RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN023W.rwl.conv LOG FILE PROCESSED: FRAN023W.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: 483 1 Roc de Perches Blancas WIDTH_RING PIMU - 483 2 France krummholz pine 2100 4236-203 1769 1977 - 483 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES --- NO GAPS IN DATA FOUND --- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 483021 1804 1977 174 1.213 0.582 1.201 4.911 0.223 0.806 2 483022 1806 1977 172 1.019 0.497 1.411 6.450 0.214 0.787 3 483031 1769 1977 209 1.075 0.588 0.803 2.664 0.152 0.896 4 483032 1804 1977 174 1.241 0.533 1.368 4.440 0.183 0.821 5 483041 1793 1925 133 1.087 0.473 0.920 2.929 0.175 0.835 6 483042 1783 1977 195 0.935 0.547 1.150 3.702 0.170 0.928 7 483051 1783 1977 195 1.151 0.523 0.712 2.989 0.172 0.872 8 483052 1806 1977 172 1.311 0.921 0.839 2.774 0.167 0.927 9 483061 1787 1977 191 0.992 0.564 1.623 6.997 0.204 0.809 10 483062 1778 1977 200 0.851 0.376 1.666 5.357 0.167 0.864 11 483071 1820 1977 158 1.182 0.589 0.129 2.146 0.136 0.938 12 483072 1809 1977 169 1.283 0.712 0.525 2.237 0.147 0.922 13 483081 1858 1977 120 1.598 0.822 1.411 4.437 0.147 0.915 14 483082 1861 1977 117 1.523 0.832 1.311 3.887 0.153 0.912 15 483091 1845 1977 133 1.346 0.743 2.222 8.796 0.160 0.874 16 483092 1838 1977 140 1.252 0.682 1.713 5.450 0.169 0.871 17 483111 1783 1977 195 1.119 0.329 1.265 5.323 0.178 0.670 18 483112 1796 1970 175 1.335 0.530 0.913 3.670 0.155 0.841 19 483121 1825 1977 153 1.465 0.926 0.292 2.152 0.184 0.916 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 483122 1834 1977 144 1.695 1.311 0.979 2.849 0.168 0.943 21 483131 1783 1977 195 1.274 0.757 1.042 4.239 0.206 0.861 22 483132 1785 1977 193 1.063 0.659 1.671 6.381 0.224 0.838 NUMBER OF SERIES READ IN: 22 FROM 1769 TO 1977 209 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 169 1.228 0.659 1.144 4.308 0.175 0.866 STANDARD DEVIATION 27 0.213 0.216 0.497 1.766 0.025 0.064 MEDIAN (50TH QUANTILE) 173 1.227 0.588 1.176 4.063 0.169 0.872 INTERQUARTILE RANGE 51 0.260 0.227 0.572 2.509 0.028 0.081 MINIMUM VALUE 117 0.851 0.329 0.129 2.146 0.136 0.670 LOWER HINGE (25TH QUANTILE) 144 1.075 0.530 0.839 2.849 0.155 0.835 UPPER HINGE (75TH QUANTILE) 195 1.335 0.757 1.411 5.357 0.184 0.916 MAXIMUM VALUE 209 1.695 1.311 2.222 8.796 0.224 0.943 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.574 0.252 0.017 -1.454 5.249 -0.356 0.908 MINIMUM CORRELATION: -0.356 SERIES 483061 AND 483071 158 YEARS MAXIMUM CORRELATION: 0.908 SERIES 483051 AND 483081 120 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.08 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1820. 1845. 1870. 1895. 1920. 1945. CORR 36. 120. 190. 231. 210. 210. RBAR 0.348 0.277 0.252 0.448 0.214 0.380 SDEV 0.242 0.281 0.312 0.206 0.347 0.467 SERR 0.040 0.026 0.023 0.014 0.024 0.032 EPS 0.890 0.880 0.878 0.947 0.855 0.928 NSS 15.2 19.2 21.4 22.0 21.6 21.1 |======================== 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 1769 1977 209 1.267 0.487 0.289 2.280 0.125 0.882 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.510 0.241 0.156 82 127 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.36 0.86 1.01 1.10 1.95 4.75 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.05 0.00 0.87 0.92 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 173. 51. 117. 144. 195. 