RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN027L.rwl.conv LOG FILE PROCESSED: FRAN027L.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: 629 1 Col de Sorba, Mt.Renoso WIDTH_LATE PINI - 629 2 France Austrian pine, black pine 1400 4204-912 1518 1980 - 629 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 3 629021 MISSING VALUES FOUND: 1 IN 1 GAPS / 1919 1919 / -------------------------------------------------------------------- 9 629051 MISSING VALUES FOUND: 2 IN 1 GAPS / 1920 1921 / -------------------------------------------------------------------- 10 629052 MISSING VALUES FOUND: 1 IN 1 GAPS / 1920 1920 / -------------------------------------------------------------------- 11 629061 MISSING VALUES FOUND: 1 IN 1 GAPS / 1882 1882 / -------------------------------------------------------------------- 12 629062 MISSING VALUES FOUND: 1 IN 1 GAPS / 1882 1882 / -------------------------------------------------------------------- 14 629072 MISSING VALUES FOUND: 1 IN 1 GAPS / 1839 1839 / -------------------------------------------------------------------- 15 629081 MISSING VALUES FOUND: 1 IN 1 GAPS / 1920 1920 / -------------------------------------------------------------------- 16 629082 MISSING VALUES FOUND: 1 IN 1 GAPS / 1920 1920 / -------------------------------------------------------------------- 17 629091 MISSING VALUES FOUND: 4 IN 3 GAPS / 1664 1665 / 1707 1707 / 1720 1720 / -------------------------------------------------------------------- 18 629092 MISSING VALUES FOUND: 1 IN 1 GAPS / 1651 1651 / -------------------------------------------------------------------- 19 629111 MISSING VALUES FOUND: 5 IN 3 GAPS / 1575 1575 / 1730 1730 / 1945 1947 / -------------------------------------------------------------------- 20 629112 MISSING VALUES FOUND: 3 IN 2 GAPS / 1575 1575 / 1733 1734 / -------------------------------------------------------------------- 23 629131 MISSING VALUES FOUND: 2 IN 1 GAPS / 1857 1858 / -------------------------------------------------------------------- 24 629132 MISSING VALUES FOUND: 2 IN 1 GAPS / 1855 1856 / -------------------------------------------------------------------- 26 629142 MISSING VALUES FOUND: 2 IN 2 GAPS / 1823 1823 / 1923 1923 / -------------------------------------------------------------------- 30 629162 MISSING VALUES FOUND: 2 IN 1 GAPS / 1803 1804 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 629011 1865 1980 116 1.296 0.651 0.310 2.481 0.227 0.822 2 629012 1834 1980 147 0.650 0.336 1.178 4.242 0.246 0.804 3 629021 1872 1980 109 0.757 0.566 0.986 3.400 0.271 0.805 4 629022 1868 1980 113 0.868 0.481 0.576 2.756 0.274 0.783 5 629031 1854 1980 127 1.019 0.526 0.997 3.767 0.267 0.749 6 629032 1852 1980 129 0.960 0.481 0.911 3.509 0.266 0.718 7 629041 1857 1980 124 0.872 0.438 1.136 4.403 0.258 0.750 8 629042 1853 1980 128 0.888 0.424 0.629 2.752 0.245 0.788 9 629051 1862 1980 119 0.808 0.495 1.373 4.851 0.342 0.731 10 629052 1853 1980 128 0.672 0.428 0.852 3.693 0.378 0.736 11 629061 1848 1980 133 0.596 0.340 0.345 2.063 0.269 0.843 12 629062 1848 1980 133 0.645 0.425 0.879 3.097 0.303 0.814 13 629071 1767 1980 214 0.587 0.321 1.306 4.123 0.285 0.754 14 629072 1788 1980 193 0.665 0.408 1.036 3.763 0.315 0.791 15 629081 1830 1980 151 0.591 0.366 1.081 3.590 0.285 0.760 16 629082 1841 1980 140 0.828 0.535 1.070 3.364 0.276 0.824 17 629091 1526 1836 311 0.359 0.264 1.644 6.195 0.340 0.754 18 629092 1541 1890 350 0.294 0.193 1.942 8.300 0.348 0.693 19 