RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN026W.rwl.conv LOG FILE PROCESSED: FRAN026W.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: 490 1 Arette, Col St. Martin WIDTH_RING ABAL - 490 2 France silver fir, European fir 1500 4259-45 1743 1977 - 490 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 12 490062 MISSING VALUES FOUND: 1 IN 1 GAPS / 1892 1892 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 490011 1855 1977 123 1.170 0.658 0.681 2.958 0.248 0.831 2 490012 1855 1976 122 0.923 0.372 0.108 2.477 0.228 0.704 3 490021 1904 1977 74 1.907 0.935 0.850 3.273 0.203 0.848 4 490022 1900 1977 78 1.684 0.631 0.446 2.767 0.210 0.796 5 490031 1837 1972 136 0.997 0.438 0.281 3.849 0.200 0.859 6 490032 1795 1966 172 0.815 0.472 1.224 4.512 0.252 0.839 7 490041 1763 1967 205 0.563 0.164 0.196 2.992 0.210 0.547 8 490042 1743 1971 229 0.495 0.170 0.579 3.233 0.207 0.661 9 490051 1855 1977 123 0.650 0.366 0.859 2.760 0.203 0.893 10 490052 1793 1977 185 0.802 0.394 1.886 6.501 0.201 0.865 11 490061 1843 1977 135 0.931 0.724 1.343 4.080 0.235 0.884 12 490062 1832 1977 146 1.035 0.625 0.284 2.220 0.199 0.908 13 490071 1800 1976 177 1.023 0.608 0.522 2.877 0.281 0.776 14 490072 1799 1974 176 0.780 0.431 0.795 3.359 0.214 0.858 15 490081 1798 1961 164 0.884 0.397 1.565 7.116 0.194 0.797 16 490082 1771 1977 207 0.779 0.366 1.151 5.342 0.174 0.855 17 490091 1828 1977 150 1.173 0.751 0.527 2.200 0.188 0.904 18 490092 1833 1977 145 0.635 0.269 -0.099 2.300 0.176 0.851 19 490101 1834 1977 144 1.494 1.194 1.505 4.714 0.198 0.927 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 490102 1825 1965 141 1.666 0.834 0.141 2.494 0.185 0.835 NUMBER OF SERIES READ IN: 20 FROM 1743 TO 1977 235 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 152 1.020 0.540 0.742 3.601 0.210 0.822 STANDARD DEVIATION 39 0.393 0.261 0.551 1.400 0.027 0.092 MEDIAN (50TH QUANTILE) 145 0.927 0.455 0.630 3.113 0.203 0.850 INTERQUARTILE RANGE 47 0.392 0.322 0.905 1.669 0.025 0.078 MINIMUM VALUE 74 0.495 0.164 -0.099 2.200 0.174 0.547 LOWER HINGE (25TH QUANTILE) 129 0.779 0.369 0.283 2.627 0.196 0.797 UPPER HINGE (75TH QUANTILE) 176 1.171 0.691 1.187 4.296 0.221 0.875 MAXIMUM VALUE 229 1.907 1.194 1.886 7.116 0.281 0.927 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.325 0.283 0.020 -0.587 3.397 -0.624 0.839 MINIMUM CORRELATION: -0.624 SERIES 490062 AND 490081 130 YEARS MAXIMUM CORRELATION: 0.839 SERIES 490021 AND 490081 58 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.40 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1825. 1850. 1875. 1900. 1925. 1950. CORR 3. 28. 36. 105. 153. 171. 91. RBAR 0.170 0.420 0.400 0.243 0.254 0.255 0.613 SDEV 0.187 0.302 0.230 0.370 0.375 0.365 0.232 SERR 0.108 0.057 0.038 0.036 0.030 0.028 0.024 EPS 0.543 0.883 0.909 0.851 0.866 0.872 0.968 NSS 5.8 10.4 15.1 17.7 18.9 19.9 19.2 |======================== 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 1743 1977 235 0.761 0.298 0.354 2.709 0.186 0.797 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.818 0.681 -0.171 111 124 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 2.49 3.68 1.00 1.31 4.99 215.45 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.20 0.00 0.80 1.00 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 146. 