209. |----------- 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 0.878 0.841 0.857 0.820 0.798 0.819 0.800 0.768 0.773 0.769 PACF 0.878 0.305 0.364 0.016 0.056 0.193 0.032 -0.048 0.040 0.056 95% C.L. 0.138 0.221 0.275 0.322 0.360 0.392 0.424 0.452 0.476 0.500 |------------------ 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 3 0.854 0.531 0.029 0.398 |================== 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 483021 1 1.70686948 0.01797515 0.00000000 0.69619179 2 483022 1 1.36059129 0.02920731 0.00000000 0.75346017 3 483031 1 2.16216969 0.00956951 0.00000000 0.14435734 4 483032 1 1.75631452 0.02012517 0.00000000 0.75896490 5 483041 1 1.74328411 0.01229180 0.00000000 0.23353884 6 483042 1 1.93969440 0.01731367 0.00000000 0.38485077 7 483051 3 0.00000000 0.00000000 -0.00743242 1.87924933 8 483052 -67 115 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 483061 1 1.87889266 0.06676731 0.00000000 0.84957367 10 483062 1 1.64696836 0.05297021 0.00000000 0.69917309 11 483071 3 0.00000000 0.00000000 -0.01158213 2.10318470 12 483072 3 0.00000000 0.00000000 -0.01231550 2.32948017 13 483081 1 3.10356259 0.03661034 0.00000000 0.91268730 14 483082 1 3.20260715 0.05198580 0.00000000 1.01127362 15 483091 1 3.40351796 0.07341138 0.00000000 1.01015973 16 483092 1 2.55824661 0.03983049 0.00000000 0.80365872 17 483111 3 0.00000000 0.00000000 -0.00349065 1.46141744 18 483112 3 0.00000000 0.00000000 -0.00768605 2.01134372 19 483121 3 0.00000000 0.00000000 -0.01842873 2.88443661 SERIES IDENT OPTION A B C D 20 483122 -67 96 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 483131 3 0.00000000 0.00000000 -0.01096862 2.34871960 22 483132 1 2.07221603 0.01726796 0.00000000 0.46856022 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 483021 1804 1977 174 1.000 0.331 1.171 5.225 0.221 0.631 2 483022 1806 1977 172 1.000 0.377 1.051 5.089 0.211 0.745 3 483031 1769 1977 209 1.006 0.269 0.730 5.452 0.151 0.664 4 483032 1804 1977 174 1.000 0.219 0.753 3.609 0.182 0.443 5 483041 1793 1925 133 1.001 0.226 0.676 3.533 0.173 0.508 6 483042 1783 1977 195 1.000 0.273 0.639 3.583 0.169 0.724 7 483051 1783 1977 195 1.001 0.257 1.089 5.580 0.171 0.592 8 483052 1806 1977 172 0.995 0.253 0.750 3.623 0.166 0.623 9 483061 1787 1977 191 1.000 0.482 1.226 4.767 0.204 0.833 10 483062 1778 1977 200 1.000 0.255 0.416 3.081 0.166 0.631 11 483071 1820 1977 158 0.992 0.227 0.337 2.795 0.135 0.735 12 483072 1809 1977 169 1.002 0.262 0.603 2.958 0.145 0.723 13 483081 1858 1977 120 1.000 0.194 0.144 3.980 0.145 0.523 14 483082 1861 1977 117 1.001 0.300 0.518 3.283 0.151 0.791 15 483091 1845 1977 133 1.001 0.282 0.765 3.830 0.158 0.710 16 483092 1838 1977 140 1.000 0.271 2.132 14.665 0.167 0.640 17 483111 1783 1977 195 1.000 0.222 0.959 4.381 0.177 0.432 18 483112 1796 1970 175 0.999 0.254 1.114 4.193 0.154 0.655 19 483121 1825 1977 153 1.045 0.523 3.573 19.809 0.184 0.732 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 483122 1834 1977 144 1.005 0.211 0.361 3.634 0.165 0.504 21 483131 1783 1977 195 1.004 0.279 0.174 2.706 0.205 0.589 22 483132 1785 1977 193 0.995 0.355 0.771 4.168 0.223 0.702 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 169 1.002 0.287 0.907 5.179 0.174 0.642 STANDARD DEVIATION 27 0.010 0.083 0.735 4.068 0.025 0.109 MEDIAN (50TH QUANTILE) 173 1.000 0.266 0.751 3.905 0.168 0.648 INTERQUARTILE RANGE 51 0.002 0.073 0.572 1.556 0.029 0.135 MINIMUM VALUE 117 0.992 0.194 0.144 2.706 0.135 0.432 LOWER HINGE (25TH QUANTILE) 144 1.000 0.227 0.518 3.533 0.154 0.589 UPPER HINGE (75TH QUANTILE) 195 1.001 0.300 1.089 5.089 0.184 0.724 MAXIMUM VALUE 209 1.045 0.523 3.573 19.809 0.223 0.833 |------------------------ 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 483021 -67 116 