RUN: 4DIG001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: MONG007T.rwl.conv LOG FILE PROCESSED: MONG007T.rwl.conv_log OPTION PLOT TREE-RING DATA TYPE 1 !TUCSON RING-WIDTH FORMAT MISSING DATA IN GAPS -9 0 !MISSING VALUES ESTIMATED (NO PLOTS) DATA TRANSFORMATION 0 0 !NO DATA TRANSFORMATION (NO PLOTS) FIRST DETRENDING 1 0 !1ST-NEG EXPONENTIAL CURVE, NO = OPT 3 SECOND DETRENDING -67 0 !2ND-SPLINE CURVE (PCT N 50% CUTOFF) ROBUST DETRENDING 1 !NON-ROBUST DETRENDING METHODS USED INTERACTIVE DETREND 0 !NO INTERACTIVE DETRENDING INDEX CALCULATION 1 !TREE-RING INDICES OR RATIOS (Rt/Gt) AR MODELING METHOD 1 0 !NON-ROBUST AUTOREGRESSIVE MODELING POOLED AR ORDER 0 0 !MINIMUM AIC POOLED AR MODEL ORDER FIT SERIES AR ORDER 0 !POOLED AR ORDER FIT TO ALL SERIES MEAN CHRONOLOGY 2 0 !ROBUST CHRONOLOGY (NO BIWEIGHT PLOTS) STABILIZE VARIANCE 1 !RBAR WEIGHTED STABILIZATION METHOD COMMON PERIOD YEARS 0 0 !NO COMMON PERIOD ANALYSIS PERFORMED SITE-TREE-CORE MASK SSSTTCC !SITE-TREE-CORE SEPARATION MASK RUNNING RBAR 50 25 0 !RUNNING RBAR WINDOW/OVERLAP (NO PLOTS) PRINTOUT OPTION 2 !SUMMARY & SERIES STATISTICS PRINTED CORE SERIES SAVE 1 !SERIES SAVED IN TUCSON RAW DATA FORMAT SUMMARY PLOT DISPLAYS 0 !NO SPAGHETTI AND MEAN CHRONOLOGY PLOTS STAND DYNAMICS ANALYSES 0 !NO STAND DYNAMICS ANALYSES DONE RUNNING MEAN WINDOW WIDTH 0 !RUNNING MEAN WINDOW WIDTH PERCENT GROWTH CHANGE 0 !PERCENT GROWTH CHANGE THRESHOLD STANDARD ERROR THRESHOLD 0 !STANDARD ERROR LIMIT THRESHOLD |======================== RAW DATA STATISTICAL ANALYSES =======================| |------------------- TREE-RING SERIES READ IN FOR PROCESSING ------------------| DATA HEADER LINES: 113 1 Turgen-charchira mountai DENSITY_LATE LADA - 113 2 Mongolia Larch 2000 4942-9133 1570 1995 - 113 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 1 113011 MISSING VALUES FOUND: 24 IN 1 GAPS / 1931 1954 / -------------------------------------------------------------------- 3 113021 MISSING VALUES FOUND: 7 IN 1 GAPS / 1824 1830 / -------------------------------------------------------------------- 4 113022 MISSING VALUES FOUND: 1 IN 1 GAPS / 1816 1816 / -------------------------------------------------------------------- 5 113051 MISSING VALUES FOUND: 3 IN 2 GAPS / 1776 1777 / 1858 1858 / -------------------------------------------------------------------- 7 113062 MISSING VALUES FOUND: 1 IN 1 GAPS / 1872 1872 / -------------------------------------------------------------------- 9 113072 MISSING VALUES FOUND: 1 IN 1 GAPS / 1951 1951 / -------------------------------------------------------------------- 10 113091 MISSING VALUES FOUND: 1 IN 1 GAPS / 1821 1821 / -------------------------------------------------------------------- 12 113101 MISSING VALUES FOUND: 6 IN 4 GAPS / 1620 1622 / 1641 1641 / 1735 1735 / 1872 1872 / -------------------------------------------------------------------- 13 113102 MISSING VALUES FOUND: 8 IN 6 GAPS / 1617 1617 / 1652 1654 / 1671 1671 / 1735 1735 / / 1830 1830 / 1872 1872 / -------------------------------------------------------------------- 14 113111 MISSING VALUES FOUND: 4 IN 3 GAPS / 1715 1715 / 1749 1750 / 1821 1821 / -------------------------------------------------------------------- 15 113112 MISSING VALUES FOUND: 6 IN 4 GAPS / 1677 1677 / 1715 1715 / 1749 1750 / 1821 1822 / -------------------------------------------------------------------- 16 113121 MISSING VALUES FOUND: 1 IN 1 GAPS / 1900 1900 / -------------------------------------------------------------------- 