RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN024X.rwl.conv LOG FILE PROCESSED: FRAN024X.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: 484 1 Formigu¸res DENSITY_MAXIMUM ABAL - 484 2 France silver fir, European fir 1700 4236-204 1742 1977 - 484 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 12 484062 MISSING VALUES FOUND: 4 IN 1 GAPS / 1870 1873 / -------------------------------------------------------------------- 14 484072 MISSING VALUES FOUND: 27 IN 1 GAPS / 1870 1896 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 484011 1795 1977 183 0.952 0.068 -0.170 2.127 0.040 0.749 2 484012 1778 1977 200 0.953 0.075 -1.627 6.528 0.040 0.741 3 484021 1766 1977 212 0.865 0.063 -0.526 3.102 0.050 0.608 4 484022 1839 1977 139 0.844 0.103 -0.858 2.746 0.061 0.802 5 484031 1759 1977 219 0.804 0.111 -0.617 2.405 0.062 0.844 6 484032 1792 1977 186 0.775 0.120 -0.353 1.896 0.067 0.841 7 484041 1793 1977 185 0.812 0.117 -0.946 3.232 0.062 0.863 8 484042 1809 1977 169 0.853 0.093 -0.592 2.569 0.054 0.809 9 484051 1841 1977 137 0.864 0.050 -0.219 3.530 0.043 0.590 10 484052 1881 1977 97 0.827 0.060 -0.984 4.532 0.052 0.567 11 484061 1781 1977 197 0.847 0.061 -0.477 2.847 0.050 0.620 12 484062 1808 1977 170 0.902 0.048 -0.428 2.868 0.037 0.569 13 484071 1742 1977 236 0.913 0.061 -1.665 6.476 0.047 0.613 14 484072 1826 1977 152 0.873 0.068 -0.598 4.399 0.068 0.381 15 484081 1801 1977 177 0.913 0.062 -1.155 4.725 0.051 0.561 16 484082 1811 1977 167 0.848 0.104 -0.843 3.249 0.061 0.814 17 484091 1860 1977 118 0.865 0.052 -0.721 4.481 0.054 0.293 18 484092 1843 1977 135 0.888 0.045 0.094 2.743 0.046 0.311 19 484101 1800 1977 178 0.964 0.047 -0.970 3.857 0.038 0.485 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 484102 1811 1977 167 0.938 0.067 -1.329 5.441 0.037 0.770 NUMBER OF SERIES READ IN: 20 FROM 1742 TO 1977 236 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 170 0.875 0.074 -0.749 3.688 0.051 0.642 STANDARD DEVIATION 35 0.052 0.025 0.462 1.344 0.010 0.177 MEDIAN (50TH QUANTILE) 173 0.865 0.065 -0.669 3.240 0.051 0.617 INTERQUARTILE RANGE 53 0.067 0.042 0.525 1.762 0.019 0.241 MINIMUM VALUE 97 0.775 0.045 -1.665 1.896 0.037 0.293 LOWER HINGE (25TH QUANTILE) 138 0.846 0.056 -0.977 2.744 0.041 0.564 UPPER HINGE (75TH QUANTILE) 191 0.913 0.098 -0.452 4.506 0.061 0.805 MAXIMUM VALUE 236 0.964 0.120 0.094 6.528 0.068 0.863 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.271 0.241 0.018 -0.340 2.518 -0.330 0.821 MINIMUM CORRELATION: -0.330 SERIES 484052 AND 484082 97 YEARS MAXIMUM CORRELATION: 0.821 SERIES 484041 AND 484082 167 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 64.16 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1825. 1850. 1875. 1900. 1925. 1950. CORR 3. 36. 91. 153. 171. 190. 190. RBAR -0.105 0.204 0.424 0.294 0.342 0.287 0.328 SDEV 0.256 0.215 0.163 0.242 0.258 0.253 0.275 SERR 0.148 0.036 0.017 0.020 0.020 0.018 0.020 EPS -5.486 0.785 0.927 0.889 0.912 0.889 0.907 NSS 8.9 14.2 17.3 19.2 19.9 20.0 20.0 |======================== 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 1742 1977 236 0.884 0.047 -0.694 3.576 0.039 0.565 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.349 -0.290 0.332 68 168 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.26 0.40 1.00 1.11 1.51 2.61 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.13 0.00 0.84 0.98 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 174. 46. 97. 146. 192. 