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 483022 -67 115 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 483031 -67 140 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 483032 -67 116 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 483041 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 483042 -67 130 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 483051 -67 130 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 483052 -67 115 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 483061 -67 127 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 483062 -67 134 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 483071 -67 105 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 483072 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 483081 -67 80 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 483082 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 483091 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 483092 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 483111 -67 130 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 483112 -67 117 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 483121 -67 102 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 483122 -67 96 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 483131 -67 130 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 483132 -67 129 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 483021 1804 1977 174 0.995 0.302 0.923 4.451 0.220 0.576 2 483022 1806 1977 172 0.991 0.343 1.800 9.158 0.212 0.697 3 483031 1769 1977 209 0.994 0.211 0.733 4.269 0.151 0.497 4 483032 1804 1977 174 0.999 0.202 0.495 3.150 0.182 0.361 5 483041 1793 1925 133 0.998 0.214 0.724 3.892 0.173 0.464 6 483042 1783 1977 195 0.997 0.257 0.474 3.050 0.169 0.685 7 483051 1783 1977 195 0.997 0.224 0.864 4.657 0.171 0.504 8 483052 1806 1977 172 0.998 0.239 0.725 3.613 0.166 0.591 9 483061 1787 1977 191 0.983 0.296 0.542 3.611 0.204 0.607 10 483062 1778 1977 200 0.998 0.244 0.474 3.397 0.166 0.592 11 483071 1820 1977 158 0.999 0.218 0.249 2.661 0.135 0.701 12 483072 1809 1977 169 0.996 0.229 0.211 2.528 0.144 0.666 13 483081 1858 1977 120 0.999 0.185 0.146 3.832 0.145 0.450 14 483082 1861 1977 117 0.994 0.246 0.204 2.847 0.151 0.671 15 483091 1845 1977 133 0.997 0.188 0.753 4.446 0.158 0.430 16 483092 1838 1977 140 0.998 0.238 2.035 13.997 0.166 0.541 17 483111 1783 1977 195 0.999 0.214 0.880 4.063 0.177 0.398 18 483112 1796 1970 175 0.997 0.235 1.068 4.267 0.154 0.607 19 483121 1825 1977 153 0.986 0.314 0.936 5.312 0.183 0.661 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 483122 1834 1977 144 0.999 0.204 0.258 3.504 0.165 0.482 21 483131 1783 1977 195 0.996 0.260 0.143 2.599 0.205 0.536 22 483132 1785 1977 193 0.993 0.274 0.889 4.550 0.223 0.461 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 169 0.996 0.243 0.706 4.448 0.174 0.554 STANDARD DEVIATION 27 0.004 0.042 0.488 2.535 0.025 0.103 MEDIAN (50TH QUANTILE) 173 0.997 0.236 0.724 3.862 0.168 0.559 INTERQUARTILE RANGE 51 0.004 0.046 0.631 1.301 0.028 0.196 MINIMUM VALUE 117 0.983 0.185 0.143 2.528 0.135 0.361 LOWER HINGE (25TH QUANTILE) 144 0.994 0.214 0.258 3.150 0.154 0.464 UPPER HINGE (75TH QUANTILE) 195 0.998 0.260 0.889 4.451 0.183 0.661 MAXIMUM VALUE 209 0.999 0.343 2.035 13.997 0.223 0.701 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.276 0.158 0.010 -0.223 2.585 -0.137 0.674 MINIMUM CORRELATION: -0.137 SERIES 483061 AND 483071 158 YEARS MAXIMUM CORRELATION: 0.674 SERIES 483071 AND 483082 117 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.08 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1820. 