RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN027W.rwl.conv LOG FILE PROCESSED: FRAN027W.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_RING 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 2.893 1.309 0.290 2.022 0.212 0.822 2 629012 1834 1980 147 1.998 0.982 0.632 2.530 0.175 0.883 3 629021 1872 1980 109 1.678 1.051 0.727 2.501 0.165 0.894 4 629022 1868 1980 113 1.711 0.920 0.355 2.067 0.209 0.885 5 629031 1854 1980 127 2.639 1.163 0.664 2.635 0.178 0.857 6 629032 1852 1980 129 2.655 1.284 1.111 3.588 0.180 0.862 7 629041 1857 1980 124 1.921 1.203 1.763 7.261 0.207 0.852 8 629042 1853 1980 128 2.183 0.895 1.057 4.502 0.187 0.787 9 629051 1862 1980 119 1.690 0.995 1.417 5.135 0.246 0.789 10 629052 1853 1980 128 1.656 1.007 0.538 2.614 0.269 0.852 11 629061 1848 1980 133 1.729 1.276 1.552 5.666 0.185 0.898 12 629062 1848 1980 133 1.869 1.397 1.608 5.277 0.198 0.907 13 629071 1767 1980 214 1.548 0.677 1.061 3.747 0.188 0.832 14 629072 1788 1980 193 1.659 0.854 0.950 3.846 0.214 0.858 15 629081 1830 1980 151 1.503 1.147 2.056 8.615 0.212 0.743 16 629082 1841 1980 140 1.676 0.943 1.087 3.542 0.202 0.866 17 629091 1526 1836 311 1.034 0.719 1.673 6.128 0.248 0.891 18 629092 1541 1890 350 0.801 0.420 1.199 4.983 0.248 0.791 19 629111 1518 1980 463 0.743 0.463 1.961 8.892 0.216 0.875 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 629112 1547 1980 434 0.772 0.420 1.501 5.797 0.228 0.818 21 629121 1689 1980 292 0.899 0.426 1.045 5.161 0.256 0.719 22 629122 1791 1980 190 1.356 0.728 0.849 3.286 0.258 0.822 23 629131 1634 1980 347 0.966 0.485 1.076 4.379 0.253 0.799 24 629132 1622 1980 359 0.859 0.485 1.421 6.195 0.231 0.783 25 629141 1700 1943 244 0.992 0.550 0.995 3.842 0.251 0.826 26 629142 1711 1943 233 1.062 0.661 2.198 8.989 0.273 0.801 27 629151 1771 1980 210 1.298 0.913 1.493 5.449 0.271 0.882 28 629152 1761 1980 220 1.370 0.780 1.118 4.006 0.247 0.840 29 629161 1722 1980 259 1.293 0.667 1.171 4.730 0.206 0.848 30 629162 1763 1980 218 1.460 0.717 0.781 2.876 0.191 0.854 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 1.530 0.851 1.178 4.675 0.220 0.838 STANDARD DEVIATION 99 0.565 0.295 0.481 1.937 0.032 0.046 MEDIAN (50TH QUANTILE) 191 1.526 0.874 1.099 4.441 0.213 0.850 INTERQUARTILE RANGE 131 0.695 0.390 0.652 2.379 0.057 0.074 MINIMUM VALUE 107 0.743 0.420 0.290 2.022 0.165 0.719 LOWER HINGE (25TH QUANTILE) 128 1.034 0.661 0.849 3.286 0.191 0.801 UPPER HINGE (75TH QUANTILE) 259 1.729 1.051 1.501 5.666 0.248 0.875 MAXIMUM VALUE 458 2.893 1.397 2.198 8.989 0.273 0.907 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 420 0.460 0.265 0.013 -0.546 2.700 -0.403 0.930 MINIMUM CORRELATION: -0.403 SERIES 629061 AND 629092 43 YEARS MAXIMUM CORRELATION: 0.930 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 0.456 0.662 0.445 0.535 0.272 0.359 0.382 0.445 0.437 0.409 SDEV 0.126 0.134 0.197 0.149 0.284 0.192 0.212 0.189 0.192 0.238 SERR 0.073 0.055 0.080 0.061 0.073 0.050 0.046 0.031 0.029 0.027 EPS 0.768 0.887 0.790 0.867 0.696 0.801 0.848 0.892 0.907 0.913 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 