511
>> pub25x Span 1847 2021 2 Indices over 3.0
Years: 1923 1938
Values: 3.018 3.285
>> pub27x Span 1867 2021 1 Indices over 3.0
Years: 1924
Values: 3.058
>> pub28x Span 1849 2021 2 Indices over 3.0
Years: 1923 1924
Values: 3.617 3.434
>> pub29x Span 1865 2021 1 Indices over 3.0
Years: 1938
Values: 3.827
>> pub30x Span 1857 2021 3 Indices over 3.0
Years: 1937 1938 1953
Values: 3.645 3.634 3.120
>> pub34x Span 1811 2021 3 Indices over 3.0
Years: 1851 1923 1924
Values: 3.004 3.226 3.902
>> pub40x Span 1874 2021 1 Indices over 3.0
Years: 1924
Values: 3.428
>> pub43x Span 1893 2021 2 Indices over 3.0
Years: 1923 1924
Values: 3.311 3.719
>> pub57x Span 1854 2021 1 Indices over 3.0
Years: 1923
Values: 3.177
>> pub59x Span 1874 2021 3 Indices over 3.0
Years: 1923 1924 1938
Values: 3.625 3.350 3.372
3481 total rings 35 absent rings 1.0055 %
13 detrended series contain 25 index values over 3.0
STATISTICS of TREE-RING MEASUREMENTS 11:41 Tue 08 Oct 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 pub03x 1873 2021 149 .755 .680 .382 .401 1.534 2.511 -.0730 .53 .52 .03 .000
2 pub05x 1938 2021 84 .501 .470 .300 .214 .674 -.234 -.0138 .60 -.03 .14 .000
3 pub06x 1890 2021 132 .532 .475 .302 .267 .965 .458 -.1532 .72 .22 -.01 .000
4 pub07x 1882 2021 140 .450 .370 .352 .313 1.910 3.615 -.1628 .72 .32 -.18 .000
5 pub10x 1948 2021 74 1.464 1.435 .298 .475 .519 .356 .1416 .43 -.01 -.10 .015
6 pub20x 1850 2021 172 .454 .385 .428 .309 1.466 2.834 -.0971 .67 .33 .06 .000
7 pub21x 1892 2021 130 .287 .235 .471 .201 3.427 19.219 .0693 .49 .31 .11 .000
8 pub25x 1847 2021 175 .456 .350 .434 .351 2.497 7.869 -.1841 .71 .30 .02 .000
9 pub27x 1867 2021 155 .289 .240 .526 .178 1.217 1.946 -.0401 .50 .27 -.05 .000
10 pub28x 1849 2021 173 .583 .470 .496 .456 1.767 3.726 -.1484 .70 .28 -.11 .000
11 pub29x 1865 2021 157 .512 .410 .534 .353 1.190 1.647 -.0421 .70 .29 .03 .000
12 pub30x 1857 2021 165 .577 .480 .444 .371 1.527 2.981 -.0521 .71 .16 -.01 .000
13 pub34x 1811 2021 211 .342 .290 .404 .225 1.572 2.804 -.0602 .75 .27 .00 .000
14 pub37x 1847 2021 175 .863 .800 .340 .508 .703 .208 -.1317 .76 .24 .09 .000
15 pub39x 1897 2021 125 .324 .290 .504 .174 .675 .265 -.0740 .49 .31 -.01 .000
16 pub40x 1874 2021 148 .530 .455 .378 .315 1.589 3.758 -.0354 .74 .33 -.06 .000
17 pub42x 1909 2021 113 .475 .430 .410 .258 .770 .570 -.0313 .66 -.02 -.08 .000
18 pub43x 1893 2021 129 .531 .480 .458 .349 1.995 5.487 -.1462 .74 .20 -.02 .000
19 pub44x 1918 2021 104 .887 .645 .238 .630 1.346 1.384 -.3599 .91 .09 -.26 .000
20 pub46x 1898 2021 124 .778 .760 .334 .326 .368 .002 .1395 .56 .21 -.09 .000
21 pub50x 1930 2021 92 .870 .820 .377 .384 .719 .349 -.2071 .49 .03 -.16 .000
22 pub52x 1951 2021 71 .473 .460 .427 .308 .996 .838 -.2928 .73 .15 -.04 .000
23 pub57x 1854 2021 168 .487 .440 .364 .249 1.129 1.632 -.0744 .58 .23 -.04 .000
24 pub582x 1936 2021 86 1.004 .995 .280 .384 .158 -.688 .0465 .62 -.04 -.20 .000
25 pub59x 1874 2021 148 .773 .610 .343 .570 1.441 1.866 -.2201 .84 .11 -.10 .000
26 puub32x 1941 2021 81 .997 .900 .454 .521 .959 .846 .2775 .58 .20 .05 .000
26 Series means 133.9 .623 .553 .395 .350 1.274 2.548 -.0741 .65 .20 -.04 .001
STATISTICS of DETRENDED SERIES 11:41 Tue 08 Oct 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 pub03x 1873 2021 149 1.000 .893 .383 .465 1.193 1.658 -.1124 .45 .46 .03 .000 Regr-D/RegrD
2 pub05x 1938 2021 84 1.000 .926 .300 .429 .876 .371 -.1876 .56 -.06 .13 .000 Regr+D/RegrD
3 pub06x 1890 2021 132 1.000 .904 .302 .476 .650 -.135 -.2457 .69 .21 -.01 .000 Regr-D/RegrD
4 pub07x 1882 2021 140 1.000 .851 .352 .621 1.473 2.305 -.2702 .69 .28 -.16 .000 Regr-D/RegrD
5 pub10x 1948 2021 74 1.000 .979 .298 .321 .450 .177 .0953 .42 -.02 -.11 .009 Regr+D/RegrD
6 pub20x 1850 2021 172 .999 .858 .427 .585 .867 .760 .0474 .67 .36 -.06 .000 NExpD/Regr-D
7 pub21x 1892 2021 130 1.000 .890 .471 .615 2.278 8.538 .0722 .49 .29 .04 .000 Regr+D/RegrD
8 pub25x 1847 2021 175 1.000 .863 .434 .570 1.297 2.255 -.0494 .65 .22 -.07 .000 NExpD/RegrD
9 pub27x 1867 2021 155 1.000 .879 .526 .588 .885 .646 -.0373 .49 .25 -.02 .000 NExpD/RegrD
10 pub28x 1849 2021 173 .998 .850 .494 .668 1.323 2.014 -.0015 .69 .26 -.10 .000 NExpD/Regr-D
11 pub29x 1865 2021 157 1.000 .862 .534 .674 1.129 1.593 -.0900 .68 .30 .04 .000 Regr-D/RegrD
12 pub30x 1857 2021 165 1.000 .866 .444 .634 1.552 3.348 -.1005 .70 .16 -.02 .000 RegrD/RegrD
13 pub34x 1811 2021 211 1.000 .853 .404 .651 1.513 2.698 -.1618 .74 .27 .00 .000 NExpD/RegrD
14 pub37x 1847 2021 175 1.000 .864 .340 .603 .977 .670 -.2335 .76 .22 .07 .000 Regr+D/RegrD
15 pub39x 1897 2021 125 1.000 .937 .504 .527 .553 .116 -.2017 .46 .32 -.01 .000 NExpD/Regr-D
16 pub40x 1874 2021 148 1.000 .910 .378 .532 1.267 2.820 -.0877 .68 .30 -.06 .000 Regr-D/RegrD
17 pub42x 1909 2021 113 1.000 .928 .410 .510 .730 .484 .1126 .56 -.08 -.08 .000 NExpD/RegrD
18 pub43x 1893 2021 129 1.000 .914 .458 .625 1.659 4.032 -.2402 .70 .20 .00 .000 NExpD/Regr-D
19 pub44x 1918 2021 104 1.001 .962 .239 .426 .394 -.766 .1483 .77 .21 -.13 .000 NExpD/Regr+D
20 pub46x 1898 2021 124 1.000 .979 .334 .419 .350 -.043 .1703 .56 .21 -.09 .000 RegrD/RegrD
21 pub50x 1930 2021 92 1.000 .978 .375 .421 .774 .919 -.0586 .48 -.02 -.22 .000 NExpD/RegrD
22 pub52x 1951 2021 71 1.008 .943 .426 .603 1.031 1.172 -.4690 .67 .14 -.08 .000 NExpD/Regr+D
23 pub57x 1854 2021 168 1.000 .914 .364 .494 1.409 3.423 -.0363 .57 .18 -.05 .000 NExpD/RegrD
24 pub582x 1936 2021 86 1.000 1.010 .280 .377 .149 -.680 -.0737 .59 -.07 -.25 .000 Regr+D/RegrD
25 pub59x 1874 2021 148 1.000 .813 .343 .726 1.372 1.680 -.3031 .84 .11 -.10 .000 RegrD/RegrD
26 puub32x 1941 2021 81 1.000 .887 .454 .470 .536 -.180 .0608 .50 .19 .00 .000 Regr+D/RegrD
26 Series means 133.9 1.000 .904 .395 .540 1.026 1.534 -.0867 .62 .19 -.05 .000
MULTIVARIATE AUTOREGRESSIVE MODELING, DETRENDED SERIES 11:41 Tue 08 Oct 2024 Page 4
------------------------------------------------------------------------------------------------------------------------------------
All series used in pooling
Pooled autocorrelations:
T= 0 1.000 T= -1 .647 T= -2 .543 T= -3 .371 T= -4 .337 T= -5 .295
T= -6 .201 T= -7 .173 T= -8 .122 T= -9 .157 T=-10 .150 T=-11 .157
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 .6473