1845. 1870. 1895. 1920. 1945. CORR 36. 120. 190. 231. 210. 210. RBAR 0.164 0.228 0.207 0.291 0.287 0.325 SDEV 0.217 0.222 0.255 0.204 0.258 0.287 SERR 0.036 0.020 0.018 0.013 0.018 0.020 EPS 0.748 0.850 0.849 0.900 0.897 0.911 NSS 15.2 19.2 21.4 22.0 21.6 21.1 |======================== 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 1769 1977 209 0.984 0.131 0.186 3.789 0.119 0.343 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.439 0.230 -0.030 70 139 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.14 0.30 1.00 1.05 1.35 3.26 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.00 0.87 0.94 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 0.341 0.172 0.247 0.087 0.031 0.045 -0.037 -0.160 -0.138 -0.187 PACF 0.341 0.063 0.193 -0.065 -0.013 -0.003 -0.061 -0.155 -0.057 -0.113 95% C.L. 0.138 0.154 0.157 0.164 0.165 0.165 0.166 0.166 0.169 0.171 |------------------ 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 0.120 0.342 |======================= 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 0.358 0.179 0.220 0.112 0.052 0.049 -0.049 -0.117 -0.137 -0.215 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 0.358 2 0.338 0.058 3 0.328 0.004 0.160 4 0.332 0.004 0.167 -0.022 5 0.332 0.006 0.167 -0.019 -0.010 6 0.332 0.006 0.167 -0.019 -0.010 0.002 7 0.332 0.005 0.165 -0.003 -0.010 0.033 -0.093 8 0.323 0.008 0.164 -0.003 0.006 0.033 -0.062 -0.094 9 0.315 0.003 0.167 -0.003 0.005 0.047 -0.061 -0.067 -0.084 10 0.304 -0.007 0.158 0.004 0.006 0.047 -0.039 -0.067 -0.041 -0.137 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) 1499.66 1472.94 1474.24 1470.83 1472.73 1474.71 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1476.71 1476.88 1477.02 1477.54 1475.57 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 0.358 R-SQUARED DUE TO POOLED AUTOREGRESSION: 12.84 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 114.73 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.358 0.128 0.046 0.016 0.006 0.002 0.001 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 483021 1 0.337 0.580 2 483022 1 0.486 0.697 3 483031 1 0.265 0.499 4 483032 1 0.137 0.362 5 483041 1 0.217 0.465 6 483042 1 0.480 0.689 7 483051 1 0.261 0.508 8 483052 1 0.366 0.591 9 483061 1 0.384 0.612 10 483062 1 0.365 0.596 11 483071 1 0.513 0.703 12 483072 1 0.485 0.673 13 483081 1 0.210 0.452 14 483082 1 0.456 0.671 15 483091 1 0.188 0.433 16 483092 1 0.303 0.549 17 483111 1 0.167 0.399 18 483112 1 0.402 0.618 19 483121 1 0.507 0.704 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 483122 1 0.236 0.486 21 483131 1 0.296 0.540 22 483132 1 0.215 0.464 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.331 0.559 STANDARD DEVIATION 0 0.121 0.106 MEDIAN 1 0.320 0.565 INTERQUARTILE RANGE 0 0.239 0.206 MINIMUM VALUE 1 0.137 0.362 LOWER HINGE 1 0.217 0.465 UPPER HINGE 1 0.456 0.671 MAXIMUM VALUE 1 0.513 0.704 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 483021 1804 1977 174 1.000 0.245 1.017 5.088 0.267 0.009 2 483022 1806 1977 172 1.000 0.246 0.984 5.703 0.261 0.017 3 483031 1769 1977 209 1.000 0.183 1.282 6.058 0.188 -0.075 4 483032 1804 1977 174 1.000 0.188 0.488 3.202 0.212 -0.028 5 483041 1793 1925 133 1.000 0.190 0.552 3.530 0.205 0.009 6 483042 1783 1977 195 1.000 0.186 0.296 2.964 0.219 -0.063 7 483051 1783 1977 195 1.000 0.193 0.665 5.193 0.211 -0.027 8 483052 1806 1977 172 1.000 0.193 0.434 3.452 0.220 -0.092 9 483061 1787 1977 191 1.000 0.234 0.479 3.775 0.266 -0.075 10 483062 1778 1977 200 