0.334 0.482 0.375 0.350 0.524 0.340 SDEV 0.281 0.245 0.275 0.224 0.194 0.275 SERR 0.027 0.024 0.024 0.012 0.011 0.015 EPS 0.892 0.950 0.940 0.939 0.969 0.933 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 1.184 0.515 1.154 4.619 0.159 0.888 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.580 0.430 0.040 132 331 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.57 1.83 1.00 1.13 2.96 243.77 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 0.886 0.801 0.739 0.701 0.651 0.613 0.590 0.572 0.543 0.513 PACF 0.886 0.074 0.076 0.105 -0.036 0.048 0.071 0.034 -0.019 -0.004 95% C.L. 0.093 0.149 0.182 0.207 0.226 0.242 0.255 0.266 0.277 0.286 |------------------ 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 0.793 0.811 0.014 -0.020 0.109 |================== 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 -0.03179906 4.75326252 2 629012 3 0.00000000 0.00000000 -0.01744777 3.28950238 3 629021 3 0.00000000 0.00000000 -0.02896570 3.26397681 4 629022 3 0.00000000 0.00000000 -0.02195497 2.96222973 5 629031 3 0.00000000 0.00000000 -0.02482869 4.22832775 6 629032 1 4.30915260 0.02366876 0.00000000 1.32615638 7 629041 1 4.16908550 0.02417877 0.00000000 0.61557287 8 629042 1 3.56288528 0.00872049 0.00000000 0.04544132 9 629051 1 3.22371340 0.01985093 0.00000000 0.44848320 10 629052 3 0.00000000 0.00000000 -0.02023776 2.95319486 11 629061 1 4.50744820 0.03148806 0.00000000 0.68400180 12 629062 1 5.14190197 0.03525311 0.00000000 0.79948580 13 629071 3 0.00000000 0.00000000 -0.00551963 2.14167833 14 629072 3 0.00000000 0.00000000 -0.00973857 2.60313511 15 629081 1 3.87027407 0.03110090 0.00000000 0.69345194 16 629082 1 3.17043400 0.01261087 0.00000000 0.19271895 17 629091 1 2.48943067 0.01656162 0.00000000 0.55342865 18 629092 1 0.90834248 0.02298634 0.00000000 0.68886787 19 629111 1 1.36922765 0.00751854 0.00000000 0.35847935 SERIES IDENT OPTION A B C D 20 629112 1 0.90295130 0.01028677 0.00000000 0.57277733 21 629121 3 0.00000000 0.00000000 -0.00091305 1.03307652 22 629122 3 0.00000000 0.00000000 -0.00233655 1.57887721 23 629131 1 2.01206160 0.14694433 0.00000000 0.92494601 24 629132 1 2.47276473 0.15006113 0.00000000 0.81542689 25 629141 3 0.00000000 0.00000000 -0.00504744 1.61068809 26 629142 1 1.91165924 0.02995735 0.00000000 0.78666395 27 629151 3 0.00000000 0.00000000 -0.00730436 2.06889534 28 629152 3 0.00000000 0.00000000 -0.00656790 2.09529877 29 629161 3 0.00000000 0.00000000 -0.00319259 1.70758462 30 629162 3 0.00000000 0.00000000 -0.00819470 2.36303949 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 629011 1865 1980 116 1.001 0.281 1.000 4.393 0.211 0.406 2 629012 1834 1980 147 1.000 0.307 0.846 3.783 0.174 0.728 3 629021 1872 1980 109 1.100 0.492 2.979 16.119 0.173 0.708 4 629022 1868 1980 113 1.005 0.346 0.219 3.151 0.207 0.776 5 629031 1854 1980 127 1.015 0.327 1.568 6.274 0.178 0.719 6 629032 1852 1980 129 0.999 0.236 0.071 3.074 0.178 0.586 7 629041 1857 1980 124 0.996 0.244 0.049 2.962 0.205 0.462 8 629042 1853 1980 128 1.000 0.243 0.154 2.739 0.185 0.591 9 629051 1862 