17 113122 MISSING VALUES FOUND: 3 IN 3 GAPS / 1900 1900 / 1911 1911 / 1950 1950 / -------------------------------------------------------------------- 20 113191 MISSING VALUES FOUND: 6 IN 3 GAPS / 1735 1736 / 1786 1788 / 1886 1886 / -------------------------------------------------------------------- 21 113192 MISSING VALUES FOUND: 12 IN 5 GAPS / 1735 1736 / 1817 1817 / 1879 1879 / 1882 1888 / / 1910 1910 / -------------------------------------------------------------------- 22 113201 MISSING VALUES FOUND: 3 IN 1 GAPS / 1822 1824 / -------------------------------------------------------------------- 23 113202 MISSING VALUES FOUND: 3 IN 1 GAPS / 1822 1824 / -------------------------------------------------------------------- 24 113211 MISSING VALUES FOUND: 8 IN 2 GAPS / 1802 1807 / 1850 1851 / -------------------------------------------------------------------- 25 113212 MISSING VALUES FOUND: 8 IN 2 GAPS / 1682 1684 / 1793 1797 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 113011 1751 1956 206 7.183 0.674 -1.290 5.501 0.070 0.526 2 113012 1736 1936 201 7.094 0.842 -0.585 3.814 0.090 0.549 3 113021 1784 1982 199 7.916 0.710 -1.276 6.178 0.076 0.347 4 113022 1766 1981 216 8.033 0.744 -1.209 4.759 0.073 0.465 5 113051 1730 2179 450 7.255 1.518 -2.716 13.631 0.103 0.743 6 113061 1751 1995 245 7.834 0.783 -1.440 6.566 0.093 0.206 7 113062 1751 1995 245 7.858 0.760 -0.868 3.744 0.087 0.309 8 113071 1755 1850 96 7.795 0.769 -1.221 4.535 0.077 0.473 9 113072 1758 1973 216 7.918 0.842 -1.198 4.356 0.079 0.548 10 113091 1755 1994 240 7.928 0.933 -1.326 5.283 0.119 0.121 11 113092 1754 1994 241 8.109 0.842 -1.446 6.442 0.100 0.157 12 113101 1613 1994 382 7.621 1.082 -0.785 3.021 0.112 0.531 13 113102 1612 1994 383 7.227 1.382 -0.395 2.475 0.125 0.697 14 113111 1601 1995 395 7.545 1.001 -0.736 3.327 0.106 0.486 15 113112 1601 1994 394 7.487 1.048 -0.519 2.854 0.122 0.433 16 113121 1760 1924 165 7.607 0.847 -0.678 3.356 0.091 0.426 17 113122 1761 1958 198 7.269 1.003 -0.648 3.469 0.112 0.447 18 113181 1752 1959 208 7.258 0.635 -0.302 3.805 0.070 0.457 19 113182 1757 1963 207 7.692 0.662 -1.111 5.784 0.077 0.346 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 113191 1570 1963 394 7.297 0.919 -0.511 2.939 0.100 0.486 21 113192 1570 1964 395 7.733 1.077 -1.548 9.785 0.103 0.434 22 113201 1792 1944 153 7.710 0.517 -0.683 3.495 0.052 0.501 23 113202 1772 1954 183 7.675 0.664 -1.008 3.849 0.052 0.728 24 113211 1661 1951 291 7.472 0.719 -0.589 3.658 0.077 0.482 25 113212 1655 1958 304 7.329 0.737 -0.467 3.632 0.084 0.475 NUMBER OF SERIES READ IN: 25 FROM 1570 TO 2179 610 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 260 7.594 0.868 -0.982 4.810 0.090 0.455 STANDARD DEVIATION 94 0.294 0.229 0.518 2.438 0.020 0.153 MEDIAN (50TH QUANTILE) 239 7.621 0.842 -0.868 3.814 0.090 0.473 INTERQUARTILE RANGE 180 0.537 0.282 0.687 2.032 0.027 0.100 MINIMUM VALUE 96 7.094 0.517 -2.716 2.475 0.052 0.121 LOWER HINGE (25TH QUANTILE) 195 7.297 0.719 -1.276 3.469 0.077 0.426 UPPER HINGE (75TH QUANTILE) 375 7.834 1.001 -0.589 5.501 0.103 0.526 MAXIMUM VALUE 447 8.109 1.518 -0.302 13.631 0.125 0.743 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 300 0.299 0.198 0.011 -0.288 3.035 -0.296 0.816 MINIMUM CORRELATION: -0.296 SERIES 113102 AND 113202 183 YEARS MAXIMUM CORRELATION: 0.816 SERIES 113091 AND 113092 240 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 33.07 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1595. 