RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN027E.rwl.conv LOG FILE PROCESSED: FRAN027E.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_EARLY 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 1.597 0.749 0.717 2.934 0.260 0.725 2 629012 1834 1980 147 1.348 0.720 0.759 2.883 0.186 0.849 3 629021 1872 1980 109 0.921 0.544 1.128 4.087 0.208 0.814 4 629022 1868 1980 113 0.842 0.481 0.324 1.869 0.250 0.872 5 629031 1854 1980 127 1.620 0.711 0.763 2.695 0.181 0.860 6 629032 1852 1980 129 1.695 0.870 1.318 4.390 0.190 0.868 7 629041 1857 1980 124 1.048 0.820 2.260 9.320 0.230 0.844 8 629042 1853 1980 128 1.294 0.598 2.539 11.260 0.192 0.775 9 629051 1862 1980 119 0.882 0.557 1.850 7.538 0.250 0.730 10 629052 1853 1980 128 0.983 0.671 0.934 3.564 0.296 0.845 11 629061 1848 1980 133 1.134 1.001 2.294 9.019 0.205 0.887 12 629062 1848 1980 133 1.223 1.066 2.389 8.913 0.209 0.901 13 629071 1767 1980 214 0.961 0.390 0.905 3.702 0.201 0.796 14 629072 1788 1980 193 0.995 0.480 1.210 5.871 0.202 0.835 15 629081 1830 1980 151 0.911 0.843 2.800 13.473 0.223 0.703 16 629082 1841 1980 140 0.848 0.475 1.666 5.939 0.191 0.835 17 629091 1526 1836 311 0.675 0.484 1.848 7.054 0.252 0.897 18 629092 1541 1890 350 0.507 0.250 0.855 3.550 0.238 0.820 19 629111 1518 1980 463 0.482 0.291 1.654 7.489 0.242 0.850 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 629112 1547 1980 434 0.422 0.215 1.418 5.909 0.234 0.784 21 629121 1689 1980 292 0.561 0.223 0.530 3.902 0.248 0.687 22 629122 1791 1980 190 0.704 0.314 0.772 3.189 0.268 0.744 23 629131 1634 1980 347 0.561 0.284 1.298 6.605 0.267 0.807 24 629132 1622 1980 359 0.494 0.289 1.733 10.155 0.250 0.776 25 629141 1700 1943 244 0.622 0.317 0.844 3.465 0.243 0.809 26 629142 1711 1943 233 0.620 0.357 1.517 5.605 0.256 0.821 27 629151 1771 1980 210 0.654 0.403 1.108 4.274 0.306 0.813 28 629152 1761 1980 220 0.695 0.340 0.985 4.453 0.270 0.731 29 629161 1722 1980 259 0.881 0.407 1.085 4.832 0.196 0.832 30 629162 1763 1980 218 0.945 0.403 0.761 3.093 0.200 0.801 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 0.904 0.518 1.342 5.701 0.232 0.810 STANDARD DEVIATION 99 0.347 0.237 0.640 2.861 0.034 0.057 MEDIAN (50TH QUANTILE) 191 0.882 0.477 1.169 4.643 0.236 0.817 INTERQUARTILE RANGE 131 0.426 0.394 0.889 3.939 0.051 0.073 MINIMUM VALUE 107 0.422 0.215 0.324 1.869 0.181 0.687 LOWER HINGE (25TH QUANTILE) 128 0.622 0.317 0.844 3.550 0.201 0.776 UPPER HINGE (75TH QUANTILE) 259 1.048 0.711 1.733 7.489 0.252 0.849 MAXIMUM VALUE 458 1.695 1.066 2.800 13.473 0.306 0.901 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 420 0.409 0.282 0.014 -0.608 2.839 -0.439 0.938 MINIMUM CORRELATION: -0.439 SERIES 629041 AND 629092 34 YEARS MAXIMUM CORRELATION: 0.938 SERIES 629061 AND 629062 133 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 0.392 0.657 0.460 0.512 0.218 0.261 0.395 0.423 0.357 0.356 SDEV 0.132 0.116 0.177 0.133 0.231 0.171 0.182 0.205 0.210 0.270 SERR 0.076 0.047 0.072 0.054 0.060 0.044 0.040 0.034 0.031 0.031 EPS 0.719 0.885 0.799 0.856 0.630 0.718 0.855 0.884 0.875 0.894 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 