1980 119 1.001 0.324 1.261 6.268 0.246 0.481 10 629052 1853 1980 128 0.998 0.412 0.218 2.470 0.272 0.688 11 629061 1848 1980 133 0.989 0.369 0.958 3.684 0.185 0.816 12 629062 1848 1980 133 0.993 0.326 0.728 3.604 0.199 0.682 13 629071 1767 1980 214 0.999 0.350 0.517 2.979 0.187 0.749 14 629072 1788 1980 193 1.016 0.412 0.379 2.917 0.212 0.776 15 629081 1830 1980 151 0.994 0.408 0.953 3.225 0.209 0.744 16 629082 1841 1980 140 1.000 0.328 0.842 3.580 0.201 0.702 17 629091 1526 1836 311 0.998 0.383 0.531 3.425 0.249 0.683 18 629092 1541 1890 350 0.999 0.487 1.596 8.199 0.248 0.753 19 629111 1518 1980 463 0.998 0.380 1.278 7.376 0.221 0.720 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 629112 1547 1980 434 1.000 0.462 1.414 5.941 0.230 0.746 21 629121 1689 1980 292 1.000 0.470 1.019 4.510 0.255 0.734 22 629122 1791 1980 190 0.999 0.532 0.933 3.527 0.257 0.818 23 629131 1634 1980 347 1.000 0.474 0.845 3.896 0.252 0.797 24 629132 1622 1980 359 1.000 0.522 1.202 5.145 0.231 0.799 25 629141 1700 1943 244 1.007 0.429 0.872 3.518 0.250 0.721 26 629142 1711 1943 233 1.000 0.445 1.086 4.028 0.276 0.694 27 629151 1771 1980 210 0.973 0.611 2.191 9.610 0.270 0.836 28 629152 1761 1980 220 0.992 0.467 1.597 7.175 0.246 0.742 29 629161 1722 1980 259 0.991 0.451 0.911 3.997 0.205 0.817 30 629162 1763 1980 218 1.005 0.315 0.132 2.888 0.189 0.654 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 211 1.002 0.394 0.945 4.815 0.220 0.704 STANDARD DEVIATION 100 0.020 0.093 0.646 2.787 0.032 0.106 MEDIAN (50TH QUANTILE) 191 1.000 0.395 0.922 3.734 0.211 0.725 INTERQUARTILE RANGE 131 0.003 0.141 0.744 2.790 0.060 0.093 MINIMUM VALUE 109 0.973 0.236 0.049 2.470 0.173 0.406 LOWER HINGE (25TH QUANTILE) 128 0.998 0.326 0.517 3.151 0.189 0.683 UPPER HINGE (75TH QUANTILE) 259 1.001 0.467 1.261 5.941 0.249 0.776 MAXIMUM VALUE 463 1.100 0.611 2.979 16.119 0.276 0.836 |------------------------ 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 0.274 0.989 4.513 0.210 0.384 2 629012 1834 1980 147 0.992 0.243 0.653 3.694 0.174 0.584 3 629021 1872 1980 109 0.995 0.271 0.574 3.346 0.172 0.639 4 629022 1868 1980 113 0.992 0.300 -0.045 3.154 0.206 0.711 5 629031 1854 1980 127 0.996 0.246 0.448 3.046 0.177 0.581 6 629032 1852 1980 129 0.997 0.218 -0.213 2.834 0.177 0.515 7 629041 1857 1980 124 0.998 0.231 0.028 3.087 0.205 0.397 8 629042 1853 1980 128 0.996 0.217 0.039 2.878 0.185 0.487 9 629051 1862 1980 119 0.998 0.315 1.279 6.209 0.246 0.451 10 629052 1853 1980 128 0.995 0.400 0.223 2.567 0.272 0.667 11 629061 1848 1980 133 0.994 0.278 0.039 3.077 0.185 0.686 12 629062 1848 1980 133 0.994 0.279 0.101 2.782 0.199 0.588 13 629071 1767 1980 214 0.990 0.281 0.182 2.795 0.187 0.642 14 629072 1788 1980 193 0.985 0.316 0.296 3.221 0.212 0.646 15 629081 1830 1980 151 0.987 0.315 0.589 2.918 0.210 0.575 16 629082 1841 1980 140 0.992 0.286 0.687 3.559 0.201 0.621 17 629091 1526 1836 311 0.996 0.367 0.492 3.566 0.249 0.659 18 629092 1541 1890 350 0.993 0.446 1.224 6.221 0.248 0.723 19 629111 1518 1980 463 0.995 0.326 0.916 6.014 0.220 0.641 