1630. 1655. 1680. 1705. 1730. 1755. 1780. 1805. 1830. CORR 1. 6. 15. 21. 28. 28. 36. 136. 253. 276. RBAR 0.747 0.315 0.551 0.516 0.456 0.577 0.453 0.273 0.315 0.353 SDEV 0.000 0.271 0.181 0.204 0.262 0.163 0.242 0.247 0.278 0.206 SERR 0.000 0.111 0.047 0.045 0.050 0.031 0.040 0.021 0.017 0.012 EPS 0.900 0.724 0.894 0.894 0.870 0.926 0.929 0.895 0.919 0.932 NSS 3.1 5.7 6.9 7.9 8.0 9.2 15.8 22.8 24.7 24.9 YEAR 1855. 1880. 1905. 1930. 1955. CORR 276. 276. 253. 190. 55. RBAR 0.350 0.381 0.428 0.444 0.370 SDEV 0.215 0.167 0.188 0.216 0.297 SERR 0.013 0.010 0.012 0.016 0.040 EPS 0.929 0.936 0.947 0.948 0.912 NSS 24.4 24.0 23.9 22.8 17.6 |======================== RAW DATA CHRONOLOGY STATISTICS ======================| |----------------- ROBUST MEAN RAW DATA CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1570 2179 610 7.500 0.793 -1.002 4.697 0.072 0.617 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.165 0.092 -0.169 121 489 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.38 1.79 1.01 1.12 2.91 71.53 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.84 0.90 0.00 0.00 0.90 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 240. 181. 96. 201. 382. 450. |----------- RAW DATA CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.616 0.447 0.430 0.441 0.391 0.392 0.372 0.351 0.304 0.293 PACF 0.616 0.109 0.192 0.160 0.042 0.116 0.040 0.040 -0.018 0.022 95% C.L. 0.081 0.107 0.119 0.129 0.138 0.145 0.152 0.158 0.163 0.167 |------------------ RAW DATA CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 4 0.436 0.484 0.007 0.111 0.176 |================== DETRENDED DATA CURVE FITS AND STATISTICS ==================| |------------------------ RESULTS OF FIRST DETRENDING -------------------------| |--------------- GROWTH CURVE USED FOR DETRENDING TREE-RING DATA --------------| CURVE OPTION -2: REGIONAL CURVE DETRENDING F(I) = ONE AGE-ALIGNED CURVE CURVE OPTION -1: FIRST-DIFFERENCES F(I) = Y(I) - Y(I-1) CURVE OPTION 1: NEG EXPON CURVE, NO = OPT 3 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 2: NEG EXPON CURVE, NO = OPT 4 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 3: LINEAR REGRESSION (ANY SLOPE) F(I) = +/-C*T(I) + D CURVE OPTION 4: LINEAR REGRESSION (NEG SLOPE) F(I) = -C*T(I) + D CURVE OPTION 5: HORIZONTAL LINE THROUGH MEAN F(I) = MEAN(Y(I)) = D CURVE OPTION 6: HUGERSHOFF GROWTH FUNCTION F(I) = A*T(I)**B * EXP(C*T(I)) CURVE OPTION 7: GENERAL EXPONENTIAL CURVE F(I) = A*T(I) * EXP(-B*T(I)) CURVE OPTION >9: CUBIC SMOOTHING SPLINE FIXED 50 PCT VARIANCE CUTOFF CURVE OPTION <-9: CUBIC SMOOTHING SPLINE PCT N 50 PCT VARIANCE CUTOFF SERIES IDENT OPTION A B C D 1 113011 3 0.00000000 0.00000000 -0.00589122 7.67710733 2 113012 3 0.00000000 0.00000000 -0.00371123 7.46886444 3 113021 1 0.31788197 0.04088282 0.00000000 7.86024046 4 113022 3 0.00000000 0.00000000 0.00197695 7.81336164 5 113051 3 0.00000000 0.00000000 -0.00282052 7.90354776 6 113061 3 0.00000000 0.00000000 -0.00003277 7.83770418 7 113062 3 0.00000000 0.00000000 0.00104581 7.72600222 8 113071 3 0.00000000 0.00000000 0.00575312 7.51555681 9 113072 3 0.00000000 0.00000000 -0.00433375 8.38099003 10 113091 3 0.00000000 0.00000000 -0.00094006 8.03362942 11 113092 3 0.00000000 0.00000000 0.00023421 8.08020878 12 113101 3 0.00000000 0.00000000 -0.00389820 8.35646629 13 113102 3 0.00000000 0.00000000 -0.00748438 8.66852188 14 113111 1 1.56040239 0.00422657 0.00000000 6.77562094 15 113112 1 1.28706992 0.00989552 