2 1.0000 .5089 .2137
3 1.0000 .5258 .2538 -.0788
4 1.0000 .5336 .2285 -.1313 .0998
5 1.0000 .5268 .2374 -.1468 .0634 .0681
6 1.0000 .5341 .2442 -.1625 .0888 .1245 -.1070
7 1.0000 .5374 .2404 -.1653 .0938 .1170 -.1234 .0307
8 1.0000 .5373 .2408 -.1657 .0935 .1176 -.1243 .0287 .0037
9 1.0000 .5370 .2385 -.1555 .0838 .1100 -.1108 .0090 -.0403 .0819
10 1.0000 .5345 .2397 -.1558 .0873 .1065 -.1134 .0139 -.0478 .0651 .0313
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)
2026.349 1913.793 1905.932 1906.618 1906.506 1907.525 1907.094 1908.894 1910.891 1911.470 1913.263
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: 2
Autoregression coefficients:
T= -1 T= -2
.5089 .2137
R-squared due to pooled autoregression = 44.55%
Impulse response function weights for AR ( 2) process:
1.0000 .5089 .4727 .3493 .2788 .2166 .1698 .1327 .1038 .0812
.0635 .0497 .0389 .0304 .0238 .0186
UNIVARIATE AUTOREGRESSIVE MODELING 11:41 Tue 08 Oct 2024 Page 5
------------------------------------------------------------------------------------------------------------------------------------
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 pub03x 1875 2021 147 1.008 .998 .417 .367 .556 .285 -.0445 -.01 .00 -.05 .409
2 pub05x 1939 2021 83 .986 .956 .372 .332 .626 .473 -.1023 .07 -.09 .09 .353
3 pub06x 1892 2021 130 1.005 .953 .363 .334 .584 .257 -.0007 -.01 -.02 -.08 .017
4 pub07x 1885 2021 137 1.007 .988 *437 .422 1.048 4.968 -.0930 .00 -.02 -.05 .444
5 pub10x 1949 2021 73 1.000 .991 .335 .292 .260 -.371 .0403 -.01 .03 -.06 .333
6 pub20x 1852 2021 170 1.003 .954 .451 .407 .705 2.215 -.0406 .02 .01 -.13 .240
7 pub21x 1894 2021 128 1.003 .966 *526 .516 2.089 10.197 .1031 -.02 -.01 .02 .029
8 pub25x 1849 2021 173 1.002 .979 .481 .424 .826 2.034 -.0098 .02 .01 -.18 .438
9 pub27x 1869 2021 153 1.004 .961 *574 .496 .342 1.003 -.0675 .02 .00 -.02 .018
10 pub28x 1851 2021 171 1.000 .998 *520 .468 .402 1.111 -.0212 .03 .03 -.15 .307
11 pub29x 1867 2021 155 .996 1.011 *553 .474 .164 1.905 .0755 -.01 -.07 -.10 .023
12 pub30x 1859 2021 163 1.003 .965 .529 .447 .836 2.350 -.0222 .00 .00 -.10 .089
13 pub34x 1813 2021 209 .999 .940 *462 .420 .548 1.879 -.0131 .00 .02 .05 .156
14 pub37x 1849 2021 173 .985 .958 .402 .356 .668 .951 .0151 -.05 -.08 .07 .346
15 pub39x 1899 2021 123 .999 .938 *523 .445 .289 .125 -.0154 .00 .00 -.06 .041
16 pub40x 1876 2021 146 1.003 1.009 .431 .374 .347 1.032 .0136 .02 .02 -.07 .079
17 pub42x 1910 2021 112 1.001 .963 *484 .424 -.025 .377 .1416 .04 -.01 -.08 .067
18 pub43x 1895 2021 127 1.008 .940 .492 .434 .576 .649 .0869 -.01 -.02 -.03 .372
19 pub44x 1920 2021 102 1.011 .997 .283 .259 .143 -.178 -.0217 .02 .11 .02 .164
20 pub46x 1900 2021 122 .996 .946 .370 .340 .303 .112 .0650 .02 .03 -.15 .394
21 pub50x 1931 2021 91 .997 .940 .445 .371 .347 .146 -.0138 .01 .09 -.18 .293
22 pub52x 1952 2021 70 .995 .969 *555 .448 .431 .815 .0067 -.10 .14 -.20 .219
23 pub57x 1856 2021 166 1.001 1.000 *420 .398 .983 3.275 -.0347 .02 .02 -.06 .110
24 pub582x 1937 2021 85 .992 .984 .356 .302 .342 -.123 -.0790 .04 .08 -.18 .454
25 pub59x 1876 2021 146 1.002 .972 .425 .391 .801 1.713 .0475 .01 .06 -.18 .306
26 puub32x 1943 2021 79 1.000 .989 .503 .400 .404 -.150 .0446 .00 .00 -.03 .450
* 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 11:41 Tue 08 Oct 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 .2405 .4704 38.21
2 .5900 35.53
3 .5370 .2247 50.61
4 .5403 .3682 -.1575 54.18
5 .4252 18.08
6 .4308 .3585 52.31
7 .3515 .2870 30.65
8 .5049 .2217 45.20
9 .3727 .2493 29.37
10 .5056 .2676 51.85
11 .4736 .3031 51.20
12 .5897 .1620 50.86
13 .5473 .2642 58.44
14 .5791 .2585 63.92
15 .3200 .3138 29.52
16 .4704 .3072 51.39
17 .5629 32.16
18 .5562 .2099 51.79
19 .6212 .2072 63.64
20 .4443 .2126 35.58
21 .4819 23.25
22 .6759 46.89
23 .4687 .1832 35.36
24 .5962 35.78
25 .7394 .1207 71.43
26 .4097 .1875 28.05
Average variance explained by autoregression = 43.66%
OUTLIERS in NORMALIZED RESIDUALS (over 3 standard deviations from mean) 11:41 Tue 08 Oct 2024 Page 7
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Seq 2 Years: 1952
Values: 3.06
Seq 4 Years: 1922
Values: 5.06
Seq 6 Years: 1922 1938
Values: 3.18 4.30
Seq 7 Years: 1964 2015
Values: 3.31 5.94
Seq 8 Years: 1923 1938
Values: 3.00 4.40
Seq 9 Years: 1872
Values: 3.43
Seq 10 Years: 1922 1995
Values: 3.01 -3.40
Seq 11 Years: 1938 1959
Values: 4.02 -3.15
Seq 12 Years: 1937 1953
Values: 4.27 3.63
Seq 13 Years: 1855 1923 1924
Values: -3.36 4.25 3.65
Seq 14 Years: 1856 1953
Values: 3.05 3.51
Seq 16 Years: 1924
Values: 3.69
Seq 18 Years: 2008
Values: 3.09
Seq 23 Years: 1895 1915 1922 1923
Values: 4.10 3.77 3.59 3.29
Seq 25 Years: 1921 1942
Values: 3.40 3.25
AUTOREGRESSIVE MODELING, RESIDUAL SERIES 11:41 Tue 08 Oct 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 .014 T= -2 .015 T= -3 -.121 T= -4 .018 T= -5 .094
T= -6 -.045 T= -7 -.016 T= -8 -.091 T= -9 .027 T=-10 .032 T=-11 .079
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 .0140
2 1.0000 .0138 .0146
3 1.0000 .0156 .0162 -.1210
4 1.0000 .0182 .0159 -.1214 .0220
5 1.0000 .0161 .0278 -.1230 .0202 .0984
6 1.0000 .0225 .0291 -.1309 .0220 .0994 -.0649
7 1.0000 .0216 .0305 -.1306 .0202 .0998 -.0646 -.0137
8 1.0000 .0207 .0262 -.1241 .0216 .0912 -.0626 -.0123 -.0659
9 1.0000 .0216 .0264 -.1231 .0203 .0909 -.0608 -.0127 -.0662 .0145
10 1.0000 .0212 .0281 -.1228 .0218 .0886 -.0613 -.0095 -.0668 .0140 .0258
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)
1875.126 1877.085 1879.041 1877.956 1879.854 1879.821 1880.938 1882.898 1883.990 1885.946 1887.807
Selected autoregression order: 0
Standard Tree-Ring Chronology 11:41 Tue 08 Oct 2024 Page 9
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Tree mask:
Sequence 1 2 3 4 5 6 7 8 91011121314151617181920212223242526
Radii 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PUR Standard chronology, no autoregressive modeling
Computed with BIWEIGHT ROBUST MEAN
Title:
All 26 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
1811 1.614 1 1 0 .00 .000 .000 .00 .000 .000 . . 1 . .
1812 1.002 1 1 0 .00 .000 .000 .00 .000 .000 . 2 . .
1813 1.086 1 1 0 .00 .000 .000 .00 .000 .000 . .3 . .
1814 .641 1 1 0 .00 .000 .000 .00 .000 .000 . 4 . . .