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 629112 1547 1980 434 0.989 0.391 1.063 4.498 0.231 0.692 21 629121 1689 1980 292 0.993 0.438 0.802 3.630 0.255 0.713 22 629122 1791 1980 190 0.987 0.453 0.599 2.920 0.256 0.762 23 629131 1634 1980 347 0.997 0.462 0.755 3.623 0.252 0.788 24 629132 1622 1980 359 0.997 0.512 1.154 4.596 0.231 0.796 25 629141 1700 1943 244 0.992 0.390 0.743 3.255 0.250 0.683 26 629142 1711 1943 233 0.996 0.415 0.936 3.586 0.276 0.648 27 629151 1771 1980 210 0.994 0.520 1.648 6.319 0.269 0.722 28 629152 1761 1980 220 0.995 0.444 1.382 5.554 0.246 0.680 29 629161 1722 1980 259 0.992 0.326 0.890 4.020 0.205 0.670 30 629162 1763 1980 218 0.995 0.292 0.138 2.838 0.189 0.620 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 211 0.994 0.342 0.620 3.811 0.220 0.632 STANDARD DEVIATION 100 0.003 0.088 0.475 1.153 0.032 0.103 MEDIAN (50TH QUANTILE) 191 0.994 0.316 0.626 3.453 0.211 0.647 INTERQUARTILE RANGE 131 0.003 0.137 0.754 1.578 0.060 0.108 MINIMUM VALUE 109 0.985 0.217 -0.213 2.567 0.172 0.384 LOWER HINGE (25TH QUANTILE) 128 0.992 0.278 0.182 2.920 0.189 0.584 UPPER HINGE (75TH QUANTILE) 259 0.996 0.415 0.936 4.498 0.249 0.692 MAXIMUM VALUE 463 0.999 0.520 1.648 6.319 0.276 0.796 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 420 0.319 0.161 0.008 -0.368 3.730 -0.441 0.731 MINIMUM CORRELATION: -0.441 SERIES 629061 AND 629092 43 YEARS MAXIMUM CORRELATION: 0.731 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 0.611 0.610 0.568 0.484 0.287 0.364 0.369 0.468 0.453 0.405 SDEV 0.081 0.145 0.140 0.153 0.252 0.188 0.178 0.202 0.187 0.270 SERR 0.047 0.059 0.057 0.063 0.065 0.048 0.039 0.034 0.028 0.031 EPS 0.861 0.862 0.860 0.842 0.711 0.805 0.841 0.901 0.912 0.912 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 0.349 0.438 0.429 0.386 0.335 0.272 SDEV 0.244 0.240 0.256 0.214 0.203 0.216 SERR 0.024 0.023 0.022 0.011 0.011 0.012 EPS 0.898 0.940 0.952 0.947 0.934 0.910 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 0.978 0.253 0.505 3.053 0.157 0.708 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.406 0.190 0.072 135 328 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.51 1.36 1.00 1.13 2.49 83.92 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 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 0.706 0.458 0.355 0.277 0.141 0.091 0.087 0.077 0.061 0.041 PACF 0.706 -0.082 0.126 -0.011 -0.129 0.079 0.013 0.017 0.016 -0.040 95% C.L. 0.093 0.131 0.145 0.152 0.156 0.157 0.158 0.158 0.158 0.159 |------------------ 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 3 0.510 0.775 -0.179 0.126 |======================= 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 0.673 0.418 0.280 0.191 0.076 0.028 0.054 0.080 0.105 0.114 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 0.673 2 0.714 -0.062 3 0.717 -0.092 0.042 4 0.717 -0.091 0.040 0.002 5 0.717 -0.087 0.031 0.072 -0.099 6 0.720 -0.090 0.030 0.075 -0.122 0.033 7 0.717 -0.080 0.024 0.073 -0.115 -0.024 0.079 8 0.715 -0.079 0.028 0.071 -0.116 -0.022 0.056 0.032 9 0.713 -0.083 0.029 0.077 -0.119 -0.023 0.060 -0.008 0.055 