0.00000000 7.15200710 16 113121 3 0.00000000 0.00000000 0.00028193 7.57679033 17 113122 3 0.00000000 0.00000000 -0.00820108 8.05945206 18 113181 3 0.00000000 0.00000000 -0.00067376 7.32834053 19 113182 3 0.00000000 0.00000000 -0.00190829 7.89039421 SERIES IDENT OPTION A B C D 20 113191 3 0.00000000 0.00000000 -0.00111968 7.50357628 21 113192 3 0.00000000 0.00000000 -0.00312083 8.31352139 22 113201 3 0.00000000 0.00000000 -0.00064700 7.75486040 23 113202 3 0.00000000 0.00000000 0.00655036 7.07378912 24 113211 3 0.00000000 0.00000000 0.00226445 7.14899635 25 113212 3 0.00000000 0.00000000 -0.00135952 7.53851080 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 113011 1751 1956 206 1.000 0.093 -0.778 3.676 0.071 0.517 2 113012 1736 1936 201 1.000 0.115 -0.635 3.544 0.090 0.512 3 113021 1784 1982 199 1.000 0.091 -1.301 6.215 0.076 0.353 4 113022 1766 1981 216 1.000 0.092 -1.013 4.228 0.074 0.441 5 113051 1730 2179 450 1.000 0.204 -2.901 14.831 0.104 0.722 6 113061 1751 1995 245 1.000 0.100 -1.440 6.565 0.093 0.205 7 113062 1751 1995 245 1.000 0.096 -0.820 3.659 0.087 0.302 8 113071 1755 1850 96 1.000 0.097 -0.996 4.563 0.076 0.461 9 113072 1758 1973 216 1.000 0.102 -1.099 4.052 0.080 0.527 10 113091 1755 1994 240 1.000 0.118 -1.312 5.181 0.119 0.113 11 113092 1754 1994 241 1.000 0.104 -1.451 6.453 0.100 0.156 12 113101 1613 1994 382 1.000 0.133 -0.664 2.975 0.112 0.452 13 113102 1612 1994 383 0.999 0.155 -0.406 2.476 0.125 0.485 14 113111 1601 1995 395 1.000 0.126 -0.826 3.280 0.106 0.423 15 113112 1601 1994 394 1.000 0.136 -0.478 2.939 0.122 0.382 16 113121 1760 1924 165 1.000 0.112 -0.661 3.307 0.092 0.447 17 113122 1761 1958 198 1.000 0.127 -0.630 3.349 0.111 0.380 18 113181 1752 1959 208 1.000 0.087 -0.376 3.789 0.069 0.450 19 113182 1757 1963 207 1.000 0.085 -1.141 5.453 0.077 0.319 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 113191 1570 1963 394 1.000 0.128 -0.618 2.971 0.100 0.510 21 113192 1570 1964 395 1.000 0.133 -1.917 11.177 0.103 0.393 22 113201 1792 1944 153 1.000 0.068 -0.736 3.446 0.053 0.472 23 113202 1772 1954 183 1.000 0.076 -0.300 3.215 0.052 0.604 24 113211 1661 1951 291 1.000 0.092 -0.497 3.624 0.076 0.432 25 113212 1655 1958 304 1.000 0.099 -0.582 3.621 0.084 0.449 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 264 1.000 0.111 -0.943 4.744 0.090 0.420 STANDARD DEVIATION 95 0.000 0.029 0.568 2.777 0.020 0.132 MEDIAN (50TH QUANTILE) 240 1.000 0.102 -0.778 3.659 0.090 0.447 INTERQUARTILE RANGE 181 0.000 0.035 0.523 1.874 0.028 0.104 MINIMUM VALUE 96 0.999 0.068 -2.901 2.476 0.052 0.113 LOWER HINGE (25TH QUANTILE) 201 1.000 0.092 -1.141 3.307 0.076 0.380 UPPER HINGE (75TH QUANTILE) 382 1.000 0.127 -0.618 5.181 0.104 0.485 MAXIMUM VALUE 450 1.000 0.204 -0.300 14.831 0.125 0.722 |------------------------ RESULTS OF SECOND DETRENDING ------------------------| |--------------- GROWTH CURVE USED FOR DETRENDING TREE-RING DATA --------------| CURVE OPTION -2: REGIONAL CURVE DETRENDING F(I) = ONE AGE-ALIGNED CURVE CURVE OPTION -1: FIRST-DIFFERENCES F(I) = Y(I) - Y(I-1) CURVE OPTION 1: NEG EXPON CURVE, NO = OPT 3 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 2: NEG EXPON CURVE, NO = OPT 4 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 3: LINEAR REGRESSION (ANY SLOPE) F(I) = +/-C*T(I) + D CURVE OPTION 4: LINEAR REGRESSION (NEG SLOPE) F(I) = -C*T(I) + D CURVE OPTION 5: HORIZONTAL LINE THROUGH MEAN F(I) = MEAN(Y(I)) = D CURVE OPTION 6: HUGERSHOFF GROWTH FUNCTION