629111 1518 1980 463 0.261 0.191 2.364 10.532 0.304 0.792 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 629112 1547 1980 434 0.350 0.226 1.556 5.695 0.318 0.750 21 629121 1689 1980 292 0.338 0.255 1.631 6.054 0.383 0.718 22 629122 1791 1980 190 0.652 0.463 1.056 3.854 0.361 0.795 23 629131 1634 1980 347 0.405 0.241 1.523 5.894 0.324 0.675 24 629132 1622 1980 359 0.365 0.242 1.733 6.567 0.318 0.704 25 629141 1700 1943 244 0.370 0.264 1.522 5.994 0.373 0.745 26 629142 1711 1943 233 0.442 0.339 3.163 16.637 0.391 0.711 27 629151 1771 1980 210 0.644 0.559 2.032 8.111 0.369 0.834 28 629152 1761 1980 220 0.675 0.494 1.605 5.924 0.341 0.775 29 629161 1722 1980 259 0.412 0.288 1.265 4.424 0.326 0.784 30 629162 1763 1980 218 0.514 0.359 0.963 3.368 0.319 0.817 NUMBER OF SERIES READ IN: 30 FROM 1518 TO 1980 463 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 210 0.626 0.387 1.289 5.113 0.311 0.767 STANDARD DEVIATION 99 0.246 0.123 0.593 2.896 0.046 0.044 MEDIAN (50TH QUANTILE) 191 0.645 0.387 1.157 4.183 0.317 0.768 INTERQUARTILE RANGE 131 0.403 0.216 0.642 2.594 0.071 0.068 MINIMUM VALUE 107 0.261 0.191 0.310 2.063 0.227 0.675 LOWER HINGE (25TH QUANTILE) 128 0.405 0.264 0.963 3.400 0.271 0.736 UPPER HINGE (75TH QUANTILE) 259 0.808 0.481 1.605 5.994 0.342 0.804 MAXIMUM VALUE 458 1.296 0.651 3.163 16.637 0.391 0.843 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 420 0.453 0.226 0.011 -0.471 2.927 -0.490 0.865 MINIMUM CORRELATION: -0.490 SERIES 629061 AND 629092 43 YEARS MAXIMUM CORRELATION: 0.865 SERIES 629081 AND 629082 140 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 96.55 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 30.19 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1570. 1595. 1620. 1645. 1670. 1695. 1720. 1745. 1770. 1795. CORR 3. 6. 6. 6. 15. 15. 21. 36. 45. 78. RBAR 0.427 0.587 0.334 0.431 0.249 0.356 0.303 0.449 0.480 0.388 SDEV 0.178 0.175 0.268 0.184 0.309 0.222 0.240 0.161 0.161 0.185 SERR 0.103 0.071 0.109 0.075 0.080 0.057 0.052 0.027 0.024 0.021 EPS 0.747 0.851 0.701 0.811 0.669 0.799 0.797 0.894 0.921 0.906 NSS 4.0 4.0 4.7 5.7 6.1 7.2 9.0 10.3 12.6 15.2 YEAR 1820. 1845. 1870. 1895. 1920. 1945. CORR 105. 105. 136. 351. 325. 325. RBAR 0.350 0.478 0.361 0.371 0.503 0.374 SDEV 0.242 0.209 0.250 0.208 0.186 0.242 SERR 0.024 0.020 0.021 0.011 0.010 0.013 EPS 0.898 0.949 0.937 0.944 0.966 0.941 NSS 16.4 20.2 26.2 28.4 28.0 27.0 |======================== 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 1518 1980 463 0.462 0.225 1.061 3.969 0.234 0.794 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.680 0.491 0.016 149 314 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.84 2.10 1.00 1.19 3.29 261.70 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.14 0.00 0.86 1.00 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 192. 131. 109. 128. 259. 463. |----------- 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 0.792 0.708 0.644 0.635 0.556 0.518 0.481 0.489 0.453 0.449 PACF 0.792 0.216 0.092 0.176 -0.087 0.035 0.022 0.109 -0.008 0.062 95% C.L. 0.093 0.140 0.168 0.188 0.206 0.218 0.229 0.237 0.246 0.253 |------------------ 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 5 0.665 0.603 0.131 -0.007 0.224 -0.082 |================== 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 629011 3 0.00000000 0.00000000 -0.01474094 2.15837932 2 629012 3 0.00000000 0.00000000 -0.00399179 0.94546080 3 629021 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 