10 0.713 -0.082 0.028 0.077 -0.118 -0.024 0.060 -0.007 0.049 0.009 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) 4034.06 3757.36 3757.58 3758.78 3760.78 3758.26 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 3759.77 3758.89 3760.42 3761.00 3762.96 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 0.673 R-SQUARED DUE TO POOLED AUTOREGRESSION: 45.23 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 182.57 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.673 0.452 0.304 0.205 0.138 0.093 0.062 0.042 0.028 0.0189 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 0.159 0.386 2 629012 1 0.359 0.599 3 629021 1 0.455 0.670 4 629022 1 0.546 0.714 5 629031 1 0.355 0.587 6 629032 1 0.270 0.519 7 629041 1 0.171 0.402 8 629042 1 0.250 0.499 9 629051 1 0.212 0.454 10 629052 1 0.449 0.670 11 629061 1 0.479 0.691 12 629062 1 0.361 0.588 13 629071 1 0.427 0.653 14 629072 1 0.425 0.652 15 629081 1 0.359 0.578 16 629082 1 0.392 0.625 17 629091 1 0.438 0.661 18 629092 1 0.552 0.741 19 629111 1 0.412 0.641 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 629112 1 0.481 0.693 21 629121 1 0.531 0.727 22 629122 1 0.603 0.764 23 629131 1 0.624 0.788 24 629132 1 0.636 0.796 25 629141 1 0.474 0.686 26 629142 1 0.432 0.649 27 629151 1 0.523 0.723 28 629152 1 0.503 0.699 29 629161 1 0.458 0.676 30 629162 1 0.393 0.625 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.424 0.639 STANDARD DEVIATION 0 0.123 0.103 MEDIAN 1 0.435 0.657 INTERQUARTILE RANGE 0 0.143 0.111 MINIMUM VALUE 1 0.159 0.386 LOWER HINGE 1 0.359 0.588 UPPER HINGE 1 0.503 0.699 MAXIMUM VALUE 1 0.636 0.796 |------------------- 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 0.252 1.003 5.298 0.245 -0.041 2 629012 1834 1980 147 1.000 0.194 0.182 3.688 0.218 0.015 3 629021 1872 1980 109 1.000 0.201 0.113 3.128 0.210 0.096 4 629022 1868 1980 113 1.000 0.210 -0.093 3.151 0.258 -0.195 5 629031 1854 1980 127 1.000 0.199 0.102 2.962 0.219 0.079 6 629032 1852 1980 129 1.000 0.186 0.116 2.385 0.215 -0.023 7 629041 1857 1980 124 1.000 0.211 0.187 3.442 0.248 -0.041 8 629042 1853 1980 128 1.000 0.187 0.084 2.956 0.223 -0.030 9 629051 1862 1980 119 1.000 0.281 1.327 5.317 0.299 -0.037 10 629052 1853 1980 128 1.000 0.296 0.590 3.400 0.330 0.005 11 629061 1848 1980 133 1.000 0.200 -0.010 3.577 0.223 0.021 12 629062 1848 1980 133 1.000 0.225 0.362 4.324 0.240 -0.088 13 629071 1767 1980 214 1.000 0.212 0.176 3.060 0.236 0.022 14 629072 1788 1980 193 1.000 0.239 0.158 3.556 0.265 -0.001 15 629081 1830 1980 151 1.000 0.256 0.589 5.772 0.268 -0.113 16 629082 1841 1980 140 1.000 0.223 0.584 3.900 0.245 0.028 17 629091 1526 1836 311 1.000 0.275 0.456 3.934 0.313 -0.025 18 629092 1541 1890 350 1.000 0.299 0.957 4.910 0.318 -0.028 19 629111 1518 1980 463 1.000 0.250 1.086 8.841 0.258 -0.005 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 629112 1547 1980 434 1.000 0.282 0.816 5.483 0.294 -0.018 21 629121 1689 1980 292 1.000 0.298 0.318 3.742 0.325 0.046 22 629122 1791 1980 190 1.000 0.292 0.548 3.503 0.295 0.166 23 629131 1634 1980 347 1.000 0.285 0.311 3.547 