1815 .725 1 1 0 .00 .000 .000 .00 .000 .000 . 5 . . .
1816 .558 1 1 0 .00 .000 .000 .00 .000 .000 . 6 . . .
1817 .363 1 1 0 .00 .000 .000 .00 .000 .000 . 7 . . .
1818 .419 1 1 0 .00 .000 .000 .00 .000 .000 . 8 . . .
1819 .335 1 1 0 .00 .000 .000 .00 .000 .000 . 9 . . .
1820 .307 1 1 0 .00 .000 .000 .00 .000 .000 . 0 . . .
1821 .224 1 1 0 .00 .000 .000 .00 .000 .000 . 1 . . .
1822 .811 1 1 0 .00 .000 .000 .00 .000 .000 . 2 . . .
1823 1.287 1 1 0 .00 .000 .000 .00 .000 .000 . . 3 . .
1824 1.092 1 1 0 .00 .000 .000 .00 .000 .000 . .4 . .
1825 .924 1 1 0 .00 .000 .000 .00 .000 .000 . 5 . . .
1826 .896 1 1 0 .00 .000 .000 .00 .000 .000 . 6 . . .
1827 .981 1 1 0 .00 .000 .000 .00 .000 .000 . 7. . .
1828 .280 1 1 0 .00 .000 .000 .00 .000 .000 . 8 . . .
1829 1.150 1 1 0 .00 .000 .000 .00 .000 .000 . . 9 . .
1830 .842 1 1 0 .00 .000 .000 .00 .000 .000 . 0 . . .
1831 .197 1 1 0 .00 .000 .000 .00 .000 .000 . 1 . . .
1832 .871 1 1 0 .00 .000 .000 .00 .000 .000 . 2 . . .
1833 .422 1 1 0 .00 .000 .000 .00 .000 .000 . 3 . . .
1834 .281 1 1 0 .00 .000 .000 .00 .000 .000 . 4 . . .
1835 .394 1 1 0 .00 .000 .000 .00 .000 .000 . 5 . . .
1836 .394 1 1 0 .00 .000 .000 .00 .000 .000 . 6 . . .
1837 .451 1 1 0 .00 .000 .000 .00 .000 .000 . 7 . . .
1838 .451 1 1 0 .00 .000 .000 .00 .000 .000 . 8 . . .
1839 .902 1 1 0 .00 .000 .000 .00 .000 .000 . 9 . . .
1840 .987 1 1 0 .00 .000 .000 .00 .000 .000 . 0. . .
1841 .818 1 1 0 .00 .000 .000 .00 .000 .000 . 1 . . .
1842 1.750 1 1 0 .00 .000 .000 .00 .000 .000 . . 2 . .
1843 1.581 1 1 0 .00 .000 .000 .00 .000 .000 . . 3 . .
1844 2.119 1 1 0 .00 .000 .000 .00 .000 .000 . . .4 .
1845 2.289 1 1 0 .00 .000 .000 .00 .000 .000 . . . 5 .
1846 2.799 1 1 0 .00 .000 .000 .00 .000 .000 . . . 6 .
1847 2.742 3 3 0 .00 .301 .174 47.56 .000 .000 . . . -------==7===--
1848 2.264 3 3 0 .00 .544 .314 64.40 .000 .000 . . -------------=====8=====-------
1849 1.669 4 4 0 .00 1.198 .599 55.92 .025 10.432 -----------------------------=========9==========------------
Series Iter St dev Coef of
Year Index Trees Eff % St err Var Skew Kurt 0 +1 +2 +3
1850 1.391 5 5 0 .00 .965 .432 53.80 .966 5.148 ------------------------=.=====0=======-------------------
1851 1.695 5 5 0 .00 1.157 .517 52.52 .793 6.302 --------------------------.-=========1========-------------
1852 1.168 5 5 0 .00 .586 .262 38.75 1.419 7.741 ---------------==.=2====--------------- .
1853 1.415 5 5 0 .00 .403 .180 42.46 4.771 14.595 . -------.--===3===---------- .
1854 1.149 6 6 2 75.21 .237 .097 36.26 4.758 12.033 . ------==4=------ . .
1855 .495 6 6 3 -16.34 .273 .111 50.76 1.128 3.488 -------=5==------- . .
1856 1.093 6 6 2 99.03 .051 .021 36.58 2.313 3.345 . --6-- . .
1857 .729 7 7 4 -21.68 .176 .067 21.56 1.915 4.473 . ----=7=---.- . .
1858 .955 7 7 3 -9.96 .314 .119 31.11 1.773 4.133 . --------==8.=-------- . .
1859 1.104 7 7 4 -47.07 .219 .083 16.59 -1.242 4.215 . ------=9=------ . .
1860 .701 7 7 4 24.61 .152 .057 23.75 3.378 7.735 . ----=0=---- . .
1861 1.012 7 7 3 81.43 .074 .028 15.54 3.044 5.724 . --=1-- . .
1862 .757 7 7 4 -37.41 .129 .049 14.47 1.012 3.213 . ----=2---- . .
1863 .635 7 7 4 -39.49 .202 .076 27.40 -1.515 2.427 . -----==3=----- . .
1864 .657 7 7 3 -10.92 .261 .099 37.64 .520 1.897 . ------==4==---.-- . .
1865 .978 8 8 2 -5.68 .423 .150 41.60 1.651 4.149 . -----------==5.==----------- . .
1866 1.255 8 8 3 -13.95 .310 .109 23.16 -.442 2.462 . ------.-==6=-------- . .
1867 .453 9 9 3 -11.44 .233 .078 48.69 .291 2.152 ------==7=------ . . .
1868 1.234 9 9 3 -11.43 .333 .111 25.62 -.060 1.568 . --------==8==--------- . .
1869 1.091 9 9 3 -9.73 .310 .103 27.49 -1.181 3.511 . --------=.9==-------- . .
1870 1.748 9 9 2 -13.06 .451 .150 24.19 .915 1.269 . ---.--------==0===------------ .
1871 1.532 9 9 2 -9.97 .292 .097 18.27 -1.084 2.021 . -.-----==1==------- .
1872 1.604 9 9 3 5.89 .550 .183 33.79 2.596 4.409 . --------.-----===2===--------------- .
1873 .774 10 10 2 80.54 .191 .060 48.05 4.380 10.432 . -----=3=--.-- . .
1874 .524 12 12 3 79.20 .194 .056 66.85 4.359 11.001 . -----=4=----- . . .
1875 .546 12 12 3 -12.02 .187 .054 32.33 .216 .782 . -----=5=----- . . .
1876 .571 12 12 2 -10.00 .211 .061 35.58 -.869 1.407 . ------=6=-----. . .
1877 .853 12 12 5 -31.55 .284 .082 30.40 -1.409 1.156 . --------=7=-.------ . .
1878 .677 12 12 2 -1.56 .209 .060 30.46 .756 2.752 . -----=8=----.- . .
1879 .855 12 12 4 33.52 .180 .052 24.18 2.567 3.778 . -----=9=-.--- . .
1880 .787 12 12 2 1.18 .216 .062 28.07 -.605 3.002 . ------=0=--.--- . .
1881 .658 12 12 3 -.89 .221 .064 32.62 1.447 2.711 . ------=1=----.- . .
1882 .313 13 13 3 70.28 .098 .027 49.60 3.819 8.640 .---=2--- . . .
1883 .273 13 13 3 -8.33 .091 .025 31.90 .352 1.414 .--=3--- . . .
1884 .240 13 13 2 -19.22 .065 .018 25.17 -.795 .749 .--4=- . . .
1885 .292 13 13 1 -15.60 .112 .031 35.39 .491 .113 .---5=--- . . .
1886 .555 13 13 3 -.03 .148 .041 27.32 -1.538 2.552 . ----6=---- . . .
1887 .615 13 13 3 2.85 .261 .072 42.43 1.349 3.138 .-------=7=-----.-- . .
1888 .401 13 13 3 -18.18 .171 .047 38.38 1.028 .855 -----=8=---- . . .
1889 .321 13 13 2 -1.21 .101 .028 31.25 .197 2.486 .---=9--- . . .
1890 .896 14 14 4 -3.91 .397 .106 41.06 1.801 1.753 .-----------==0==----------- . .
1891 .317 14 14 2 -11.28 .111 .030 33.29 .268 -.053 .---=1--- . . .
1892 .561 15 15 4 45.70 .174 .045 38.15 2.148 3.969 . -----2=----- . . .
1893 .639 16 16 3 -4.56 .191 .048 28.25 1.101 1.327 . -----=3------ . .
1894 .420 16 16 3 -.35 .154 .038 35.85 1.140 1.858 .-----4=---- . . .
1895 .707 16 16 3 64.53 .279 .070 59.35 3.896 10.553 . --------=5=---.---- . .
1896 .650 16 16 3 -6.96 .236 .059 35.10 -.040 1.108 . -------=6=----.- . .
1897 .656 17 17 3 -4.37 .364 .088 53.46 1.168 .911 -----------=7=----.------ . .
1898 .983 18 18 3 2.66 .383 .090 39.08 .761 2.176 . -----------=8.=---------- . .
1899 .263 18 18 1 61.51 .136 .032 71.50 3.368 9.311 ----=9---- . . .