629022 3 0.00000000 0.00000000 -0.01043000 1.46229768 5 629031 3 0.00000000 0.00000000 -0.00941829 1.62166858 6 629032 3 0.00000000 0.00000000 -0.00985767 1.60098112 7 629041 3 0.00000000 0.00000000 -0.00967235 1.47686076 8 629042 3 0.00000000 0.00000000 -0.00830048 1.42374015 9 629051 1 1.55443084 0.01559461 0.00000000 0.09745092 10 629052 3 0.00000000 0.00000000 -0.00562948 1.03202295 11 629061 3 0.00000000 0.00000000 -0.00729941 1.08543801 12 629062 3 0.00000000 0.00000000 -0.00870276 1.22913635 13 629071 3 0.00000000 0.00000000 -0.00273936 0.88139659 14 629072 3 0.00000000 0.00000000 -0.00483507 1.13261318 15 629081 3 0.00000000 0.00000000 -0.00558497 1.01388001 16 629082 3 0.00000000 0.00000000 -0.00875832 1.44272923 17 629091 1 0.74977350 0.01275962 0.00000000 0.17345057 18 629092 1 0.23141846 0.02029005 0.00000000 0.26165557 19 629111 1 0.55744767 0.01018642 0.00000000 0.14245062 SERIES IDENT OPTION A B C D 20 629112 1 0.49448356 0.00901621 0.00000000 0.22655541 21 629121 3 0.00000000 0.00000000 0.00025829 0.30044767 22 629122 3 0.00000000 0.00000000 -0.00108454 0.75567919 23 629131 3 0.00000000 0.00000000 -0.00040813 0.47386524 24 629132 1 0.64895904 0.13074742 0.00000000 0.35120523 25 629141 3 0.00000000 0.00000000 -0.00208809 0.62599576 26 629142 1 2.15558505 0.15336315 0.00000000 0.38344005 27 629151 3 0.00000000 0.00000000 -0.00350645 1.01416910 28 629152 3 0.00000000 0.00000000 -0.00387886 1.10406852 29 629161 3 0.00000000 0.00000000 -0.00158848 0.61800843 30 629162 3 0.00000000 0.00000000 -0.00446704 1.00764942 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 629011 1865 1980 116 0.984 0.336 1.367 5.716 0.226 0.587 2 629012 1834 1980 147 0.988 0.410 1.278 4.865 0.244 0.713 3 629021 1872 1980 109 1.001 0.346 0.334 2.922 0.267 0.527 4 629022 1868 1980 113 0.988 0.374 0.411 2.892 0.271 0.645 5 629031 1854 1980 127 1.001 0.379 0.990 3.795 0.266 0.608 6 629032 1852 1980 129 1.008 0.294 0.061 2.371 0.264 0.399 7 629041 1857 1980 124 1.011 0.277 0.336 2.615 0.256 0.391 8 629042 1853 1980 128 0.996 0.312 0.595 3.043 0.242 0.569 9 629051 1862 1980 119 1.001 0.404 1.405 6.528 0.339 0.389 10 629052 1853 1980 128 0.981 0.559 0.922 3.287 0.377 0.668 11 629061 1848 1980 133 1.012 0.345 0.267 3.302 0.268 0.606 12 629062 1848 1980 133 1.113 0.788 4.287 27.804 0.304 0.490 13 629071 1767 1980 214 1.000 0.423 0.815 3.144 0.284 0.617 14 629072 1788 1980 193 1.034 0.537 1.441 7.793 0.315 0.633 15 629081 1830 1980 151 1.023 0.481 0.989 3.540 0.282 0.705 16 629082 1841 1980 140 1.010 0.469 1.077 3.677 0.271 0.704 17 629091 1526 1836 311 1.000 0.497 0.931 4.199 0.337 0.607 18 629092 1541 1890 350 0.999 0.655 2.392 11.822 0.345 0.680 19 629111 1518 1980 463 0.999 0.418 0.846 3.592 0.309 0.572 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 629112 1547 1980 434 1.000 0.563 1.915 8.455 0.318 0.638 21 629121 1689 1980 292 1.000 0.749 1.714 6.920 0.382 0.693 22 629122 1791 1980 190 0.999 0.711 1.142 4.161 0.360 0.795 23 629131 1634 1980 347 1.000 0.582 1.231 4.421 0.331 0.680 24 629132 1622 1980 359 1.000 0.651 1.850 7.398 0.317 0.714 25 629141 1700 1943 244 1.012 0.580 1.225 4.730 0.372 0.647 26 629142 1711 1943 233 1.001 0.564 1.454 5.157 0.392 0.586 27 629151 1771 1980 210 0.970 0.821 2.787 13.463 0.367 0.819 28 629152 1761 1980 220 0.988 0.650 2.730 14.394 0.340 0.663 29 629161 1722 1980 259 0.974 0.583 1.137 4.068 0.326 0.706 30 629162 1763 1980 218 1.089 0.604 2.123 9.692 0.315 0.741 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 