0.285 0.434 0.363 0.263 0.443 0.245 SDEV 0.290 0.239 0.266 0.241 0.199 0.275 SERR 0.028 0.023 0.023 0.013 0.011 0.015 EPS 0.867 0.939 0.937 0.910 0.957 0.897 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 0.708 0.303 1.556 6.794 0.143 0.905 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.547 0.406 0.048 141 322 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.51 2.02 1.00 1.13 3.15 31.03 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 0.903 0.827 0.773 0.720 0.680 0.651 0.626 0.599 0.565 0.528 PACF 0.903 0.064 0.083 0.008 0.052 0.061 0.036 0.004 -0.035 -0.032 95% C.L. 0.093 0.151 0.186 0.212 0.232 0.249 0.263 0.275 0.287 0.296 |------------------ 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 1 0.819 0.905 |================== 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 -0.01705812 2.59488297 2 629012 3 0.00000000 0.00000000 -0.01345598 2.34404159 3 629021 3 0.00000000 0.00000000 -0.01389203 1.68064010 4 629022 3 0.00000000 0.00000000 -0.01147922 1.49643970 5 629031 1 2.40691185 0.01824069 0.00000000 0.69244242 6 629032 1 2.93820286 0.03175094 0.00000000 1.00046909 7 629041 1 2.95260978 0.03645088 0.00000000 0.41405708 8 629042 1 3.53616047 0.15653969 0.00000000 1.13111377 9 629051 1 1.72400928 0.02362552 0.00000000 0.30230802 10 629052 3 0.00000000 0.00000000 -0.01461182 1.92001796 11 629061 1 4.34999132 0.06361102 0.00000000 0.63352269 12 629062 1 4.69718647 0.06147606 0.00000000 0.66417450 13 629071 3 0.00000000 0.00000000 -0.00278028 1.26028168 14 629072 3 0.00000000 0.00000000 -0.00489648 1.46935558 15 629081 1 3.19113207 0.04347498 0.00000000 0.43232197 16 629082 1 1.66479445 0.03334963 0.00000000 0.49806178 17 629091 1 1.77846956 0.01932061 0.00000000 0.38099283 18 629092 1 0.68485212 0.02458552 0.00000000 0.42814291 19 629111 1 0.84623504 0.00546447 0.00000000 0.17199361 SERIES IDENT OPTION A B C D 20 629112 1 0.41052967 0.01201554 0.00000000 0.34354967 21 629121 1 0.40587783 0.00939767 0.00000000 0.42327970 22 629122 3 0.00000000 0.00000000 -0.00125200 0.82319802 23 629131 1 1.19050658 0.12346958 0.00000000 0.53260034 24 629132 1 1.89029908 0.16720134 0.00000000 0.46419862 25 629141 3 0.00000000 0.00000000 -0.00295935 0.98469239 26 629142 1 0.93129349 0.01140251 0.00000000 0.29290318 27 629151 3 0.00000000 0.00000000 -0.00379790 1.05472636 28 629152 3 0.00000000 0.00000000 -0.00269012 0.99180323 29 629161 3 0.00000000 0.00000000 -0.00160411 1.08957624 30 629162 3 0.00000000 0.00000000 -0.00372808 1.35438728 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 629011 1865 1980 116 1.012 0.341 1.570 7.342 0.257 0.264 2 629012 1834 1980 147 1.021 0.354 1.283 6.146 0.187 0.696 3 629021 1872 1980 109 1.028 0.305 0.310 3.285 0.205 0.557 4 629022 1868 1980 113 1.032 0.437 0.531 3.643 0.248 0.751 5 629031 1854 1980 127 1.001 0.257 0.888 4.042 0.181 0.595 6 629032 1852 1980 129 0.999 0.269 0.096 2.941 0.187 0.634 7 629041 1857 1980 124 0.992 0.306 -0.027 2.775 0.230 0.582 8 629042 1853 1980 128 1.000 0.279 0.412 2.803 0.191 0.642 9 629051 1862 1980 119 1.001 0.336 0.908 4.151 0.246 0.422 10 629052 1853 1980 128 1.140 