1.000 0.196 0.270 3.631 0.218 -0.069 11 483071 1820 1977 158 1.000 0.155 0.494 3.282 0.180 -0.133 12 483072 1809 1977 169 1.000 0.169 0.449 3.469 0.198 -0.163 13 483081 1858 1977 120 1.000 0.165 0.460 3.943 0.179 -0.038 14 483082 1861 1977 117 1.000 0.182 0.788 4.070 0.193 -0.069 15 483091 1845 1977 133 1.000 0.169 0.779 4.661 0.196 -0.010 16 483092 1838 1977 140 1.000 0.199 1.740 11.639 0.209 0.033 17 483111 1783 1977 195 1.000 0.196 0.826 4.287 0.213 -0.038 18 483112 1796 1970 175 1.000 0.184 0.785 4.893 0.213 -0.102 19 483121 1825 1977 153 1.000 0.223 0.742 3.871 0.245 -0.054 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 483122 1834 1977 144 1.000 0.179 0.143 3.735 0.199 -0.007 21 483131 1783 1977 195 1.000 0.218 0.188 2.717 0.258 -0.043 22 483132 1785 1977 193 1.000 0.242 0.579 4.072 0.263 0.006 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 169 1.000 0.197 0.656 4.420 0.219 -0.046 STANDARD DEVIATION 27 0.000 0.027 0.371 1.832 0.028 0.050 MEDIAN (50TH QUANTILE) 173 1.000 0.191 0.566 3.907 0.212 -0.041 INTERQUARTILE RANGE 51 0.000 0.036 0.339 1.425 0.048 0.068 MINIMUM VALUE 117 1.000 0.155 0.143 2.717 0.179 -0.163 LOWER HINGE (25TH QUANTILE) 144 1.000 0.182 0.449 3.469 0.198 -0.075 UPPER HINGE (75TH QUANTILE) 195 1.000 0.218 0.788 4.893 0.245 -0.007 MAXIMUM VALUE 209 1.000 0.246 1.740 11.639 0.267 0.033 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.382 0.106 0.007 0.347 3.444 0.080 0.721 MINIMUM CORRELATION: 0.080 SERIES 483041 AND 483051 133 YEARS MAXIMUM CORRELATION: 0.721 SERIES 483081 AND 483082 117 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.08 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1820. 1845. 1870. 1895. 1920. 1945. CORR 36. 120. 190. 231. 210. 210. RBAR 0.301 0.366 0.355 0.402 0.422 0.393 SDEV 0.147 0.157 0.154 0.142 0.136 0.157 SERR 0.024 0.014 0.011 0.009 0.009 0.011 EPS 0.867 0.917 0.922 0.937 0.940 0.932 NSS 15.2 19.2 21.4 22.0 21.6 21.1 |======================== 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 1769 1977 209 0.993 0.125 0.393 3.217 0.154 -0.223 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.355 0.154 -0.007 75 134 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.22 0.57 1.00 1.06 1.62 6.88 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.00 0.86 0.94 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 -0.222 -0.125 0.199 -0.054 -0.044 0.100 0.005 -0.122 -0.007 -0.046 PACF -0.222 -0.183 0.136 0.006 -0.010 0.059 0.045 -0.094 -0.085 -0.109 95% C.L. 0.138 0.145 0.147 0.152 0.152 0.153 0.154 0.154 0.156 0.156 |------------------ 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 3 0.100 -0.238 -0.147 0.141 |---------- 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 -0.040 -0.142 0.177 -0.023 -0.037 0.101 0.001 -0.134 -0.046 -0.083 PACF -0.040 -0.144 0.169 -0.034 0.011 0.066 0.010 -0.114 -0.083 -0.126 95% C.L. 0.138 0.139 0.141 0.146 0.146 0.146 0.147 0.147 0.149 0.150 |----------------- 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 0.023 -0.040 |========================= 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 1769 1977 209 0.992 0.127 0.246 3.649 0.119 0.295 |------------ 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 0.293 0.027 0.164 0.034 0.001 0.075 -0.030 -0.170 -0.151 -0.182 PACF 0.293 -0.064 0.192 -0.083 0.035 0.040 -0.069 -0.151 -0.091 -0.132 95% C.L. 0.138 0.150 0.150 0.153 0.153 0.153 0.154 0.154 0.158 0.160 |------------------- 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 0.090 0.294 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 1.60 MINUTES