Series Iter St dev Coef of
Year Index Trees Eff % St err Var Skew Kurt 0 +1 +2 +3
1900 .586 18 18 3 -.40 .271 .064 45.15 1.526 1.534 --------=0=-----.-- . .
1901 .467 18 18 4 22.15 .230 .054 51.85 2.204 3.900 ------=1=------ . . .
1902 .868 18 18 3 -7.01 .340 .080 37.59 .819 .377 . ---------=2==--------- . .
1903 .408 18 18 2 -8.21 .122 .029 28.79 .023 .092 . ----3---- . . .
1904 .692 18 18 2 -5.35 .230 .054 32.27 .513 .146 . -------=4----.-- . .
1905 .793 18 18 2 -8.68 .315 .074 37.65 .567 1.029 . ---------=5=--.------ . .
1906 .624 18 18 2 -7.70 .227 .054 35.15 -.200 .137 . -------6=-----.- . .
1907 .731 18 18 4 17.85 .261 .062 38.29 .999 3.528 . -------=7=---.---- . .
1908 .952 18 18 3 15.16 .413 .097 45.44 1.486 3.391 . -----------==8=------------ . .
1909 1.088 19 19 3 32.61 .428 .098 45.05 2.091 4.801 . ------------=.9=-------------. .
1910 .851 19 19 3 -1.20 .382 .088 43.67 1.202 1.551 .-----------=0==---------- . .
1911 1.498 19 19 3 -4.73 .580 .133 37.65 .565 .585 . -----------.----==1===---------------- .
1912 .958 19 19 3 -10.00 .300 .069 29.82 .050 -.192 . ---------=2=-------- . .
1913 1.521 19 19 3 -10.09 .557 .128 34.96 -.146 -.240 . ----------.-----==3==---------------- .
1914 .531 19 19 3 -12.16 .221 .051 39.30 -.011 .311 .------=4=------. . .
1915 1.512 19 19 5 -11.21 .486 .111 29.23 .935 .990 . --------.-----==5=-------------- .
1916 1.372 19 19 4 -1.81 .402 .092 28.67 .776 1.417 . -------.---=6==----------- .
1917 1.376 19 19 2 -10.30 .365 .084 25.37 -.313 .438 . ------.---==7=---------- .
1918 1.267 20 20 3 -9.98 .419 .094 31.54 -.112 .103 . ----------.-==8=------------ .
1919 1.089 20 20 3 -7.94 .325 .073 28.64 .183 .802 . ---------=9=--------- . .
1920 1.131 20 20 2 4.49 .330 .074 29.04 .944 1.556 . ---------==0=--------- . .
1921 1.612 20 20 4 10.18 .391 .087 25.17 1.478 2.840 . ---.-------=1==----------- .
1922 2.207 20 20 2 -11.59 .618 .138 26.51 -.052 -.356 . -.----------------==2==-----------
1923 2.559 20 20 3 -8.37 .675 .151 25.30 .257 -.580 . . -------------------==3===-----
1924 2.592 20 20 2 -6.99 .772 .173 28.76 .315 -.576 . ----------------------===4===----
1925 1.877 20 20 3 -10.29 .561 .125 28.38 .398 -.420 . ----.-----------==5==---------------.
1926 1.724 20 20 4 1.49 .405 .091 23.67 -.094 1.771 . --.---------=6==----------- .
1927 1.857 20 20 1 -8.09 .503 .113 26.12 -.239 .332 . ---.----------==7==-------------- .
1928 1.573 20 20 3 -8.76 .434 .097 26.42 .096 -.186 . -----.------==8=------------- .
1929 1.161 20 20 3 -5.89 .349 .078 29.15 .562 .046 . ----------=9=---------- . .
1930 1.008 21 21 3 -7.53 .413 .090 39.23 .703 .069 . ------------==0=------------ . .
1931 1.305 21 21 4 -13.60 .617 .135 43.92 .596 -.204 .---------------.-==1===----------------- .
1932 .971 21 21 4 -2.44 .440 .096 43.42 1.307 1.025 .------------==2.=------------ . .
1933 1.574 21 21 4 -17.64 .583 .127 33.74 .761 -.295 . ----------.------==3==---------------- .
1934 1.151 21 21 3 -6.28 .328 .071 27.23 .925 .804 . ----------=4=--------- . .
1935 1.212 21 21 3 -6.50 .357 .078 28.53 .086 .769 . ---------.-=5=---------- . .
1936 1.081 22 22 2 3.90 .396 .085 36.38 1.154 1.508 . -----------=.6=----------- . .
1937 1.624 22 22 3 45.33 .435 .093 34.22 2.445 5.941 . ----.-------=7==------------ .
1938 2.118 23 23 4 -2.75 .770 .161 34.34 1.030 .753 . -------.--------------==8===------------
1939 1.606 23 23 3 -9.44 .520 .108 30.65 .863 .022 . -------.------==9==--------------- .
1940 1.074 23 23 3 -9.70 .433 .090 38.56 -.107 -.521 . ------------=.0=-------------. .
1941 .649 24 24 2 -6.42 .251 .051 37.50 -.180 -.531 . -------=1=----.-- . .
1942 1.239 24 24 3 -7.05 .469 .096 36.43 .365 .236 . ------------.-=2==------------- .
1943 1.183 24 24 4 35.28 .311 .064 30.47 1.577 2.238 . ---------=3=--------- . .
1944 1.042 24 24 3 -7.44 .302 .062 28.23 -.465 .757 . ---------=4=--------- . .
1945 1.290 24 24 3 4.92 .397 .081 31.16 .735 1.836 . ---------.--=5=------------ .
1946 .802 24 24 2 -3.21 .219 .045 26.71 .499 .919 . -------6=--.--- . .
1947 .419 24 24 2 8.69 .148 .030 35.81 1.012 1.459 .-----7=---- . . .
1948 .611 25 25 2 -7.01 .207 .041 32.68 -.010 -.418 . ------8=------ . .
1949 .408 25 25 2 10.06 .165 .033 40.88 1.501 1.793 .----=9=---- . . .
Series Iter St dev Coef of
Year Index Trees Eff % St err Var Skew Kurt 0 +1 +2 +3
1950 .545 25 25 3 -1.03 .269 .054 48.13 1.243 .987 -------=0=------.- . .
1951 .708 26 26 2 2.46 .286 .056 40.27 1.025 1.528 . --------=1=---.---- . .
1952 1.244 26 26 4 -10.71 .458 .090 34.64 .744 -.206 . -----------.-=2==------------- .
1953 1.481 26 26 3 19.10 .523 .103 37.47 1.598 2.282 . ----------.-----=3==--------------- .
1954 1.334 26 26 3 -1.63 .490 .096 36.01 .939 .959 . -----------.--==4=--------------- .
1955 1.458 26 26 2 -7.41 .330 .065 21.79 .344 .006 . ----.-----=5=--------- .
1956 1.865 26 26 4 -14.01 .514 .101 25.47 .934 -.134 . ---.-----------=6==--------------- .
1957 1.345 26 26 3 21.31 .422 .083 34.08 1.735 2.814 . --------.---=7=------------- .
1958 1.237 26 26 2 47.77 .312 .061 32.89 2.698 6.690 . -------.-=8=--------- . .
1959 .990 26 26 3 27.86 .380 .075 45.01 .228 3.481 . -----------=9.=----------- . .
1960 .788 26 26 4 43.02 .207 .041 32.18 2.166 3.094 . ------=0=--.--- . .
1961 1.022 26 26 3 5.37 .275 .054 27.17 1.497 1.581 . --------=1=-------- . .
1962 .770 26 26 3 3.22 .220 .043 28.79 .557 1.372 . ------=2=--.--- . .
1963 1.186 26 26 2 -7.89 .375 .074 30.28 .266 .711 . -----------=3==---------- . .
1964 1.394 26 26 3 13.21 .434 .085 32.41 1.539 2.144 . --------.---==4=------------- .
1965 1.460 26 26 3 -9.08 .325 .064 21.05 .672 .499 . ----.-----=5=--------- .
1966 .718 26 26 3 14.05 .262 .051 40.84 -1.612 2.005 . -------=6=---.--- . .
1967 1.010 26 26 2 29.79 .195 .038 23.11 -.094 2.529 . ------=7------ . .
1968 .520 26 26 3 30.89 .102 .020 24.18 -.924 2.654 . ---8--- . . .
1969 .794 26 26 2 -8.50 .139 .027 16.76 .232 .083 . ----9=--.- . .
1970 .560 26 26 3 -3.39 .202 .040 35.57 -.163 .700 . ------0=------. . .
1971 .455 26 26 3 4.16 .187 .037 42.55 -.892 1.542 .-----=1------ . . .
1972 .553 26 26 3 16.84 .177 .035 34.25 1.553 3.406 . -----2=----- . . .
1973 .294 26 26 1 59.81 .139 .027 68.70 2.411 7.662 ----3=---- . . .
1974 .574 26 26 3 -1.84 .152 .030 25.82 .860 .887 . ----=4----- . . .
1975 .232 26 26 3 -3.59 .198 .039 82.33 .685 .632 ------5=------ . . .
1976 .706 26 26 3 13.21 .248 .049 36.76 1.799 2.705 . -------=6=---.--- . .