F(I) = A*T(I)**B * EXP(C*T(I)) CURVE OPTION 7: GENERAL EXPONENTIAL CURVE F(I) = A*T(I) * EXP(-B*T(I)) CURVE OPTION >9: CUBIC SMOOTHING SPLINE FIXED 50 PCT VARIANCE CUTOFF CURVE OPTION <-9: CUBIC SMOOTHING SPLINE PCT N 50 PCT VARIANCE CUTOFF SERIES IDENT OPTION A B C D 1 113011 -67 138 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 113012 -67 134 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 113021 -67 133 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 113022 -67 144 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 113051 -67 301 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 113061 -67 164 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 113062 -67 164 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 113071 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 113072 -67 144 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 113091 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 113092 -67 161 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 113101 -67 255 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 113102 -67 256 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 113111 -67 264 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 113112 -67 263 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 113121 -67 110 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 113122 -67 132 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 113181 -67 139 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 113182 -67 138 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 113191 -67 263 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 113192 -67 264 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 113201 -67 102 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 113202 -67 122 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 113211 -67 194 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 25 113212 -67 203 SMOOTHING SPLINE CURVE AND WINDOW WIDTH |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 113011 1751 1956 206 1.000 0.087 -0.798 4.307 0.071 0.448 2 113012 1736 1936 201 0.999 0.108 -0.715 3.823 0.090 0.447 3 113021 1784 1982 199 1.000 0.088 -1.385 6.572 0.076 0.304 4 113022 1766 1981 216 1.000 0.083 -1.141 4.407 0.074 0.331 5 113051 1730 2179 450 0.999 0.199 -3.093 16.266 0.104 0.703 6 113061 1751 1995 245 1.000 0.098 -1.494 6.981 0.093 0.181 7 113062 1751 1995 245 1.000 0.094 -0.889 3.776 0.087 0.269 8 113071 1755 1850 96 0.999 0.082 -1.227 5.484 0.076 0.242 9 113072 1758 1973 216 1.000 0.097 -1.156 4.325 0.080 0.462 10 113091 1755 1994 240 1.000 0.117 -1.385 5.405 0.119 0.094 11 113092 1754 1994 241 1.000 0.102 -1.636 7.078 0.100 0.141 12 113101 1613 1994 382 1.000 0.126 -0.575 3.114 0.112 0.381 13 113102 1612 1994 383 0.999 0.140 -0.310 3.072 0.125 0.354 14 113111 1601 1995 395 1.000 0.123 -0.879 3.400 0.106 0.396 15 113112 1601 1994 394 1.000 0.133 -0.549 2.975 0.122 0.360 16 113121 1760 1924 165 1.000 0.108 -0.736 3.377 0.092 0.412 17 113122 1761 1958 198 1.000 0.120 -0.781 3.774 0.111 0.317 18 113181 1752 1959 208 1.000 0.084 -0.318 3.765 0.069 0.407 19 113182 1757 1963 207 1.000 0.084 -1.130 5.464 0.077 0.311 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 113191 1570 1963 394 0.999 0.121 -0.726 3.077 0.100 0.465 21 113192 1570 1964 395 0.999 0.126 -2.043 12.826 0.103 0.333 22 113201 1792 1944 153 1.000 0.060 -0.874 3.964 0.053 0.325 23 113202 1772 1954 183 1.000 0.061 -0.171 2.806 0.052 0.383 24 113211 