0.777 3.234 16.283 0.299 0.750 11 629061 1848 1980 133 0.995 0.491 1.153 3.681 0.207 0.864 12 629062 1848 1980 133 0.997 0.382 1.101 3.953 0.208 0.719 13 629071 1767 1980 214 0.999 0.343 0.406 3.069 0.200 0.732 14 629072 1788 1980 193 1.010 0.394 0.471 3.786 0.199 0.760 15 629081 1830 1980 151 0.992 0.448 0.951 3.176 0.219 0.779 16 629082 1841 1980 140 0.999 0.280 0.754 3.708 0.192 0.613 17 629091 1526 1836 311 0.997 0.379 0.404 3.085 0.253 0.669 18 629092 1541 1890 350 0.999 0.426 0.812 4.638 0.238 0.762 19 629111 1518 1980 463 0.997 0.412 1.857 13.446 0.244 0.684 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 629112 1547 1980 434 1.000 0.450 1.179 4.810 0.237 0.738 21 629121 1689 1980 292 1.000 0.365 0.493 3.162 0.248 0.671 22 629122 1791 1980 190 0.999 0.435 0.779 3.257 0.267 0.723 23 629131 1634 1980 347 1.000 0.456 0.511 3.029 0.271 0.785 24 629132 1622 1980 359 1.000 0.508 0.653 3.400 0.249 0.817 25 629141 1700 1943 244 1.005 0.400 0.929 3.688 0.242 0.695 26 629142 1711 1943 233 0.999 0.414 0.839 3.770 0.264 0.694 27 629151 1771 1980 210 0.978 0.479 1.236 5.211 0.305 0.637 28 629152 1761 1980 220 0.995 0.409 1.488 10.786 0.269 0.567 29 629161 1722 1980 259 0.996 0.422 0.805 4.025 0.195 0.813 30 629162 1763 1980 218 1.000 0.319 0.192 3.211 0.197 0.634 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 211 1.006 0.396 0.874 4.810 0.231 0.675 STANDARD DEVIATION 100 0.027 0.099 0.627 3.192 0.034 0.120 MEDIAN (50TH QUANTILE) 191 1.000 0.397 0.809 3.698 0.237 0.695 INTERQUARTILE RANGE 131 0.004 0.101 0.682 1.462 0.054 0.117 MINIMUM VALUE 109 0.978 0.257 -0.027 2.775 0.181 0.264 LOWER HINGE (25TH QUANTILE) 128 0.997 0.336 0.471 3.176 0.199 0.634 UPPER HINGE (75TH QUANTILE) 259 1.001 0.437 1.153 4.638 0.253 0.751 MAXIMUM VALUE 463 1.140 0.777 3.234 16.283 0.305 0.864 |------------------------ 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 0.999 0.311 1.248 5.855 0.257 0.190 2 629012 1834 1980 147 0.990 0.252 0.509 3.809 0.186 0.504 3 629021 1872 1980 109 0.997 0.273 0.688 4.062 0.205 0.499 4 629022 1868 1980 113 0.988 0.340 0.032 3.200 0.246 0.620 5 629031 1854 1980 127 0.998 0.225 0.348 3.021 0.180 0.511 6 629032 1852 1980 129 0.996 0.244 -0.088 2.836 0.187 0.546 7 629041 1857 1980 124 0.995 0.272 -0.024 2.921 0.229 0.457 8 629042 1853 1980 128 0.996 0.206 -0.159 2.828 0.191 0.374 9 629051 1862 1980 119 0.997 0.325 1.080 4.683 0.245 0.376 10 629052 1853 1980 128 0.995 0.417 0.196 2.554 0.299 0.625 11 629061 1848 1980 133 0.992 0.292 0.011 3.027 0.207 0.647 12 629062 1848 1980 133 0.994 0.285 0.176 2.844 0.209 0.556 13 629071 1767 1980 214 0.991 0.287 0.171 3.027 0.200 0.630 14 629072 1788 1980 193 0.986 0.306 0.403 4.132 0.199 0.644 15 629081 1830 1980 151 0.987 0.314 0.471 3.304 0.218 0.528 16 629082 1841 1980 140 0.996 0.249 0.489 3.331 0.193 0.508 17 629091 1526 1836 311 0.995 0.357 0.263 2.999 0.253 0.633 18 629092 1541 1890 350 0.994 0.399 0.754 4.648 0.238 0.736 19 629111 1518 1980 463 0.994 0.351 1.345 10.007 0.244 0.590 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 629112 1547 1980 434 0.990 0.384 0.935 4.144 0.237 0.678 21 629121 1689 