1977 .681 26 26 3 47.51 .161 .032 31.47 2.298 7.928 . -----7=----- . .
1978 .732 26 26 2 -5.27 .217 .042 28.68 .559 .382 . -------8=---.-- . .
1979 .836 26 26 3 -3.96 .311 .061 36.10 .769 .659 . ---------=9=-.------- . .
1980 .457 26 26 3 10.93 .165 .032 38.14 -.015 2.214 . ----=0----- . . .
1981 .792 26 26 3 4.67 .241 .047 30.62 1.207 1.855 . -------=1=--.---- . .
1982 .864 26 26 3 -4.54 .217 .043 24.46 .518 .616 . -------2=-.---- . .
1983 1.077 26 26 3 -4.66 .381 .075 34.49 .231 .405 . -----------=3=----------- . .
1984 1.084 26 26 3 2.84 .325 .064 30.00 1.114 1.374 . ----------=4=--------- . .
1985 .706 26 26 3 -5.92 .238 .047 32.65 .336 .397 . -------=5=---.-- . .
1986 .281 26 26 1 -8.90 .228 .045 77.58 .058 -.607 ------=6=------ . . .
1987 .780 26 26 3 -3.91 .220 .043 27.43 .680 .674 . ------=7=--.--- . .
1988 .793 26 26 2 -.71 .241 .047 30.17 .314 .993 . -------=8=--.---- . .
1989 1.004 26 26 2 -8.61 .294 .058 28.14 -.048 -.450 . ---------=9--------- . .
1990 .944 26 26 3 -8.60 .270 .053 27.36 .219 -.535 . --------=0-------- . .
1991 1.263 26 26 3 -11.85 .346 .068 25.82 .214 -.025 . -------.--=1=----------. .
1992 .830 26 26 4 -4.45 .307 .060 35.52 .846 .705 . ---------=2=-.------- . .
1993 1.401 26 26 3 7.88 .420 .082 30.76 .751 1.804 . --------.----=3=------------ .
1994 1.222 26 26 3 3.07 .405 .079 32.86 1.008 1.381 . ----------.-=4=------------ .
1995 .576 26 26 3 -9.89 .379 .074 62.80 -.082 -.228 -----------=5=-----.----- . .
1996 1.061 26 26 3 -8.48 .214 .042 19.30 .320 .277 . ------6=------ . .
1997 .283 26 26 2 -8.93 .226 .044 76.55 .030 -.518 ------=7=------ . . .
1998 1.037 26 26 2 -3.66 .283 .056 26.88 -.276 .426 . --------=8=-------- . .
1999 .673 26 26 2 -2.88 .246 .048 36.02 .193 .926 . -------=9=----.-- . .
2000 .622 26 26 3 8.69 .170 .033 28.34 1.172 2.754 . -----0=-----. . .
2001 .475 26 26 2 -7.14 .132 .026 26.86 -.393 -.018 . ----1=--- . . .
2002 .685 26 26 2 15.22 .175 .034 27.31 1.505 3.535 . -----2=----- . .
2003 1.035 26 26 3 -7.38 .277 .054 25.77 .227 .222 . --------=3=-------- . .
2004 1.090 26 26 2 16.78 .244 .048 24.16 1.438 3.269 . -------=4=------- . .
2005 .791 26 26 3 -12.07 .208 .041 24.75 .534 -.290 . ------=5=--.--- . .
2006 1.188 26 26 2 -6.70 .266 .052 21.56 .342 .590 . ------.-=6-------- . .
2007 1.423 26 26 3 -10.52 .365 .072 24.45 -.335 -.519 . -----.----=7=----------- .
2008 1.772 26 26 3 -4.20 .428 .084 23.44 .867 .632 . --.----------=8=------------- .
2009 .971 26 26 3 -3.48 .269 .053 27.43 -.533 .943 . --------=9=-------- . .
2010 .877 26 26 3 -6.73 .218 .043 24.15 -.385 .299 . ------=0-.----- . .
2011 1.126 26 26 3 1.56 .281 .055 24.73 1.052 1.058 . --------=1--------- . .
2012 1.555 26 26 3 -7.89 .325 .064 20.03 .831 -.066 . --.------=2=---------- .
2013 1.368 26 26 3 -5.31 .265 .052 18.79 .647 .202 . ---.----3=-------- . .
2014 1.215 26 26 3 -8.92 .260 .051 20.44 .388 -.410 . -----.-=4=------- . .
2015 1.212 26 26 2 87.03 .247 .049 51.06 5.554 21.859 . -----.-=5=------- . .
2016 1.023 26 26 4 5.11 .288 .056 27.90 1.258 .948 . --------=6=-------- . .
2017 .952 26 26 4 5.23 .290 .057 30.46 1.358 1.811 . ---------=7=-------- . .
2018 1.145 26 26 3 -2.52 .317 .062 27.05 .933 .709 . ---------=8=--------- . .
2019 .772 26 26 3 -2.81 .285 .056 35.89 .933 .807 . --------=9=--.----- . .
2020 .534 26 26 3 .75 .182 .036 33.29 1.223 .980 . -----=0=----- . . .
2021 .955 26 26 4 .18 .442 .087 44.82 1.264 .923 .------------==1=------------- . .
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 = .316 Avge std error of index means = .08004 Unadjusted mean = .978
Correlation between indices and their standard deviations = .719
Improved indices using robust estimation = 59 Average gain in efficiency over Gaussian estimates = 25.590%
Unimproved indices using robust estimation = 109 Average loss in efficiency over Gaussian estimates = -8.733%
Average error variance of arithmetic means reduced by robust estimation 3.429%
Average error variance reduced by robust estimation in common interval 2.436%
Time span 1811 2021 211 years Mean .978 Median .924 Range .197 2.799 Mean sens .347
Variance .252 Std dev .502 Coef of variation .513 Skewness 1.055 Kurtosis 1.478
Autocorrelations, lags 1 to 10: .720 .640 .485 .396 .326 .228 .172 .076 .066 .046
Approx 95 pct confidence limits: .138 .197 .233 .251 .263 .270 .274 .276 .276 .277
Partial autocorrelations: .720 .251 -.091 -.009 .040 -.085 -.013 -.087 .065 .045
Ljung-Box Portmanteau Q 326.3168 DF 25 Prob .0000
Trend in variance (%) = -.1033
Residual Chronology from AR Modeling of detrended series 11:41 Tue 08 Oct 2024 Page 10
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PUR Residual chronology without rewhitening
Computed with BIWEIGHT ROBUST MEAN
Title:
All 26 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
1813 .923 1 1 0 .00 .000 .000 .00 .000 .000 . 3 . . .
1814 .593 1 1 0 .00 .000 .000 .00 .000 .000 . 4 . . .
1815 .899 1 1 0 .00 .000 .000 .00 .000 .000 . 5 . . .
1816 .803 1 1 0 .00 .000 .000 .00 .000 .000 . 6 . . .
1817 .677 1 1 0 .00 .000 .000 .00 .000 .000 . 7 . . .
1818 .884 1 1 0 .00 .000 .000 .00 .000 .000 . 8 . . .
1819 .822 1 1 0 .00 .000 .000 .00 .000 .000 . 9 . . .
1820 .825 1 1 0 .00 .000 .000 .00 .000 .000 . 0 . . .
1821 .778 1 1 0 .00 .000 .000 .00 .000 .000 . 1 . . .
1822 1.419 1 1 0 .00 .000 .000 .00 .000 .000 . . 2 . .
1823 1.596 1 1 0 .00 .000 .000 .00 .000 .000 . . 3 . .
1824 .985 1 1 0 .00 .000 .000 .00 .000 .000 . 4. . .
1825 .798 1 1 0 .00 .000 .000 .00 .000 .000 . 5 . . .
1826 .914 1 1 0 .00 .000 .000 .00 .000 .000 . 6 . . .
1827 1.058 1 1 0 .00 .000 .000 .00 .000 .000 . 7 . .
1828 .318 1 1 0 .00 .000 .000 .00 .000 .000 . 8 . . .
1829 1.549 1 1 0 .00 .000 .000 .00 .000 .000 . . 9 . .
1830 .950 1 1 0 .00 .000 .000 .00 .000 .000 . 0. . .
1831 .243 1 1 0 .00 .000 .000 .00 .000 .000 . 1 . . .
1832 1.352 1 1 0 .00 .000 .000 .00 .000 .000 . . 2 . .
1833 .705 1 1 0 .00 .000 .000 .00 .000 .000 . 3 . . .
1834 .632 1 1 0 .00 .000 .000 .00 .000 .000 . 4 . . .
1835 .940 1 1 0 .00 .000 .000 .00 .000 .000 . 5. . .
1836 .916 1 1 0 .00 .000 .000 .00 .000 .000 . 6 . . .
1837 .942 1 1 0 .00 .000 .000 .00 .000 .000 . 7. . .
1838 .912 1 1 0 .00 .000 .000 .00 .000 .000 . 8 . . .
1839 1.348 1 1 0 .00 .000 .000 .00 .000 .000 . . 9 . .
1840 1.186 1 1 0 .00 .000 .000 .00 .000 .000 . . 0 . .