1661 1951 291 1.000 0.087 -0.593 3.830 0.076 0.359 25 113212 1655 1958 304 1.000 0.093 -0.635 3.883 0.084 0.382 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 264 1.000 0.105 -1.010 5.110 0.090 0.352 STANDARD DEVIATION 95 0.000 0.029 0.619 3.130 0.020 0.120 MEDIAN (50TH QUANTILE) 240 1.000 0.098 -0.874 3.883 0.090 0.359 INTERQUARTILE RANGE 181 0.000 0.035 0.591 2.065 0.028 0.096 MINIMUM VALUE 96 0.999 0.060 -3.093 2.806 0.052 0.094 LOWER HINGE (25TH QUANTILE) 201 1.000 0.087 -1.227 3.400 0.076 0.311 UPPER HINGE (75TH QUANTILE) 382 1.000 0.121 -0.635 5.464 0.104 0.407 MAXIMUM VALUE 450 1.000 0.199 -0.171 16.266 0.125 0.703 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 300 0.343 0.159 0.009 -0.129 3.088 -0.076 0.820 MINIMUM CORRELATION: -0.076 SERIES 113091 AND 113211 197 YEARS MAXIMUM CORRELATION: 0.820 SERIES 113091 AND 113092 240 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 33.07 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1595. 1630. 1655. 1680. 1705. 1730. 1755. 1780. 1805. 1830. CORR 1. 6. 15. 21. 28. 28. 36. 136. 253. 276. RBAR 0.711 0.315 0.568 0.523 0.467 0.567 0.492 0.287 0.328 0.352 SDEV 0.000 0.286 0.164 0.195 0.242 0.166 0.232 0.219 0.250 0.216 SERR 0.000 0.117 0.042 0.043 0.046 0.031 0.039 0.019 0.016 0.013 EPS 0.883 0.724 0.900 0.896 0.875 0.923 0.939 0.902 0.923 0.931 NSS 3.1 5.7 6.9 7.9 8.0 9.2 15.8 22.8 24.7 24.9 YEAR 1855. 1880. 1905. 1930. 1955. CORR 276. 276. 253. 190. 55. RBAR 0.358 0.373 0.449 0.454 0.376 SDEV 0.206 0.169 0.173 0.208 0.301 SERR 0.012 0.010 0.011 0.015 0.041 EPS 0.932 0.935 0.951 0.950 0.914 NSS 24.4 24.0 23.9 22.8 17.6 |======================== STANDARD CHRONOLOGY STATISTICS ======================| *** VARIANCE STABILIZED WITH BRIFFA RBAR-WEIGHTED METHOD *** |----------------- ROBUST MEAN STANDARD CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1570 2179 610 1.007 0.090 -0.936 4.144 0.075 0.423 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.210 -0.114 0.171 134 476 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.40 1.36 1.00 1.14 2.51 43.14 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.84 0.91 0.00 0.00 0.91 1.00 |----------- STANDARD CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.422 0.189 0.187 0.190 0.118 0.106 0.101 0.089 0.030 0.030 PACF 0.422 0.013 0.125 0.082 -0.005 0.043 0.020 0.020 -0.042 0.009 95% C.L. 0.081 0.094 0.097 0.099 0.101 0.102 0.103 0.104 0.104 0.104 |------------------ STANDARD CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.179 0.423 |======================= POOLED AUTOREGRESSION ANALYSIS =======================| POOLED AUTOCORRELATIONS: LAG T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 0.318 0.063 0.099 0.070 0.027 0.012 0.051 0.038 0.072 -0.001 YULE-WALKER ESTIMATES OF AUTOREGRESSION: ORDER T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 1 0.318 2 0.331 -0.043 3 0.336 -0.077 0.102 4 0.335 -0.076 0.099 0.010 5 0.334 -0.076 0.099 0.009 0.002 6 0.334 -0.076 0.099 0.009 0.003 -0.003 7 0.335 -0.076 0.099 0.004 0.007 -0.019 0.047 8 0.334 -0.076 0.099 0.004 0.006 -0.019 0.046 0.005 9 0.334 -0.079 0.100 0.004 0.006 -0.025 0.051 -0.017 0.066 10 0.338 -0.080 0.103 0.003 0.006 -0.025 0.056 -0.021 0.085 -0.057 LAST TERM IN EACH ROW ABOVE EQUALS THE PARTIAL AUTOCORRELATION COEFFICIENT AKAIKE INFORMATION CRITERION: AR( 0) AR( 1) AR( 2) AR( 3) AR( 4) AR( 5) 3876.26 3813.40 3814.28 3809.85 3811.79 3813.79 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 3815.78 