236. |----------- 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 0.562 0.541 0.490 0.478 0.383 0.368 0.361 0.382 0.336 0.300 PACF 0.562 0.330 0.165 0.139 -0.029 0.023 0.066 0.113 0.018 -0.035 95% C.L. 0.130 0.166 0.194 0.214 0.231 0.242 0.251 0.260 0.269 0.276 |------------------ 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 0.437 0.284 0.232 0.136 0.151 |================== 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 484011 1 0.39724764 0.00322274 0.00000000 0.65237051 2 484012 3 0.00000000 0.00000000 -0.00090061 1.04341102 3 484021 3 0.00000000 0.00000000 0.00012139 0.85164714 4 484022 3 0.00000000 0.00000000 0.00088623 0.78170472 5 484031 3 0.00000000 0.00000000 0.00009323 0.79362613 6 484032 3 0.00000000 0.00000000 0.00052947 0.72592443 7 484041 3 0.00000000 0.00000000 0.00006776 0.80618507 8 484042 3 0.00000000 0.00000000 0.00038123 0.82043535 9 484051 1 0.09962047 0.04458722 0.00000000 0.84854025 10 484052 1 0.11319936 0.10387247 0.00000000 0.81634927 11 484061 3 0.00000000 0.00000000 0.00011195 0.83637935 12 484062 3 0.00000000 0.00000000 -0.00016699 0.91612464 13 484071 3 0.00000000 0.00000000 0.00019795 0.88950920 14 484072 3 0.00000000 0.00000000 0.00001525 0.85807586 15 484081 3 0.00000000 0.00000000 0.00009933 0.90387136 16 484082 3 0.00000000 0.00000000 0.00051339 0.80442029 17 484091 3 0.00000000 0.00000000 -0.00013505 0.87328988 18 484092 3 0.00000000 0.00000000 -0.00011692 0.89639473 19 484101 3 0.00000000 0.00000000 -0.00020937 0.98283947 SERIES IDENT OPTION A B C D 20 484102 3 0.00000000 0.00000000 -0.00083180 1.00759614 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 484011 1795 1977 183 1.000 0.047 -0.448 3.317 0.040 0.389 2 484012 1778 1977 200 1.000 0.059 -1.822 8.714 0.040 0.546 3 484021 1766 1977 212 1.000 0.072 -0.539 3.122 0.050 0.599 4 484022 1839 1977 139 1.000 0.116 -0.805 2.948 0.060 0.760 5 484031 1759 1977 219 1.000 0.138 -0.608 2.432 0.062 0.839 6 484032 1792 1977 186 1.000 0.152 -0.234 1.965 0.067 0.822 7 484041 1793 1977 185 1.000 0.144 -0.945 3.242 0.062 0.859 8 484042 1809 1977 169 1.000 0.108 -0.389 2.588 0.054 0.797 9 484051 1841 1977 137 1.000 0.052 -0.437 3.751 0.043 0.481 10 484052 1881 1977 97 1.000 0.069 -1.184 4.856 0.051 0.516 11 484061 1781 1977 197 1.000 0.072 -0.450 2.792 0.049 0.612 12 484062 1808 1977 170 1.000 0.052 -0.403 2.832 0.036 0.552 13 484071 1742 1977 236 1.000 0.066 -1.373 5.567 0.047 0.592 14 484072 1826 1977 152 1.000 0.082 -0.272 3.446 0.066 0.465 15 484081 1801 1977 177 1.000 0.067 -1.181 4.806 0.051 0.556 16 484082 1811 1977 167 1.000 0.119 -0.904 3.279 0.061 0.792 17 484091 1860 1977 118 1.000 0.060 -0.691 4.530 0.053 0.284 18 484092 1843 1977 135 1.000 0.050 0.104 2.687 0.046 0.306 19 484101 1800 1977 178 1.000 0.047 -1.006 3.800 0.038 0.456 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 484102 1811 1977 167 1.000 0.060 -0.873 5.008 0.037 0.663 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 1.000 0.082 -0.723 3.784 0.051 0.594 STANDARD DEVIATION 34 0.000 0.035 0.451 1.511 0.010 0.174 MEDIAN (50TH QUANTILE) 173 1.000 0.068 -0.650 3.298 0.050 0.574 INTERQUARTILE RANGE 46 0.000 0.056 0.555 1.856 0.019 0.303 MINIMUM VALUE 97 1.000 0.047 -1.822 1.965 0.036 0.284 LOWER HINGE (25TH QUANTILE) 145 1.000 0.056 -0.976 2.812 0.041 0.473 UPPER HINGE (75TH QUANTILE) 191 1.000 0.112 -0.420 4.668 0.061 0.776 MAXIMUM VALUE 236 1.000 0.152 0.104 8.714 0.067 0.859 |------------------------ 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 484011 -67 122 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 484012 -67 134 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 484021 -67 142 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 484022 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 484031 -67 146 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 484032 -67 124 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 