1841 .851 1 1 0 .00 .000 .000 .00 .000 .000 . 1 . . .
1842 1.853 1 1 0 .00 .000 .000 .00 .000 .000 . . 2 . .
1843 1.219 1 1 0 .00 .000 .000 .00 .000 .000 . . 3 . .
1844 1.602 1 1 0 .00 .000 .000 .00 .000 .000 . . 4 . .
1845 1.523 1 1 0 .00 .000 .000 .00 .000 .000 . . 5 . .
1846 1.798 1 1 0 .00 .000 .000 .00 .000 .000 . . 6 . .
1847 1.617 1 1 0 .00 .000 .000 .00 .000 .000 . . 7 . .
1848 .726 1 1 0 .00 .000 .000 .00 .000 .000 . 8 . . .
1849 1.147 3 3 0 .00 .129 .074 12.24 .000 .000 . ---=9=--- . .
Series Iter St dev Coef of
Year Index Trees Eff % St err Var Skew Kurt 0 +1 +2 +3
1850 1.510 3 3 0 .00 .084 .048 14.58 .000 .000 . . --=0-- . .
1851 1.388 4 4 0 .00 .257 .129 16.29 .789 14.534 . ---.---==1==------ . .
1852 .731 5 5 0 .00 .196 .088 52.46 -1.462 4.873 . -----=2==--.- . .
1853 1.218 5 5 0 .00 .172 .077 23.32 3.339 13.004 . ---.-=3=---- . .
1854 .928 5 5 0 .00 .167 .075 16.65 2.754 10.394 . ----=4==---- . .
1855 .209 5 5 0 .00 .055 .025 239.51 -3.774 14.196 .-=5-- . . .
1856 1.580 6 6 4 -25.42 .381 .155 21.36 1.633 3.659 . ---.-----===6==---------- .
1857 .658 6 6 3 -16.98 .304 .124 43.14 -1.307 5.943 --------==7==---.---- . .
1858 1.006 6 6 3 -12.29 .230 .094 21.57 1.025 3.422 . ------==8=------ . .
1859 1.162 7 7 3 -18.43 .172 .065 13.58 .812 1.847 . ----=9=----- . .
1860 .700 7 7 3 -8.29 .268 .101 36.72 .066 2.470 . -------==0=---.--- . .
1861 1.222 7 7 4 -29.56 .174 .066 12.51 .701 1.295 . ---.-=1=----- . .
1862 .768 7 7 2 -1.51 .110 .041 14.05 2.915 6.601 . ---=2---. . .
1863 .727 7 7 3 -9.31 .131 .050 17.28 .183 2.089 . ---=3=---. . .
1864 .918 7 7 3 -13.83 .231 .087 23.59 -.503 1.182 . ------=4==------ . .
1865 1.152 7 7 4 48.56 .245 .093 27.77 4.242 9.819 . ------==5=------- . .
1866 1.353 7 7 3 -16.84 .227 .086 15.29 2.204 4.984 . --.---=6==----- . .
1867 .310 8 8 4 21.77 .140 .049 50.11 .319 5.941 ----7=---- . . .
1868 1.458 8 8 3 -29.19 .294 .104 17.61 .581 3.345 . ---.----==8=-------- .
1869 1.137 9 9 3 36.35 .202 .067 22.95 -3.936 9.067 . ------=9=----- . .
1870 1.631 9 9 3 -7.97 .377 .126 21.91 2.054 3.172 . --.-------==0==---------- .
1871 1.139 9 9 2 -5.89 .271 .090 23.21 -1.312 2.322 . -------==1=------- . .
1872 1.020 9 9 3 81.05 .264 .088 49.57 4.359 9.433 . -------==2=------- . .
1873 .361 9 9 2 78.75 .161 .054 74.73 4.202 9.754 ----=3=---- . . .
1874 .548 9 9 3 11.21 .189 .063 35.84 3.342 7.452 . -----=4=----- . . .
1875 .840 10 10 3 89.14 .107 .034 43.33 -4.828 11.803 . --=5--- . .
1876 .922 12 12 2 42.05 .188 .054 27.83 -3.349 7.941 . -----=6=----- . .
1877 1.144 12 12 3 1.13 .161 .047 14.29 -1.591 3.131 . ----=7=---- . .
1878 .888 12 12 3 -20.30 .178 .051 18.22 .328 1.616 . -----=8=---- . .
1879 1.119 12 12 3 -1.63 .153 .044 13.58 -.405 2.756 . ----9=---- . .
1880 .911 12 12 3 9.54 .148 .043 17.28 -1.492 3.945 . ----=0=---- . .
1881 .808 12 12 3 -16.68 .184 .053 20.94 .557 1.731 . -----1=--.-- . .
1882 .551 12 12 3 37.39 .181 .052 39.21 3.194 6.828 . ----=2=----- . . .
1883 .703 12 12 4 1.04 .187 .054 27.64 -1.818 2.597 . -----=3=---.- . .
1884 .779 12 12 2 -2.42 .060 .017 7.63 -.900 2.595 . --4-- . . .
1885 .869 13 13 3 -36.52 .103 .028 10.16 -.464 .579 . ---5=-.- . .
1886 1.093 13 13 3 -13.66 .118 .033 10.07 .681 .599 . ---=6=--- . .
1887 1.016 13 13 3 46.89 .126 .035 16.53 3.104 7.234 . ---=7---- . .
1888 .724 13 13 3 -8.82 .127 .035 16.86 .143 1.426 . ----8=---. . .
1889 .719 13 13 3 -5.99 .131 .036 17.75 -.487 1.148 . ---=9=---. . .
1890 1.436 13 13 4 -11.84 .317 .088 20.40 1.700 1.586 . ----.----=0==--------- .
1891 .561 13 13 2 35.26 .124 .035 28.83 -1.609 3.299 . ----1=--- . . .
1892 .942 14 14 2 9.86 .169 .045 19.08 -1.206 3.612 . -----=2----- . .
1893 1.041 14 14 3 20.57 .130 .035 13.79 2.045 2.977 . ----3=--- . .
1894 .726 15 15 3 6.78 .108 .028 15.56 -1.357 2.744 . ---4=---. . .
1895 1.025 16 16 3 93.74 .105 .026 36.02 5.039 14.633 . --=5--- . .
1896 .965 16 16 3 62.42 .143 .036 25.49 -3.149 8.139 . ----=6=---- . .
1897 .856 16 16 3 -6.16 .194 .049 21.93 .345 1.478 . -----=7=-.--- . .
1898 1.205 16 16 4 16.55 .234 .059 20.54 2.051 2.827 . -----.-=8=------ . .
1899 .374 17 17 3 -4.97 .235 .057 60.84 .275 1.534 -------9=------- . . .
Series Iter St dev Coef of
Year Index Trees Eff % St err Var Skew Kurt 0 +1 +2 +3
1900 .920 18 18 2 25.17 .151 .036 18.67 2.463 5.991 . -----0=---- . .
1901 .880 18 18 3 11.31 .136 .032 16.01 1.487 1.920 . ----=1-.-- . .
1902 1.214 18 18 3 -4.65 .184 .043 14.74 .764 1.066 . ---.-=2=----- . .
1903 .617 18 18 2 -8.26 .183 .043 28.62 -.326 .002 . -----3=-----. . .
1904 .996 18 18 3 2.45 .098 .023 9.94 1.413 2.186 . ---4=--- . .
1905 1.107 18 18 4 -25.27 .214 .050 17.10 .453 1.011 . ------=5=------ . .
1906 .802 18 18 2 -7.26 .150 .035 18.04 -.316 -.292 . ----6=--.- . .
1907 .968 18 18 3 10.63 .222 .052 23.88 1.637 3.051 . ------=7=------ . .
1908 1.188 18 18 3 8.48 .273 .064 23.69 1.825 2.909 . -------==8=------- . .
1909 1.221 18 18 3 2.81 .236 .056 19.42 1.650 2.005 . -----.-=9=------- . .
1910 .794 19 19 3 -5.65 .169 .039 20.72 .163 .508 . -----0=--.-- . .
1911 1.517 19 19 2 -9.02 .321 .074 20.27 .045 -.484 . --.------=1=--------- .
1912 .779 19 19 3 21.97 .165 .038 24.39 -1.051 3.684 . ----=2=--.- . .
1913 1.401 19 19 3 -9.43 .299 .068 20.40 -.247 -.186 . ----.----=3=--------. .
1914 .304 19 19 2 1.01 .161 .037 52.15 1.116 1.714 -----4=---- . . .
1915 1.610 19 19 4 19.88 .285 .065 19.30 1.729 2.939 . --------=5=-------- .
1916 1.244 19 19 3 -6.43 .293 .067 22.71 .827 .641 . ------.-=6=--------- . .
1917 1.007 19 19 3 -2.22 .211 .048 20.59 1.032 1.218 . ------=7------ . .
1918 1.020 19 19 3 -2.14 .211 .048 20.24 1.380 1.253 . ------=8=------ . .
1919 .880 19 19 3 -10.67 .140 .032 15.09 .482 .494 . ----=9-.-- . .
1920 1.022 20 20 3 40.09 .132 .029 16.39 .750 2.481 . ---=0---- . .
1921 1.525 20 20 3 -.63 .313 .070 20.25 1.244 1.527 . --.------=1=--------- .