3816.42 3818.40 3817.71 3817.73 SELECTED AUTOREGRESSION ORDER: 1 AR ORDER SELECTION CRITERION: IPP=0 FIRST-MINIMUM AIC SELECTION THE AIC TRACE SHOULD BE CHECKED TO SEE IF AR ORDER SELECTION CRITERION IS ADEQUATE. E.G. IF AR-ORDERS OF THE FIRST-MINIMUM AND THE FULL-MINIMUM AIC ARE CLOSE, AN ARSTAN RUN WITH FULL-MINIMUM AIC ORDER SELECTION MIGHT BE TRIED AUTOREGRESSION COEFFICIENTS: T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 0.318 R-SQUARED DUE TO POOLED AUTOREGRESSION: 10.09 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 111.22 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.318 0.101 0.032 0.010 0.003 0.001 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 113011 1 0.208 0.455 2 113012 1 0.219 0.450 3 113021 1 0.098 0.308 4 113022 1 0.111 0.333 5 113051 1 0.518 0.703 6 113061 1 0.035 0.186 7 113062 1 0.076 0.273 8 113071 1 0.059 0.243 9 113072 1 0.217 0.465 10 113091 1 0.015 0.095 11 113092 1 0.022 0.141 12 113101 1 0.149 0.383 13 113102 1 0.134 0.359 14 113111 1 0.158 0.397 15 113112 1 0.134 0.362 16 113121 1 0.177 0.419 17 113122 1 0.113 0.318 18 113181 1 0.169 0.409 19 113182 1 0.108 0.313 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 113191 1 0.249 0.465 21 113192 1 0.138 0.333 22 113201 1 0.107 0.325 23 113202 1 0.157 0.387 24 113211 1 0.152 0.361 25 113212 1 0.151 0.383 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.147 0.355 STANDARD DEVIATION 0 0.098 0.120 MEDIAN 1 0.138 0.361 INTERQUARTILE RANGE 0 0.061 0.096 MINIMUM VALUE 1 0.015 0.095 LOWER HINGE 1 0.107 0.313 UPPER HINGE 1 0.169 0.409 MAXIMUM VALUE 1 0.518 0.703 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 113011 1751 1956 206 1.000 0.078 -0.790 5.432 0.083 -0.010 2 113012 1736 1936 201 1.000 0.096 -0.736 4.074 0.104 0.066 3 113021 1784 1982 199 1.000 0.084 -1.592 8.097 0.087 0.022 4 113022 1766 1981 216 1.000 0.079 -1.212 4.640 0.086 -0.009 5 113051 1730 2179 450 1.000 0.139 -0.975 16.696 0.143 -0.143 6 113061 1751 1995 245 1.000 0.096 -1.556 7.329 0.100 0.000 7 113062 1751 1995 245 1.000 0.090 -1.011 4.385 0.098 -0.010 8 113071 1755 1850 96 1.000 0.079 -1.409 6.412 0.084 0.005 9 113072 1758 1973 216 1.000 0.086 -1.178 4.938 0.097 -0.014 10 113091 1755 1994 240 1.000 0.116 -1.477 5.798 0.124 0.007 11 113092 1754 1994 241 1.000 0.101 -1.719 7.460 0.104 0.006 12 113101 1613 1994 382 1.000 0.116 -0.635 3.088 0.129 -0.017 13 113102 1612 1994 383 1.000 0.131 -0.391 3.308 0.146 -0.024 14 113111 1601 1995 395 1.000 0.113 -0.987 4.190 0.124 0.007 15 113112 1601 1994 394 1.000 0.124 -0.761 3.509 0.144 -0.020 16 113121 1760 1924 165 1.000 0.098 -0.950 4.338 0.107 0.014 17 113122 1761 1958 198 1.000 0.114 -0.758 3.712 0.123 0.038 18 113181 1752 1959 208 1.000 0.076 -0.604 4.890 0.082 -0.019 19 113182 1757 1963 207 1.000 0.080 -1.100 4.875 0.086 0.033 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 113191 1570 1963 394 1.000 0.107 -0.728 3.519 0.125 -0.095 21 113192 1570 1964 395 1.000 0.118 -2.182 16.638 0.119 -0.054 22 113201 1792 1944 153 1.000 0.056 -1.284 5.060 0.062 -0.013 23 113202 1772 1954 183 1.000 0.056 -0.453 3.470 0.063 -0.039 24 113211 1661 1951 291 1.000 0.081 -0.709 4.440 0.090 -0.057 25 113212 1655 1958 304 1.000 0.086 -0.566 3.776 0.100 -0.028 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 264 1.000 0.096 -1.031 5.763 0.104 -0.014 STANDARD DEVIATION 95 0.000 0.022 0.440 3.540 0.024 0.042 MEDIAN (50TH QUANTILE) 240 1.000 0.096 -0.975 4.640 0.100 -0.010 INTERQUARTILE RANGE 181 