211 1.006 0.512 1.335 6.326 0.310 0.626 STANDARD DEVIATION 100 0.029 0.151 0.885 5.160 0.046 0.107 MEDIAN (50TH QUANTILE) 191 1.000 0.517 1.184 4.310 0.315 0.642 INTERQUARTILE RANGE 131 0.014 0.225 0.868 4.096 0.072 0.118 MINIMUM VALUE 109 0.970 0.277 0.061 2.371 0.226 0.389 LOWER HINGE (25TH QUANTILE) 128 0.996 0.379 0.846 3.302 0.268 0.586 UPPER HINGE (75TH QUANTILE) 259 1.010 0.604 1.714 7.398 0.340 0.704 MAXIMUM VALUE 463 1.113 0.821 4.287 27.804 0.392 0.819 |------------------------ 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 629011 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 629012 -67 98 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 629021 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 629022 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 629031 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 629032 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 629041 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 629042 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 629051 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 629052 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 629061 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 629062 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 629071 -67 143 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 629072 -67 129 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 629081 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 629082 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 629091 -67 208 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 629092 -67 234 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 629111 -67 310 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 629112 -67 290 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 629121 -67 195 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 629122 -67 127 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 629131 -67 232 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 629132 -67 240 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 25 629141 -67 163 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 26 629142 -67 156 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 27 629151 -67 140 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 28 629152 -67 147 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 29 629161 -67 173 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 30 629162 -67 146 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 629011 1865 1980 116 0.998 0.304 1.207 5.615 0.226 0.523 2 629012 1834 1980 147 0.990 0.299 1.099 5.213 0.243 0.514 3 629021 1872 1980 109 0.997 0.338 0.374 3.023 0.267 0.512 4 629022 1868 1980 113 0.994 0.345 0.422 3.484 0.271 0.592 5 629031 1854 1980 127 0.993 0.325 0.615 3.270 0.264 0.483 6 629032 1852 1980 129 0.998 0.284 0.132 2.394 0.264 0.374 7 629041 1857 1980 124 0.999 0.261 0.308 2.751 0.256 0.329 8 629042 1853 1980 128 0.993 0.260 0.413 2.880 0.243 0.359 9 629051 1862 1980 119 0.998 0.397 1.318 6.016 0.339 0.373 10 629052 1853 1980 128 0.995 0.492 0.541 2.651 0.377 0.577 11 629061 1848 1980 133 0.996 0.319 0.155 3.254 0.268 0.550 12 629062 1848 1980 133 0.985 0.378 0.878 5.000 0.302 0.412 13 629071 1767 1980 214 0.987 0.345 0.634 3.593 0.283 0.489 14 629072 1788 1980 193 0.982 0.397 0.614 3.381 0.314 0.504 15 629081 1830 1980 151 0.984 0.386 0.586 2.629 0.281 0.597 16 629082 1841 1980 140 0.985 0.387 0.808 3.383 