1922 1.820 20 20 2 2.29 .485 .109 26.74 1.417 2.034 . ---.----------==2=-------------- .
1923 1.798 20 20 3 -11.62 .525 .117 27.55 .278 -.095 . -----.---------==3==--------------- .
1924 1.460 20 20 4 -12.78 .567 .127 35.78 .706 .623 . -----------.----==4==---------------- .
1925 .698 20 20 2 .59 .248 .055 35.70 -.100 1.653 . -------=5=---.--- . .
1926 .883 20 20 3 -8.70 .345 .077 37.46 .183 -.263 . ---------==6=---------- . .
1927 1.297 20 20 3 -2.10 .360 .081 27.75 -.808 1.359 . -------.--=7==---------- .
1928 .965 20 20 2 -7.12 .321 .072 32.06 .334 .261 . ---------=8=--------- . .
1929 .665 20 20 2 -1.98 .236 .053 34.91 .469 1.256 . ------=9=----.-- . .
1930 .773 20 20 3 -6.78 .268 .060 33.16 .896 .566 . --------=0=--.---- . .
1931 1.249 21 21 3 -8.74 .362 .079 27.56 .673 .482 . --------.-=1==----------. .
1932 .836 21 21 2 -5.77 .152 .033 17.68 -.193 .440 . ----=2--.-- . .
1933 1.496 21 21 2 -7.46 .246 .054 15.84 .113 .088 . -------3=-------. .
1934 .861 21 21 3 -9.06 .223 .049 24.89 -.413 .036 . -------4=-.---- . .
1935 .934 21 21 4 -2.08 .232 .051 23.63 1.020 .924 . -------5=------- . .
1936 .930 21 21 3 -6.81 .328 .072 33.87 .784 .335 . ---------=6==--------- . .
1937 1.561 22 22 3 60.00 .236 .050 23.17 2.508 8.475 . .-------7=------- .
1938 1.777 22 22 3 9.59 .467 .099 26.91 1.442 1.611 . ---.---------==8==------------- .
1939 .845 23 23 3 -2.33 .328 .068 38.47 -.217 1.046 . ---------=9=-.-------- . .
1940 .503 23 23 4 46.00 .192 .040 54.54 -1.635 6.418 .------=0------ . . .
1941 .461 23 23 3 4.97 .174 .036 38.93 -.339 1.845 .-----=1----- . . .
1942 1.382 23 23 3 3.36 .314 .066 22.96 .979 1.963 . ----.----=2=--------- .
1943 1.185 24 24 3 -4.86 .313 .064 25.44 .661 .836 . ---------=3=--------- . .
1944 .824 24 24 3 -8.10 .235 .048 27.33 .203 .313 . -------=4--.---- . .
1945 1.200 24 24 3 11.39 .270 .055 23.50 .897 2.114 . ------.-=5=------- . .
1946 .661 24 24 2 -3.60 .139 .028 20.57 .284 .836 . ----6=----. . .
1947 .477 24 24 1 23.90 .179 .037 44.35 -1.511 4.384 .------7=----- . . .
1948 .916 24 24 2 -1.45 .129 .026 13.97 .185 1.085 . ----8=--- . .
1949 .735 25 25 2 -4.59 .169 .034 22.41 .348 .653 . -----9=---.- . .
Series Iter St dev Coef of
Year Index Trees Eff % St err Var Skew Kurt 0 +1 +2 +3
1950 .899 25 25 3 20.98 .164 .033 20.09 1.572 3.417 . ----=0-.--- . .
1951 1.029 25 25 3 4.32 .193 .039 19.04 1.031 1.825 . -----=1=----- . .
1952 1.454 26 26 4 -20.91 .337 .066 20.73 .813 -.040 . ----.-----=2=---------- .
1953 1.437 26 26 4 5.17 .416 .082 28.97 1.405 1.510 . -------.----=3==------------ .
1954 1.010 26 26 3 -4.91 .267 .052 25.72 .363 .456 . --------=4=------- . .
1955 1.170 26 26 3 -4.70 .198 .039 16.65 -.655 .469 . ----.-5=------ . .
1956 1.578 26 26 3 -6.24 .356 .070 21.73 .524 .462 . ---.-------=6=---------- .
1957 .825 26 26 3 6.06 .380 .075 46.10 1.004 1.557 .-----------=7=-.--------- . .
1958 .908 26 26 4 43.40 .203 .040 29.05 1.346 5.472 . -----=8=------ . .
1959 .864 26 26 3 69.58 .230 .045 54.36 -2.611 5.891 . -------9=-.----- . .
1960 .744 26 26 1 64.85 .160 .031 34.41 3.650 13.005 . -----0=---.- . .
1961 1.112 26 26 3 -1.63 .185 .036 16.51 .188 .981 . ------1=----- . .
1962 .791 26 26 3 -6.32 .216 .042 26.73 -.708 .446 . ------=2=--.--- . .
1963 1.316 26 26 2 19.55 .289 .057 24.88 -1.138 2.900 . -----.---=3--------- . .
1964 1.318 26 26 3 55.07 .243 .048 26.24 2.919 7.760 . ---.---=4------- . .
1965 1.229 26 26 2 8.12 .188 .037 15.90 1.029 2.520 . ---.--5=----- . .
1966 .388 26 26 2 -6.25 .234 .046 60.16 -.943 .411 -------=6------- . . .
1967 1.047 26 26 3 23.69 .210 .041 22.41 .863 1.885 . ------7=------ . .
1968 .575 26 26 2 -2.29 .160 .031 27.33 .917 .748 . ----=8----- . . .
1969 1.039 26 26 3 -9.65 .109 .021 10.05 -.368 -.375 . ---9---- . .
1970 .770 26 26 3 7.78 .164 .032 22.37 -.985 2.469 . ----=0---.- . .
1971 .706 26 26 3 26.19 .136 .027 22.43 -.022 3.775 . ----=1----. . .
1972 .934 26 26 3 -4.48 .163 .032 16.94 .616 .623 . -----2=----- . .
1973 .655 26 26 2 3.24 .174 .034 27.07 -.094 1.532 . -----=3=----- . .
1974 1.007 26 26 3 -.97 .140 .027 13.75 .977 1.134 . ----=4---- . .
1975 .590 26 26 1 7.98 .175 .034 30.70 1.263 2.768 . -----=5------. . .
1976 1.150 26 26 3 22.43 .227 .045 21.71 1.073 1.432 . ------=6=------ . .
1977 1.007 26 26 3 -9.88 .152 .030 14.42 .007 -.341 . ----=7---- . .
1978 .933 26 26 3 -7.33 .160 .031 16.37 .832 .521 . -----8=----- . .
1979 1.035 26 26 3 .41 .208 .041 20.02 .382 1.122 . ------=9=------ . .
1980 .605 26 26 3 5.68 .240 .047 41.67 -.599 1.671 .-------=0=-----.- . .
1981 1.109 26 26 3 7.86 .198 .039 18.41 1.491 2.466 . ------1=------ . .
1982 1.077 26 26 3 1.96 .144 .028 13.39 .438 1.248 . ----=2---- . .
1983 1.174 26 26 2 7.21 .276 .054 24.22 .948 2.328 . --------=3=-------- . .
1984 1.089 26 26 3 -.93 .244 .048 22.40 -.321 1.101 . -------=4=------- . .
1985 .671 26 26 3 -.11 .144 .028 21.40 -.076 1.073 . ----5=----. . .
1986 .428 26 26 2 -2.73 .165 .032 38.30 -.616 .733 .-----6=----- . . .
1987 1.201 26 26 3 -.13 .204 .040 16.83 1.188 1.038 . ----.-=7------ . .
1988 1.043 26 26 3 .61 .176 .035 16.80 1.033 1.446 . -----8=----- . .
1989 1.140 26 26 2 -4.46 .216 .042 18.52 -.089 .413 . ------=9------- . .
1990 .976 26 26 3 -4.83 .173 .034 17.15 .617 .740 . -----0=----- . .
1991 1.290 26 26 3 -3.27 .198 .039 15.08 .290 .785 . --.---1=----- . .
1992 .722 26 26 3 -2.36 .197 .039 26.80 .370 .906 . -----=2=---.- . .
1993 1.434 26 26 3 6.40 .288 .056 20.50 .928 1.794 . ---.-----3=--------- .
1994 1.079 26 26 3 5.45 .254 .050 24.10 .270 1.572 . -------=4=------- . .
1995 .351 26 26 2 -.65 .402 .079 114.64 -.076 1.047 ------------=5=---------.-- . .
1996 1.247 26 26 2 -11.11 .173 .034 13.14 .000 -.369 . --.--6=----- . .
1997 .364 26 26 3 -6.23 .218 .043 60.28 -.757 .758 -------7=------ . . .
1998 1.385 26 26 3 -6.60 .269 .053 18.82 -.090 .204 . ---.----=8=------- . .
1999 .782 26 26 2 24.73 .212 .042 30.28 1.895 4.464 . ------=9=--.--- . .
2000 .790 26 26 1 24.62 .163 .032 23.88 -.551 3.343 . -----0=--.- . .
2001 .739 26 26 3 2.12 .141 .028 19.63 -1.189 1.301 . ----1=---- . .