0.000 0.034 0.556 2.022 0.038 0.031 MINIMUM VALUE 96 1.000 0.056 -2.182 3.088 0.062 -0.143 LOWER HINGE (25TH QUANTILE) 201 1.000 0.080 -1.284 3.776 0.086 -0.024 UPPER HINGE (75TH QUANTILE) 382 1.000 0.114 -0.728 5.798 0.124 0.007 MAXIMUM VALUE 450 1.000 0.139 -0.391 16.696 0.146 0.066 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 300 0.364 0.146 0.008 -0.105 3.410 -0.069 0.826 MINIMUM CORRELATION: -0.069 SERIES 113112 AND 113211 291 YEARS MAXIMUM CORRELATION: 0.826 SERIES 113091 AND 113092 240 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 33.07 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1595. 1630. 1655. 1680. 1705. 1730. 1755. 1780. 1805. 1830. CORR 1. 6. 15. 21. 28. 28. 36. 136. 253. 276. RBAR 0.645 0.359 0.621 0.579 0.512 0.558 0.466 0.339 0.388 0.385 SDEV 0.000 0.269 0.124 0.182 0.194 0.159 0.210 0.216 0.208 0.212 SERR 0.000 0.110 0.032 0.040 0.037 0.030 0.035 0.019 0.013 0.013 EPS 0.847 0.761 0.918 0.916 0.893 0.921 0.933 0.921 0.940 0.940 NSS 3.1 5.7 6.9 7.9 8.0 9.2 15.8 22.8 24.7 24.9 YEAR 1855. 1880. 1905. 1930. 1955. CORR 276. 276. 253. 190. 55. RBAR 0.379 0.359 0.397 0.443 0.414 SDEV 0.199 0.168 0.161 0.199 0.251 SERR 0.012 0.010 0.010 0.014 0.034 EPS 0.937 0.931 0.940 0.948 0.926 NSS 24.4 24.0 23.9 22.8 17.6 |======================== RESIDUAL CHRONOLOGY STATISTICS ======================| *** VARIANCE STABILIZED WITH BRIFFA RBAR-WEIGHTED METHOD *** |----------------- ROBUST MEAN RESIDUAL CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1570 2179 610 1.003 0.078 -0.982 4.206 0.087 -0.018 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.187 -0.105 0.155 138 472 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.29 0.85 1.00 1.10 1.95 119.22 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.83 0.91 0.00 0.00 0.91 1.00 |----------- RESIDUAL CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF -0.018 -0.081 0.064 0.103 -0.005 0.026 0.038 0.036 -0.025 -0.009 PACF -0.018 -0.082 0.061 0.100 0.009 0.038 0.027 0.033 -0.023 -0.015 95% C.L. 0.081 0.081 0.082 0.082 0.083 0.083 0.083 0.083 0.083 0.083 |------------------ RESIDUAL CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 4 0.021 -0.020 -0.073 0.063 0.102 |---------- REWHITENED CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS -----------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF -0.001 -0.081 0.064 0.104 -0.003 0.026 0.039 0.037 -0.024 -0.009 PACF -0.001 -0.081 0.064 0.099 0.008 0.039 0.027 0.032 -0.024 -0.015 95% C.L. 0.081 0.081 0.082 0.082 0.083 0.083 0.083 0.083 0.083 0.083 |----------------- REWHITENED CHRONOLOGY AUTOREGRESSIVE MODEL -----------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.007 -0.001 |========================= ARSTAN CHRONOLOGY STATISTICS =======================| |----------------- ROBUST MEAN ARSTAN CHRONOLOGY STATISTICS -------------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1570 2179 610 1.003 0.082 -1.016 4.135 0.076 0.302 |------------ ARSTAN CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS -------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.302 0.052 0.108 0.132 0.051 0.055 0.061 0.045 -0.008 -0.005 PACF 0.302 -0.043 0.115 0.075 -0.010 0.042 0.018 0.012 -0.035 -0.006 95% C.L. 0.081 0.088 0.088 0.089 0.090 0.091 0.091 0.091 0.091 0.091 |------------------- ARSTAN CHRONOLOGY AUTOREGRESSIVE MODEL -------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.093 0.303 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.39 MINUTES