1980 292 0.997 0.356 0.441 3.089 0.248 0.653 22 629122 1791 1980 190 0.994 0.393 0.531 3.042 0.266 0.673 23 629131 1634 1980 347 0.998 0.442 0.462 3.085 0.271 0.774 24 629132 1622 1980 359 0.997 0.500 0.770 3.569 0.249 0.807 25 629141 1700 1943 244 0.995 0.374 0.885 3.785 0.242 0.663 26 629142 1711 1943 233 0.995 0.395 0.806 3.560 0.264 0.650 27 629151 1771 1980 210 0.996 0.438 1.055 4.238 0.305 0.509 28 629152 1761 1980 220 0.996 0.395 1.356 8.666 0.269 0.522 29 629161 1722 1980 259 0.992 0.316 0.956 4.778 0.196 0.652 30 629162 1763 1980 218 0.993 0.294 0.159 3.150 0.197 0.585 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 211 0.994 0.333 0.542 3.940 0.231 0.578 STANDARD DEVIATION 100 0.003 0.071 0.433 1.654 0.034 0.126 MEDIAN (50TH QUANTILE) 191 0.995 0.321 0.480 3.318 0.237 0.605 INTERQUARTILE RANGE 131 0.004 0.108 0.709 1.117 0.054 0.143 MINIMUM VALUE 109 0.986 0.206 -0.159 2.554 0.180 0.190 LOWER HINGE (25TH QUANTILE) 128 0.992 0.285 0.176 3.027 0.199 0.509 UPPER HINGE (75TH QUANTILE) 259 0.996 0.393 0.885 4.144 0.253 0.652 MAXIMUM VALUE 463 0.999 0.500 1.356 10.007 0.305 0.807 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 420 0.267 0.153 0.007 -0.209 3.800 -0.456 0.684 MINIMUM CORRELATION: -0.456 SERIES 629061 AND 629092 43 YEARS MAXIMUM CORRELATION: 0.684 SERIES 629061 AND 629062 133 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 0.580 0.602 0.569 0.471 0.211 0.270 0.389 0.445 0.370 0.359 SDEV 0.076 0.127 0.142 0.134 0.227 0.177 0.162 0.216 0.208 0.304 SERR 0.044 0.052 0.058 0.055 0.059 0.046 0.035 0.036 0.031 0.034 EPS 0.845 0.858 0.861 0.835 0.621 0.727 0.852 0.893 0.881 0.895 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 0.289 0.392 0.416 0.313 0.252 0.229 SDEV 0.264 0.235 0.243 0.202 0.192 0.211 SERR 0.026 0.023 0.021 0.011 0.011 0.012 EPS 0.870 0.929 0.949 0.928 0.904 0.889 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 0.982 0.239 0.499 3.287 0.143 0.717 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.364 0.174 0.093 133 330 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.31 0.85 1.00 1.09 1.94 58.99 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.13 0.00 0.87 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 0.715 0.508 0.368 0.281 0.176 0.125 0.118 0.091 0.068 0.038 PACF 0.715 -0.008 0.016 0.028 -0.077 0.037 0.059 -0.033 0.007 -0.030 95% C.L. 0.093 0.132 0.148 0.156 0.160 0.162 0.163 0.163 0.164 0.164 |------------------ 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 0.512 0.716 |======================= 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 0.676 0.460 0.290 0.177 0.092 0.042 0.076 0.092 0.103 0.097 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 0.676 2 0.671 0.007 3 0.671 0.037 -0.044 4 0.671 0.037 -0.038 -0.009 5 0.670 0.036 -0.037 0.008 -0.025 6 0.670 0.036 -0.037 0.008 -0.023 -0.004 7 0.671 0.039 -0.038 0.012 -0.027 -0.081 0.115 8 0.669 0.040 -0.038 0.012 -0.026 -0.082 0.105 0.015 9 0.669 0.038 -0.036 0.012 -0.026 -0.081 0.104 0.004 0.016 10 0.669 0.038 -0.036 0.012 -0.026 -0.081 0.105 0.004 0.015 0.001 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) 