0.272 0.610 17 629091 1526 1836 311 0.994 0.478 0.910 4.188 0.337 0.583 18 629092 1541 1890 350 0.991 0.580 1.598 6.619 0.346 0.636 19 629111 1518 1980 463 0.996 0.391 0.722 3.503 0.309 0.526 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 629112 1547 1980 434 0.989 0.487 1.422 5.931 0.318 0.589 21 629121 1689 1980 292 0.980 0.660 1.331 4.977 0.381 0.652 22 629122 1791 1980 190 0.976 0.604 0.982 3.854 0.359 0.713 23 629131 1634 1980 347 0.996 0.566 1.189 4.282 0.331 0.676 24 629132 1622 1980 359 0.991 0.617 1.705 6.468 0.317 0.703 25 629141 1700 1943 244 0.986 0.515 0.943 3.601 0.372 0.591 26 629142 1711 1943 233 0.996 0.516 1.317 4.819 0.392 0.534 27 629151 1771 1980 210 1.000 0.693 1.822 6.919 0.366 0.717 28 629152 1761 1980 220 0.992 0.614 2.292 10.591 0.340 0.596 29 629161 1722 1980 259 0.991 0.449 1.179 5.269 0.325 0.544 30 629162 1763 1980 218 0.994 0.418 0.766 3.999 0.315 0.553 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 211 0.992 0.437 0.943 4.452 0.309 0.547 STANDARD DEVIATION 100 0.006 0.125 0.516 1.740 0.046 0.103 MEDIAN (50TH QUANTILE) 191 0.993 0.397 0.894 3.926 0.315 0.551 INTERQUARTILE RANGE 131 0.009 0.178 0.730 1.999 0.072 0.092 MINIMUM VALUE 109 0.976 0.260 0.132 2.394 0.226 0.329 LOWER HINGE (25TH QUANTILE) 128 0.987 0.338 0.586 3.270 0.268 0.504 UPPER HINGE (75TH QUANTILE) 259 0.996 0.516 1.317 5.269 0.340 0.597 MAXIMUM VALUE 463 1.000 0.693 2.292 10.591 0.392 0.717 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 420 0.321 0.153 0.007 -0.541 4.056 -0.388 0.783 MINIMUM CORRELATION: -0.388 SERIES 629061 AND 629092 43 YEARS MAXIMUM CORRELATION: 0.783 SERIES 629081 AND 629082 140 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 96.55 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 30.19 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1570. 1595. 1620. 1645. 1670. 1695. 1720. 1745. 1770. 1795. CORR 3. 6. 6. 6. 15. 15. 21. 36. 45. 78. RBAR 0.544 0.537 0.444 0.385 0.274 0.356 0.293 0.457 0.488 0.393 SDEV 0.133 0.191 0.208 0.178 0.263 0.213 0.215 0.164 0.152 0.197 SERR 0.077 0.078 0.085 0.072 0.068 0.055 0.047 0.027 0.023 0.022 EPS 0.825 0.823 0.789 0.780 0.698 0.799 0.789 0.897 0.923 0.908 NSS 4.0 4.0 4.7 5.7 6.1 7.2 9.0 10.3 12.6 15.2 YEAR 1820. 1845. 1870. 1895. 1920. 1945. CORR 105. 105. 136. 351. 325. 325. RBAR 0.371 0.434 0.406 0.389 0.362 0.280 SDEV 0.210 0.205 0.227 0.200 0.202 0.211 SERR 0.020 0.020 0.019 0.011 0.011 0.012 EPS 0.906 0.939 0.947 0.948 0.941 0.913 NSS 16.4 20.2 26.2 28.4 28.0 27.0 |======================== 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 1518 1980 463 0.962 0.312 0.580 3.061 0.232 0.596 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.518 0.270 0.072 129 334 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.41 1.32 1.00 1.14 2.46 171.06 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.14 0.00 0.86 1.00 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 0.595 0.334 0.272 0.227 0.091 0.049 0.030 0.031 0.025 0.010 PACF 0.595 -0.031 0.133 0.029 -0.118 0.038 -0.028 0.033 0.014 -0.023 95% C.L. 0.093 0.121 0.129 0.134 0.137 0.138 0.138 0.138 0.138 0.138 |------------------ 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 0.355 0.595 |======================= 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 0.568 0.302 0.227 0.179 0.042 0.008 0.004 0.035 0.079 0.094 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 0.568 2 0.585 -0.030 3 0.588 -0.088 0.099 4 0.585 -0.086 0.086 0.023 5 0.588 -0.075 0.075 