0.297 0.072 24 629132 1622 1980 359 1.000 0.310 1.070 5.896 0.304 0.063 25 629141 1700 1943 244 1.000 0.284 0.501 3.573 0.304 0.060 26 629142 1711 1943 233 1.000 0.315 0.660 3.421 0.331 0.083 27 629151 1771 1980 210 1.000 0.359 1.224 7.561 0.351 -0.005 28 629152 1761 1980 220 1.000 0.316 1.018 5.146 0.297 0.121 29 629161 1722 1980 259 1.000 0.239 0.499 3.344 0.260 0.029 30 629162 1763 1980 218 1.000 0.227 0.209 4.101 0.248 -0.038 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 211 1.000 0.254 0.505 4.231 0.271 0.007 STANDARD DEVIATION 100 0.000 0.047 0.398 1.425 0.041 0.072 MEDIAN (50TH QUANTILE) 191 1.000 0.251 0.478 3.633 0.263 0.002 INTERQUARTILE RANGE 131 0.000 0.081 0.640 1.747 0.064 0.090 MINIMUM VALUE 109 1.000 0.186 -0.093 2.385 0.210 -0.195 LOWER HINGE (25TH QUANTILE) 128 1.000 0.211 0.176 3.400 0.240 -0.030 UPPER HINGE (75TH QUANTILE) 259 1.000 0.292 0.816 5.146 0.304 0.060 MAXIMUM VALUE 463 1.000 0.359 1.327 8.841 0.351 0.166 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 420 0.333 0.118 0.006 -0.015 2.757 0.037 0.688 MINIMUM CORRELATION: 0.037 SERIES 629031 AND 629092 37 YEARS MAXIMUM CORRELATION: 0.688 SERIES 629071 AND 629072 193 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 0.292 0.261 0.203 0.249 0.249 0.317 0.381 0.459 0.459 0.420 SDEV 0.341 0.361 0.389 0.231 0.167 0.171 0.168 0.112 0.136 0.170 SERR 0.197 0.147 0.159 0.094 0.043 0.044 0.037 0.019 0.020 0.019 EPS 0.620 0.586 0.544 0.653 0.670 0.770 0.848 0.898 0.914 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 0.436 0.481 0.446 0.364 0.291 0.321 SDEV 0.136 0.128 0.133 0.140 0.147 0.148 SERR 0.013 0.013 0.011 0.007 0.008 0.008 EPS 0.927 0.949 0.955 0.942 0.920 0.927 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 0.992 0.171 0.210 3.170 0.180 0.111 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.332 0.200 -0.007 145 318 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.29 0.69 1.00 1.09 1.78 66.05 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 0.110 -0.108 0.046 0.129 -0.048 -0.046 0.033 0.018 0.032 0.023 PACF 0.110 -0.122 0.075 0.103 -0.067 -0.008 0.017 -0.003 0.054 0.016 95% C.L. 0.093 0.094 0.095 0.095 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 4 0.047 0.125 -0.118 0.061 0.104 |---------- 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 0.013 -0.128 0.045 0.132 -0.059 -0.045 0.037 0.011 0.028 0.025 PACF 0.013 -0.129 0.049 0.116 -0.053 -0.016 0.015 -0.007 0.052 0.027 95% C.L. 0.093 0.093 0.094 0.095 0.096 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 0.017 0.013 |========================= 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 0.225 0.416 2.861 0.147 0.659 |------------ 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 0.658 0.409 0.334 0.275 0.148 0.094 0.094 0.077 0.062 0.034 PACF 0.658 -0.041 0.143 0.012 -0.106 0.037 0.026 0.001 0.027 -0.044 95% C.L. 0.093 0.127 0.138 0.145 0.149 0.150 0.151 0.151 0.152 0.152 |------------------- 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 0.434 0.658 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.37 MINUTES