484041 -67 123 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 484042 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 484051 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 484052 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 484061 -67 131 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 484062 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 484071 -67 158 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 484072 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 484081 -67 118 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 484082 -67 111 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 484091 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 484092 -67 90 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 484101 -67 119 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 484102 -67 111 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 484011 1795 1977 183 1.000 0.043 -0.382 3.452 0.040 0.282 2 484012 1778 1977 200 1.000 0.049 -1.780 10.077 0.039 0.372 3 484021 1766 1977 212 1.000 0.063 -0.551 3.619 0.050 0.480 4 484022 1839 1977 139 0.999 0.098 -0.727 3.167 0.060 0.673 5 484031 1759 1977 219 0.998 0.086 -0.338 3.652 0.062 0.561 6 484032 1792 1977 186 0.999 0.122 -0.231 3.030 0.067 0.735 7 484041 1793 1977 185 0.998 0.108 -0.385 3.354 0.062 0.737 8 484042 1809 1977 169 0.999 0.073 -0.330 3.142 0.054 0.537 9 484051 1841 1977 137 1.000 0.048 -0.385 3.893 0.043 0.381 10 484052 1881 1977 97 1.000 0.058 -1.416 5.353 0.051 0.297 11 484061 1781 1977 197 1.000 0.064 -0.407 2.944 0.049 0.510 12 484062 1808 1977 170 1.000 0.048 -0.351 2.918 0.036 0.478 13 484071 1742 1977 236 1.000 0.062 -1.347 5.694 0.047 0.537 14 484072 1826 1977 152 1.000 0.065 -0.684 4.447 0.066 0.112 15 484081 1801 1977 177 1.000 0.057 -1.022 4.470 0.051 0.372 16 484082 1811 1977 167 0.998 0.086 -0.700 3.852 0.060 0.590 17 484091 1860 1977 118 1.000 0.055 -0.913 4.617 0.053 0.168 18 484092 1843 1977 135 1.000 0.045 0.085 2.736 0.046 0.148 19 484101 1800 1977 178 1.000 0.042 -0.875 4.005 0.038 0.327 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 484102 1811 1977 167 1.000 0.057 -0.708 5.233 0.037 0.621 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 0.999 0.066 -0.672 4.183 0.051 0.446 STANDARD DEVIATION 34 0.001 0.022 0.453 1.631 0.010 0.187 MEDIAN (50TH QUANTILE) 173 1.000 0.060 -0.617 3.752 0.050 0.479 INTERQUARTILE RANGE 46 0.001 0.031 0.528 1.389 0.019 0.263 MINIMUM VALUE 97 0.998 0.042 -1.780 2.736 0.036 0.112 LOWER HINGE (25TH QUANTILE) 145 0.999 0.048 -0.894 3.154 0.041 0.312 UPPER HINGE (75TH QUANTILE) 191 1.000 0.079 -0.366 4.543 0.060 0.576 MAXIMUM VALUE 236 1.000 0.122 0.085 10.077 0.067 0.737 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.304 0.148 0.011 -0.291 3.230 -0.150 0.667 MINIMUM CORRELATION: -0.150 SERIES 484022 AND 484031 139 YEARS MAXIMUM CORRELATION: 0.667 SERIES 484091 AND 484092 118 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 64.16 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1825. 1850. 1875. 1900. 1925. 1950. CORR 3. 36. 91. 153. 171. 190. 190. RBAR 0.011 0.231 0.298 0.277 0.343 0.282 0.358 SDEV 0.080 0.226 0.181 0.218 0.232 0.217 0.207 SERR 0.046 0.038 0.019 0.018 0.018 0.016 0.015 EPS 0.090 0.810 0.880 0.880 0.912 0.887 0.918 NSS 8.9 14.2 17.3 19.2 19.9 20.0 20.0 |======================== 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 1742 1977 236 1.003 0.043 -0.650 3.841 0.037 0.356 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.357 -0.207 0.256 101 135 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.66 1.10 1.01 1.20 2.30 30.18 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.13 