0.095 -0.122 6 0.592 -0.078 0.073 0.097 -0.140 0.030 7 0.592 -0.080 0.074 0.098 -0.141 0.037 -0.011 8 0.593 -0.082 0.082 0.092 -0.145 0.041 -0.047 0.061 9 0.588 -0.078 0.079 0.103 -0.152 0.035 -0.041 0.016 0.076 10 0.587 -0.079 0.080 0.102 -0.150 0.033 -0.042 0.017 0.067 0.016 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) 4267.92 4089.83 4091.41 4088.83 4090.58 4085.62 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 4087.20 4089.15 4089.41 4088.71 4090.59 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 0.568 R-SQUARED DUE TO POOLED AUTOREGRESSION: 32.22 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 147.55 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.568 0.322 0.183 0.104 0.059 0.033 0.019 0.011 0.006 0.0035 0.002 0.001 0.001 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 629011 1 0.297 0.523 2 629012 1 0.274 0.521 3 629021 1 0.280 0.523 4 629022 1 0.411 0.600 5 629031 1 0.236 0.484 6 629032 1 0.147 0.380 7 629041 1 0.118 0.329 8 629042 1 0.136 0.362 9 629051 1 0.140 0.374 10 629052 1 0.335 0.578 11 629061 1 0.308 0.550 12 629062 1 0.205 0.438 13 629071 1 0.243 0.492 14 629072 1 0.258 0.508 15 629081 1 0.364 0.599 16 629082 1 0.378 0.614 17 629091 1 0.346 0.586 18 629092 1 0.430 0.652 19 629111 1 0.279 0.527 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 629112 1 0.351 0.589 21 629121 1 0.443 0.666 22 629122 1 0.539 0.715 23 629131 1 0.470 0.686 24 629132 1 0.494 0.703 25 629141 1 0.355 0.593 26 629142 1 0.291 0.535 27 629151 1 0.522 0.722 28 629152 1 0.386 0.616 29 629161 1 0.298 0.546 30 629162 1 0.308 0.555 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.321 0.552 STANDARD DEVIATION 0 0.112 0.103 MEDIAN 1 0.308 0.553 INTERQUARTILE RANGE 0 0.128 0.107 MINIMUM VALUE 1 0.118 0.329 LOWER HINGE 1 0.258 0.508 UPPER HINGE 1 0.386 0.614 MAXIMUM VALUE 1 0.539 0.722 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 629011 1865 1980 116 1.000 0.259 1.056 6.071 0.283 -0.093 2 629012 1834 1980 147 1.000 0.255 0.576 3.961 0.288 0.037 3 629021 1872 1980 109 1.000 0.287 0.369 3.109 0.319 0.038 4 629022 1868 1980 113 1.000 0.276 0.447 3.025 0.329 -0.166 5 629031 1854 1980 127 1.000 0.284 0.221 2.840 0.324 -0.021 6 629032 1852 1980 129 1.000 0.263 0.192 2.360 0.309 -0.028 7 629041 1857 1980 124 1.000 0.247 0.349 2.948 0.293 -0.033 8 629042 1853 1980 128 1.000 0.242 0.494 2.986 0.280 -0.030 9 629051 1862 1980 119 1.000 0.368 1.335 5.859 0.386 0.006 10 629052 1853 1980 128 1.001 0.399 0.190 2.726 0.471 -0.017 11 629061 1848 1980 133 1.000 0.266 0.124 3.093 0.312 0.048 12 629062 1848 1980 133 1.000 0.340 1.299 6.932 0.338 -0.024 13 629071 1767 1980 214 1.000 0.300 0.588 3.493 0.340 -0.009 14 629072 1788 1980 193 1.001 0.340 0.382 3.376 0.369 0.003 15 629081 1830 1980 151 1.000 0.309 0.237 3.417 0.353 -0.053 16 629082 1841 1980 140 1.000 0.306 0.646 3.384 0.336 0.026 17 629091 1526 1836 311 1.000 0.387 0.848 4.217 0.420 -0.032 18 629092 1541 1890 350 1.000 0.439 1.226 5.304 0.446 -0.040 19 629111 1518 1980 463 1.000 0.333 0.646 3.814 0.372 -0.027 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 629112 1547 1980 434 1.001 0.391 1.466 7.692 0.396 -0.036 21 629121 1689 1980 292 1.004 0.479 1.236 6.282 0.455 0.042 22 629122 1791 1980 190 1.000 0.422 0.764 3.822 0.424 0.171 23 629131 1634 1980 347 1.002 0.404 0.844 4.442 0.409 0.007 24 629132 1622 1980 359 1.001 0.435 1.333 7.001 0.441 0.001 25 629141 1700 1943 244 1.000 0.415 0.742 3.686 0.444 0.038 26 629142 1711 1943 233 1.000 