3934.66 3654.40 3656.38 3657.48 3659.44 3661.15 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 3663.14 3658.97 3660.87 3662.75 3664.75 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 0.676 R-SQUARED DUE TO POOLED AUTOREGRESSION: 45.64 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 183.98 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.676 0.456 0.308 0.208 0.141 0.095 0.064 0.043 0.029 0.0198 0.013 0.009 0.006 0.004 0.003 0.002 0.001 0.001 0.001 0.0004 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 0.037 0.191 2 629012 1 0.279 0.523 3 629021 1 0.256 0.504 4 629022 1 0.436 0.621 5 629031 1 0.292 0.517 6 629032 1 0.309 0.549 7 629041 1 0.239 0.467 8 629042 1 0.145 0.375 9 629051 1 0.169 0.381 10 629052 1 0.412 0.636 11 629061 1 0.434 0.651 12 629062 1 0.356 0.556 13 629071 1 0.415 0.644 14 629072 1 0.431 0.652 15 629081 1 0.328 0.531 16 629082 1 0.262 0.511 17 629091 1 0.410 0.635 18 629092 1 0.565 0.749 19 629111 1 0.354 0.590 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 629112 1 0.466 0.679 21 629121 1 0.439 0.662 22 629122 1 0.456 0.675 23 629131 1 0.600 0.775 24 629132 1 0.652 0.807 25 629141 1 0.443 0.665 26 629142 1 0.441 0.653 27 629151 1 0.284 0.511 28 629152 1 0.286 0.532 29 629161 1 0.437 0.661 30 629162 1 0.358 0.590 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.366 0.583 STANDARD DEVIATION 0 0.132 0.126 MEDIAN 1 0.384 0.605 INTERQUARTILE RANGE 0 0.156 0.143 MINIMUM VALUE 1 0.037 0.191 LOWER HINGE 1 0.284 0.517 UPPER HINGE 1 0.439 0.661 MAXIMUM VALUE 1 0.652 0.807 |------------------- 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 0.305 1.174 6.047 0.283 -0.002 2 629012 1834 1980 147 1.000 0.214 0.276 4.094 0.234 -0.046 3 629021 1872 1980 109 1.000 0.236 0.354 4.279 0.253 -0.029 4 629022 1868 1980 113 1.000 0.267 0.638 5.206 0.309 -0.177 5 629031 1854 1980 127 1.000 0.192 0.205 3.040 0.219 0.099 6 629032 1852 1980 129 1.000 0.204 0.315 2.889 0.221 -0.057 7 629041 1857 1980 124 1.000 0.240 0.015 3.336 0.282 -0.070 8 629042 1853 1980 128 1.000 0.191 -0.104 3.116 0.225 -0.027 9 629051 1862 1980 119 1.000 0.300 1.237 5.837 0.304 -0.063 10 629052 1853 1980 128 1.000 0.321 0.641 3.844 0.353 -0.068 11 629061 1848 1980 133 1.000 0.221 0.119 4.140 0.252 -0.093 12 629062 1848 1980 133 1.000 0.237 0.148 3.404 0.261 -0.143 13 629071 1767 1980 214 1.000 0.219 0.157 3.056 0.243 0.005 14 629072 1788 1980 193 1.000 0.231 0.334 4.072 0.259 -0.074 15 629081 1830 1980 151 1.000 0.266 0.806 7.119 0.270 -0.135 16 629082 1841 1980 140 1.000 0.214 0.140 3.829 0.247 -0.025 17 629091 1526 1836 311 1.000 0.276 0.279 3.549 0.320 -0.068 18 629092 1541 1890 350 1.000 0.264 0.614 3.783 0.297 -0.061 19 629111 1518 1980 463 1.000 0.283 1.644 14.924 0.293 -0.057 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 629112 1547 1980 434 1.000 0.281 0.571 4.854 0.306 -0.061 21 629121 1689 1980 292 1.000 0.265 0.141 2.979 0.320 -0.045 22 629122 1791 1980 190 1.000 0.290 0.364 3.574 0.330 0.018 23 629131 1634 1980 347 1.000 0.280 0.275 3.172 0.317 0.004 24 629132 1622 1980 359 1.000 0.295 0.957 4.879 0.308 0.033 25 629141 1700 1943 244 