0.00 0.86 0.99 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 0.355 0.328 0.300 0.301 0.256 0.210 0.231 0.206 0.195 0.126 PACF 0.355 0.231 0.155 0.140 0.067 0.015 0.068 0.033 0.031 -0.046 95% C.L. 0.130 0.146 0.158 0.167 0.176 0.182 0.186 0.191 0.195 0.198 |------------------ 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 4 0.228 0.206 0.164 0.136 0.154 |======================= 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 0.332 0.342 0.325 0.287 0.351 0.244 0.233 0.219 0.218 0.117 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 0.332 2 0.246 0.261 3 0.197 0.215 0.186 4 0.177 0.191 0.165 0.110 5 0.156 0.161 0.130 0.077 0.184 6 0.153 0.160 0.127 0.074 0.181 0.017 7 0.153 0.157 0.126 0.073 0.179 0.015 0.014 8 0.153 0.157 0.123 0.071 0.177 0.013 0.012 0.016 9 0.152 0.156 0.123 0.065 0.175 0.008 0.006 0.010 0.037 10 0.156 0.157 0.124 0.066 0.192 0.015 0.018 0.026 0.052 -0.100 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) 1070.85 1045.28 1030.69 1024.34 1023.49 1017.34 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1019.27 1021.22 1023.17 1024.85 1024.49 SELECTED AUTOREGRESSION ORDER: 5 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 0.156 0.161 0.130 0.077 0.184 R-SQUARED DUE TO POOLED AUTOREGRESSION: 23.59 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 130.88 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 5) PROCESS OUT TO ORDER 50: 1.0000 0.156 0.185 0.184 0.156 0.274 0.135 0.134 0.124 0.108 0.1151 0.087 0.080 0.073 0.064 0.060 0.051 0.046 0.042 0.037 0.0335 0.030 0.027 0.024 0.021 0.019 0.017 0.015 0.014 0.012 0.0109 0.010 0.009 0.008 0.007 0.006 0.006 0.005 0.004 0.004 0.0036 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.001 0.001 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 484011 5 0.158 0.177 0.167 0.114 0.102 0.012 2 484012 5 0.195 0.311 0.100 0.066 -0.009 0.139 3 484021 5 0.298 0.335 0.141 0.144 0.095 -0.035 4 484022 5 0.559 0.406 0.373 0.243 -0.158 -0.119 5 484031 5 0.373 0.398 0.125 0.071 0.149 0.000 6 484032 5 0.584 0.589 0.046 0.014 0.130 0.067 7 484041 5 0.599 0.484 0.209 0.156 -0.011 0.006 8 484042 5 0.332 0.447 0.016 0.152 -0.015 0.112 9 484051 5 0.267 0.260 0.204 -0.038 0.114 0.126 10 484052 5 0.155 0.309 0.017 -0.061 0.127 -0.115 11 484061 5 0.307 0.424 0.121 0.024 -0.019 0.119 12 484062 5 0.296 0.337 0.162 0.012 0.064 0.140 13 484071 5 0.378 0.329 0.261 0.071 0.074 0.009 14 484072 5 0.030 0.113 0.036 0.092 -0.074 0.054 15 484081 5 0.220 0.242 0.176 0.042 0.047 0.158 16 484082 5 0.395 0.429 0.142 0.087 0.011 0.084 17 484091 5 0.044 0.166 0.047 -0.032 0.113 -0.023 18 484092 5 0.037 0.146 0.031 0.053 -0.040 0.086 19 484101 5 0.164 0.274 0.246 -0.058 -0.068 0.074 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 484102 5 0.497 0.378 0.420 0.147 -0.129 -0.159 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 5 0.294 0.328 0.152 0.065 0.025 0.037 STANDARD DEVIATION 0 0.175 0.122 0.112 0.080 0.090 0.092 MEDIAN 5 0.297 0.332 0.141 0.069 0.029 0.061 INTERQUARTILE RANGE 0 0.225 0.164 0.160 0.116 0.137 0.127 MINIMUM VALUE 5 0.030 0.113 0.016 -0.061 -0.158 -0.159 LOWER HINGE 5 0.161 0.251 0.046 0.013 -0.030 -0.011 UPPER HINGE 5 0.386 0.415 0.206 0.129 0.108 0.116 MAXIMUM VALUE 5 0.599 0.589 0.420 0.243 0.149 0.158 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 484011 1795 1977 183 1.000 0.040 -0.395 3.864 0.043 -0.002 2 484012 1778 1977 200 1.000 0.044 -1.699 8.920 0.046 0.014 3 484021 1766 1977 212 1.000 0.053 -0.677 4.483 0.057 0.000 4 484022 1839 1977 139 1.000 0.065 0.227 4.635 0.071 -0.015 5 484031 1759 1977 219 1.000 0.068 -0.579 4.080 0.073 0.000 6 484032 1792 1977 186 1.000 0.080 -1.080 8.144 0.085 