2002 1.028 26 26 2 10.80 .166 .033 16.94 1.192 2.851 . ----=2----- . .
2003 1.283 26 26 3 -6.42 .210 .041 15.85 .413 .677 . ---.--=3=------ . .
2004 1.147 26 26 2 -7.37 .208 .041 17.44 .675 .315 . ------=4=------ . .
2005 .728 26 26 3 -8.91 .150 .029 19.59 .667 .021 . -----5=---- . .
2006 1.275 26 26 3 -8.12 .187 .037 14.06 .682 .119 . --.--=6------ . .
2007 1.375 26 26 3 -6.55 .284 .056 20.02 -.110 -.123 . ----.----7=---------. .
2008 1.535 26 26 3 -1.54 .324 .064 20.80 1.033 .901 . --.------=8=--------- .
2009 .508 26 26 2 -4.33 .227 .045 43.89 -.041 .407 -------=9-------. . .
2010 .748 26 26 2 -.05 .200 .039 26.67 .209 1.065 . ------0=---.-- . .
2011 1.211 26 26 3 18.53 .202 .040 18.04 1.616 2.048 . ----.-=1=----- . .
2012 1.495 26 26 2 18.66 .197 .039 14.42 1.763 2.864 . .------2=------ . .
2013 1.075 26 26 2 2.09 .198 .039 18.64 -.430 1.519 . ------=3------ . .
2014 .925 26 26 2 -2.49 .183 .036 19.53 .092 .784 . ------4=----- . .
2015 1.044 26 26 2 96.49 .113 .022 51.74 6.417 26.766 . ---5=--- . .
2016 .891 26 26 3 45.97 .251 .049 39.81 -1.433 5.521 . -------=6=------- . .
2017 .857 26 26 2 10.95 .224 .044 27.59 .069 2.072 . -------7=-.---- . .
2018 1.164 26 26 3 -8.74 .196 .038 16.19 -.534 -.035 . ----.-8=----- . .
2019 .708 26 26 3 -1.54 .196 .038 27.35 .648 .951 . -----=9----.- . .
2020 .622 26 26 2 -4.57 .144 .028 22.76 -.495 .528 . ----0=---- . . .
2021 1.245 26 26 3 -1.18 .344 .067 27.23 .830 .877 . --------.-=1=---------- . .
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
.002 should be added to each index to adjust chronology mean to 1.0
------------------------------------------------------------------------------------------------------------------------------------
Avge std dev of index means = .215 Avge std error of index means = .05198 Unadjusted mean = .998
Correlation between indices and their standard deviations = .517
Improved indices using robust estimation = 73 Average gain in efficiency over Gaussian estimates = 23.766%
Unimproved indices using robust estimation = 93 Average loss in efficiency over Gaussian estimates = -7.772%
Average error variance of arithmetic means reduced by robust estimation 7.578%
Average error variance reduced by robust estimation in common interval 4.823%
Time span 1813 2021 209 years Mean .998 Median .965 Range .209 1.853 Mean sens .385
Variance .113 Std dev .336 Coef of variation .336 Skewness .212 Kurtosis -.088
Autocorrelations, lags 1 to 10: .034 .082 .028 .027 .093 .007 .069 -.104 -.010 .048
Approx 95 pct confidence limits: .138 .139 .139 .140 .140 .141 .141 .141 .143 .143
Partial autocorrelations: .034 .081 .023 .019 .088 -.002 .055 -.114 -.017 .056
Ljung-Box Portmanteau Q 19.7067 DF 23 Prob .3400
Trend in variance (%) = -.0263
No rewhitening needed for Residual chronology
ARSTAN CHRONOLOGY
PUR ARS chronology is Residual chronology with pooled autoregression added
Drift = .2774
Autoregressive coefficients: .5089 .2137
Starting values for adding autoregression: 1.6137 1.0021
Time span 1811 2021 211 years Mean 1.001 Median .949 Range .217 2.722 Mean sens .332
Variance .245 Std dev .495 Coef of variation .495 Skewness 1.022 Kurtosis 1.098
Autocorrelations, lags 1 to 10: .711 .635 .506 .422 .360 .263 .213 .111 .092 .071
Approx 95 pct confidence limits: .138 .195 .231 .251 .264 .273 .278 .281 .282 .283
Partial autocorrelations: .711 .263 -.030 -.005 .032 -.081 -.004 -.104 .043 .050
Ljung-Box Portmanteau Q 350.6126 DF 25 Prob .0000
Trend in variance (%) = -.1070
Comparison of Standard & ARSTAN Chronologies 11:41 Tue 08 Oct 2024 Page 11
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Variance and correlation of Standard and Autoregressive (ARSTAN) chronologies
Interval Standard ARSTAN Standard ARSTAN Standard variance % Standard vs ARSTAN First order autocorr
Mean Mean Variance Variance reduced by ARSTAN Correlations Standard ARSTAN
1811 1860 1.016 1.132 .4096 .4180 -2.037 .963 .795 .779
1825 1874 1.092 1.188 .3817 .3884 -1.755 .957 .740 .720
1850 1899 .804 .892 .1541 .2265 -47.042 .944 .533 .579
1875 1924 .867 .891 .2948 .2624 10.973 .997 .673 .670
1900 1949 1.197 1.161 .2758 .2543 7.787 .996 .661 .652
1925 1974 1.097 1.056 .1969 .1831 6.985 .995 .659 .640
1950 1999 .893 .883 .1333 .1312 1.527 .997 .500 .491
1972 2021 .890 .891 .1139 .1171 -2.833 .998 .447 .469
----------------------------------------------------------------------------------------------------------------------------
1811 2021 .978 1.001 .2522 .2453 2.727 .977 .720 .711
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For the modeled time interval 1849 to 2021:
Standard chronology when modeled as an AR( 2) process using the first-minimum AIC
coefficients: .4842 .2704
ARSTAN chronology when modeled as an AR( 2) process using the first-minimum AIC
coefficients: .5007 .2520
Variance due to autoregression in Standard chronology 48.678% Residual variance .1033
Variance due to autoregression in ARSTAN chronology 48.659% Residual variance .1071
Difference in variance due to autoregression alone .019%
Error variance in ARSTAN chronology relative to Standard chronolog 51.435% Standard error variance .011458
Reduced error variance in ARSTAN 48.565% ARSTAN error variance .005893
ARSTAN chronology error variance is lower
Error variance in ARSTAN relative to Standard for common interval 86.090% Standard error variance .005500
Reduced error variance in ARSTAN for common interval 13.910% ARSTAN error variance .004735
In Common Interval, ARSTAN chronology error variance is lower
COMMON INTERVAL ANALYSIS of DETRENDED SERIES 11:41 Tue 08 Oct 2024 Page 12
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Seq 2, Series pub05x 1939 to 2021 does not cover interval, not analyzed
Seq 5, Series pub10x 1949 to 2021 does not cover interval, not analyzed
Seq 17, Series pub42x 1910 to 2021 does not cover interval, not analyzed
Seq 19, Series pub44x 1920 to 2021 does not cover interval, not analyzed
Seq 21, Series pub50x 1931 to 2021 does not cover interval, not analyzed
Seq 22, Series pub52x 1952 to 2021 does not cover interval, not analyzed
Seq 24, Series pub582x 1937 to 2021 does not cover interval, not analyzed
Seq 26, Series puub32x 1943 to 2021 does not cover interval, not analyzed
Trees separate after sequence numbers:
1 3 4 6 7 8 9 10 11 12 13 14 15 16 18 20 23 25
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 pub03x 1900 2021 122 1.062 .980 .387 .475 1.156 1.352 -.2075 .42 .47 .00 .000
3 pub06x 1900 2021 122 1.040 .972 .300 .471 .581 -.158 -.2627 .66 .20 -.02 .000
4 pub07x 1900 2021 122 1.051 .881 .338 .635 1.445 2.019 -.4299 .69 .28 -.19 .000
6 pub20x 1900 2021 122 1.078 .960 .424 .623 .700 .481 -.1018 .69 .34 -.08 .000
7 pub21x 1900 2021 122 1.025 .929 .464 .624 2.246 8.278 .0776 .48 .27 .05 .000
8 pub25x 1900 2021 122 1.075 .941 .422 .606 1.210 1.858 -.2978 .67 .17 -.04 .000
9 pub27x 1900 2021 122 1.025 .902 .508 .575 .787 .590 .0282 .54 .24 .06 .000
10 pub28x 1900 2021 122 1.111 1.023 .474 .707 1.162 1.499 -.1636 .69 .23 -.08 .000
11 pub29x 1900 2021 122 1.115 .981 .563 .703 .920 1.160 -.2275 .65 .28 .02 .000
12 pub30x 1900 2021 122 1.078 .960 .457 .673 1.484 2.958 -.2815 .72 .13 -.04 .000
13 pub34x 1900 2021 122 1.034 .940 .377 .590 1.867 5.456 -.3514 .70 .11 -.05 .000
14 pub37x 1900 2021 122 1.051 1.004 .320 .552 .858 .773 -.3507 .73 .18 .07 .000
15 pub39x 1900 2021 122 1.001 .935 .494 .527 .586 .148 -.2105 .47 .32 -.02 .000