1.000 0.279 0.346 4.067 0.304 0.001 26 629142 1711 1943 233 1.000 0.298 0.503 3.751 0.304 0.100 27 629151 1771 1980 210 1.002 0.369 0.837 5.395 0.367 -0.072 28 629152 1761 1980 220 1.000 0.333 1.727 11.784 0.330 -0.030 29 629161 1722 1980 259 1.000 0.236 0.536 4.694 0.248 0.013 30 629162 1763 1980 218 1.000 0.237 0.546 5.706 0.261 -0.076 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 211 1.000 0.261 0.527 4.814 0.284 -0.040 STANDARD DEVIATION 100 0.000 0.043 0.450 2.577 0.039 0.061 MEDIAN (50TH QUANTILE) 191 1.000 0.266 0.359 4.069 0.288 -0.051 INTERQUARTILE RANGE 131 0.000 0.059 0.435 1.802 0.056 0.071 MINIMUM VALUE 109 1.000 0.191 -0.104 2.889 0.219 -0.177 LOWER HINGE (25TH QUANTILE) 128 1.000 0.231 0.205 3.404 0.252 -0.070 UPPER HINGE (75TH QUANTILE) 259 1.000 0.290 0.641 5.206 0.309 0.001 MAXIMUM VALUE 463 1.002 0.369 1.727 14.924 0.367 0.100 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 420 0.242 0.116 0.006 0.138 2.966 -0.092 0.550 MINIMUM CORRELATION: -0.092 SERIES 629042 AND 629092 38 YEARS MAXIMUM CORRELATION: 0.550 SERIES 629081 AND 629121 151 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 0.293 0.278 0.211 0.198 0.170 0.182 0.315 0.394 0.372 0.322 SDEV 0.245 0.300 0.343 0.236 0.164 0.183 0.178 0.120 0.134 0.177 SERR 0.142 0.122 0.140 0.097 0.042 0.047 0.039 0.020 0.020 0.020 EPS 0.622 0.606 0.555 0.583 0.556 0.616 0.806 0.871 0.882 0.879 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 0.302 0.332 0.368 0.260 0.173 0.259 SDEV 0.160 0.146 0.145 0.157 0.154 0.155 SERR 0.016 0.014 0.012 0.008 0.009 0.009 EPS 0.877 0.910 0.938 0.909 0.854 0.904 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 0.993 0.159 0.295 3.291 0.168 0.100 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.247 0.160 0.045 147 316 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.26 0.72 1.00 1.10 1.83 11.14 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.15 0.00 0.85 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 0.099 0.024 0.055 0.065 -0.021 -0.023 0.058 0.050 0.021 0.006 PACF 0.099 0.014 0.051 0.055 -0.035 -0.023 0.058 0.040 0.017 -0.003 95% C.L. 0.093 0.094 0.094 0.094 0.095 0.095 0.095 0.095 0.095 0.095 |------------------ 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 1 0.010 0.100 |---------- 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 0.009 0.047 0.063 -0.026 -0.027 0.056 0.043 0.016 0.006 PACF -0.001 0.009 0.047 0.063 -0.026 -0.031 0.051 0.043 0.022 0.003 95% C.L. 0.093 0.093 0.093 0.093 0.094 0.094 0.094 0.094 0.094 0.094 |----------------- 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 0.000 -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 1518 1980 463 0.992 0.221 0.343 2.958 0.136 0.700 |------------ 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 0.698 0.506 0.386 0.291 0.193 0.145 0.142 0.117 0.079 0.040 PACF 0.698 0.037 0.039 -0.002 -0.050 0.030 0.065 -0.014 -0.030 -0.035 95% C.L. 0.093 0.131 0.147 0.155 0.160 0.162 0.163 0.164 0.165 0.165 |------------------- 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 0.488 0.698 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.39 MINUTES