0.010 7 484041 1793 1977 185 1.000 0.068 -0.037 3.311 0.078 -0.001 8 484042 1809 1977 169 1.000 0.060 -0.035 3.402 0.065 0.008 9 484051 1841 1977 137 1.000 0.042 -0.364 3.014 0.047 0.027 10 484052 1881 1977 97 1.000 0.054 -1.088 4.839 0.058 -0.021 11 484061 1781 1977 197 1.000 0.054 -0.181 3.048 0.058 0.015 12 484062 1808 1977 170 1.000 0.040 -0.397 3.662 0.043 0.005 13 484071 1742 1977 236 1.000 0.049 -0.537 4.009 0.054 -0.007 14 484072 1826 1977 152 1.000 0.064 -0.636 4.147 0.070 -0.001 15 484081 1801 1977 177 1.000 0.050 -0.451 3.320 0.057 -0.006 16 484082 1811 1977 167 1.000 0.067 -0.300 3.545 0.072 -0.002 17 484091 1860 1977 118 1.000 0.054 -0.941 4.820 0.058 0.000 18 484092 1843 1977 135 1.000 0.044 0.042 2.741 0.049 -0.004 19 484101 1800 1977 178 1.000 0.038 -0.659 3.715 0.043 0.007 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 484102 1811 1977 167 1.000 0.040 -0.286 3.387 0.043 -0.019 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 1.000 0.054 -0.504 4.254 0.058 0.000 STANDARD DEVIATION 34 0.000 0.012 0.452 1.584 0.013 0.011 MEDIAN (50TH QUANTILE) 173 1.000 0.053 -0.424 3.789 0.058 0.000 INTERQUARTILE RANGE 46 0.000 0.022 0.434 1.205 0.024 0.013 MINIMUM VALUE 97 1.000 0.038 -1.699 2.741 0.043 -0.021 LOWER HINGE (25TH QUANTILE) 145 1.000 0.043 -0.668 3.353 0.046 -0.005 UPPER HINGE (75TH QUANTILE) 191 1.000 0.064 -0.233 4.559 0.070 0.008 MAXIMUM VALUE 236 1.000 0.080 0.227 8.920 0.085 0.027 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.366 0.108 0.008 0.003 2.843 0.098 0.707 MINIMUM CORRELATION: 0.098 SERIES 484022 AND 484031 139 YEARS MAXIMUM CORRELATION: 0.707 SERIES 484091 AND 484092 118 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 64.16 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1825. 1850. 1875. 1900. 1925. 1950. CORR 3. 36. 91. 153. 171. 190. 190. RBAR 0.178 0.280 0.373 0.393 0.366 0.293 0.451 SDEV 0.084 0.153 0.138 0.141 0.147 0.176 0.142 SERR 0.049 0.025 0.014 0.011 0.011 0.013 0.010 EPS 0.659 0.847 0.911 0.925 0.920 0.892 0.943 NSS 8.9 14.2 17.3 19.2 19.9 20.0 20.0 |======================== 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 1742 1977 236 1.002 0.035 -0.289 3.800 0.039 -0.125 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.115 -0.068 0.107 86 150 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.30 0.56 1.01 1.11 1.67 9.85 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.12 0.00 0.86 0.99 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 -0.124 0.024 0.031 -0.018 0.018 0.022 0.052 0.029 0.085 0.055 PACF -0.124 0.009 0.036 -0.010 0.013 0.026 0.059 0.041 0.092 0.076 95% C.L. 0.130 0.132 0.132 0.132 0.132 0.132 0.133 0.133 0.133 0.134 |------------------ 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 0.016 -0.125 |---------- 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 0.000 0.000 -0.001 -0.003 0.001 0.030 0.059 0.048 0.102 0.050 PACF 0.000 0.000 -0.001 -0.003 0.001 0.030 0.059 0.048 0.103 0.053 95% C.L. 0.130 0.130 0.130 0.130 0.130 0.130 0.130 0.131 0.131 0.132 |----------------- 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 5 0.001 0.000 0.000 -0.001 -0.003 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 1742 1977 236 1.003 0.040 -0.588 3.542 0.034 0.354 |------------ 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 0.353 0.362 0.340 0.307 0.369 0.254 0.258 0.237 0.241 0.196 PACF 0.353 0.271 0.187 0.115 0.188 0.005 0.027 0.018 0.045 -0.024 95% C.L. 0.130 0.145 0.160 0.172 0.181 0.193 0.199 0.204 0.209 0.214 |------------------- 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 5 0.266 0.155 0.165 0.136 0.088 0.191 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.25 MINUTES