0.436 0.995 4.278 0.456 0.044 27 629151 1771 1980 210 1.003 0.474 1.674 8.465 0.467 -0.005 28 629152 1761 1980 220 1.002 0.479 1.346 6.436 0.444 0.088 29 629161 1722 1980 259 1.000 0.376 0.958 4.862 0.394 0.002 30 629162 1763 1980 218 1.000 0.348 0.610 4.008 0.386 -0.001 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 211 1.000 0.352 0.773 4.463 0.376 -0.002 STANDARD DEVIATION 100 0.001 0.075 0.440 1.643 0.061 0.057 MEDIAN (50TH QUANTILE) 191 1.000 0.344 0.694 3.891 0.379 -0.003 INTERQUARTILE RANGE 131 0.001 0.130 0.844 2.750 0.117 0.066 MINIMUM VALUE 109 1.000 0.242 0.124 2.360 0.280 -0.166 LOWER HINGE (25TH QUANTILE) 128 1.000 0.284 0.382 3.109 0.324 -0.030 UPPER HINGE (75TH QUANTILE) 259 1.001 0.415 1.226 5.859 0.441 0.037 MAXIMUM VALUE 463 1.004 0.479 1.674 8.465 0.471 0.171 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 420 0.346 0.118 0.006 -0.270 3.097 -0.018 0.700 MINIMUM CORRELATION: -0.018 SERIES 629011 AND 629142 79 YEARS MAXIMUM CORRELATION: 0.700 SERIES 629161 AND 629162 218 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 96.55 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 30.19 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1570. 1595. 1620. 1645. 1670. 1695. 1720. 1745. 1770. 1795. CORR 3. 6. 6. 6. 15. 15. 21. 36. 45. 78. RBAR 0.249 0.236 0.196 0.265 0.298 0.346 0.371 0.495 0.481 0.422 SDEV 0.395 0.377 0.414 0.248 0.197 0.177 0.183 0.124 0.139 0.149 SERR 0.228 0.154 0.169 0.101 0.051 0.046 0.040 0.021 0.021 0.017 EPS 0.567 0.553 0.533 0.671 0.723 0.792 0.842 0.910 0.921 0.917 NSS 4.0 4.0 4.7 5.7 6.1 7.2 9.0 10.3 12.6 15.2 YEAR 1820. 1845. 1870. 1895. 1920. 1945. CORR 105. 105. 136. 351. 325. 325. RBAR 0.448 0.508 0.434 0.382 0.362 0.329 SDEV 0.131 0.117 0.135 0.142 0.138 0.157 SERR 0.013 0.011 0.012 0.008 0.008 0.009 EPS 0.930 0.954 0.953 0.946 0.941 0.930 NSS 16.4 20.2 26.2 28.4 28.0 27.0 |======================== 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 1518 1980 463 0.984 0.243 0.413 3.340 0.272 0.024 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.410 0.247 0.026 135 328 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.53 1.09 1.00 1.12 2.22 123.00 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.14 0.00 0.86 1.00 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 0.023 -0.111 0.058 0.156 -0.030 -0.034 -0.021 0.030 0.025 0.007 PACF 0.023 -0.112 0.064 0.142 -0.026 -0.005 -0.044 0.010 0.030 0.019 95% C.L. 0.093 0.093 0.094 0.094 0.097 0.097 0.097 0.097 0.097 0.097 |------------------ 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 2 0.017 0.026 -0.112 |---------- 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 0.003 -0.113 0.057 0.155 -0.033 -0.033 -0.021 0.030 0.025 0.007 PACF 0.003 -0.113 0.058 0.144 -0.023 -0.005 -0.045 0.008 0.030 0.020 95% C.L. 0.093 0.093 0.094 0.094 0.097 0.097 0.097 0.097 0.097 0.097 |----------------- 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 0.013 0.003 |========================= 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 1518 1980 463 0.984 0.292 0.633 3.178 0.218 0.555 |------------ 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 0.553 0.287 0.252 0.232 0.096 0.033 0.020 0.040 0.036 0.013 PACF 0.553 -0.029 0.152 0.053 -0.106 -0.002 -0.018 0.043 0.016 -0.014 95% C.L. 0.093 0.118 0.124 0.128 0.132 0.132 0.133 0.133 0.133 0.133 |------------------- 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 0.307 0.554 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.65 MINUTES