48. 74. 129. 176. 229. |----------- 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 0.794 0.733 0.670 0.635 0.590 0.581 0.541 0.494 0.456 0.472 PACF 0.794 0.277 0.087 0.091 0.025 0.104 -0.008 -0.053 -0.014 0.140 95% C.L. 0.130 0.196 0.238 0.268 0.293 0.312 0.330 0.345 0.357 0.367 |------------------ 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 0.677 0.531 0.206 0.048 0.099 |================== 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 490011 3 0.00000000 0.00000000 -0.01261166 1.95159805 2 490012 3 0.00000000 0.00000000 -0.00710453 1.36004341 3 490021 1 3.27331758 0.04868465 0.00000000 1.04471111 4 490022 1 1.14224410 0.03223826 0.00000000 1.27318716 5 490031 3 0.00000000 0.00000000 -0.00314026 1.21246076 6 490032 3 0.00000000 0.00000000 -0.00105549 0.90641576 7 490041 3 0.00000000 0.00000000 0.00053773 0.50739455 8 490042 3 0.00000000 0.00000000 -0.00020400 0.51800162 9 490051 1 0.91655165 0.11349629 0.00000000 0.58824450 10 490052 3 0.00000000 0.00000000 0.00130410 0.68044829 11 490061 1 2.48182368 0.08630389 0.00000000 0.72753209 12 490062 1 0.83946604 0.06561827 0.00000000 0.94473851 13 490071 3 0.00000000 0.00000000 0.00098265 0.93599063 14 490072 3 0.00000000 0.00000000 -0.00186014 0.94416755 15 490081 3 0.00000000 0.00000000 -0.00260040 1.09813035 16 490082 3 0.00000000 0.00000000 -0.00202594 0.99011821 17 490091 3 0.00000000 0.00000000 -0.01553379 2.34606791 18 490092 3 0.00000000 0.00000000 -0.00450220 0.96362644 19 490101 -67 96 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 490102 3 0.00000000 0.00000000 -0.01689713 2.86558247 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 490011 1855 1977 123 1.000 0.458 1.007 3.883 0.247 0.705 2 490012 1855 1976 122 0.998 0.361 2.064 11.228 0.226 0.526 3 490021 1904 1977 74 1.000 0.290 0.383 3.670 0.199 0.653 4 490022 1900 1977 78 1.000 0.352 0.696 3.028 0.206 0.751 5 490031 1837 1972 136 0.996 0.435 0.261 3.386 0.198 0.847 6 490032 1795 1966 172 0.999 0.583 1.310 4.707 0.250 0.836 7 490041 1763 1967 205 1.000 0.287 0.275 3.245 0.209 0.525 8 490042 1743 1971 229 1.000 0.342 0.549 3.148 0.206 0.656 9 490051 1855 1977 123 0.999 0.556 1.387 4.442 0.201 0.887 10 490052 1793 1977 185 1.000 0.461 1.579 5.588 0.200 0.842 11 490061 1843 1977 135 0.999 0.740 2.177 8.181 0.232 0.904 12 490062 1832 1977 146 0.999 0.626 0.589 2.612 0.204 0.922 13 490071 1800 1976 177 0.999 0.592 0.539 2.908 0.279 0.767 14 490072 1799 1974 176 0.996 0.523 0.569 2.855 0.213 0.836 15 490081 1798 1961 164 0.997 0.448 2.139 9.072 0.193 0.792 16 490082 1771 1977 207 0.998 0.492 2.000 8.036 0.173 0.867 17 490091 1828 1977 150 1.245 1.281 6.002 42.194 0.185 0.680 18 490092 1833 1977 145 0.986 0.322 0.492 3.398 0.175 0.771 19 490101 1834 1977 144 0.976 0.363 0.802 3.503 0.196 0.755 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 490102 1825 1965 141 0.980 0.314 0.510 2.867 0.183 0.744 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 152 1.008 0.491 1.266 6.598 0.209 0.763 STANDARD DEVIATION 39 0.056 0.224 1.295 8.729 0.027 0.113 MEDIAN (50TH QUANTILE) 145 0.999 0.453 0.749 3.587 0.202 0.769 INTERQUARTILE RANGE 47 0.003 0.222 1.265 3.724 0.025 0.152 MINIMUM VALUE 74 0.976 0.287 0.261 2.612 0.173 0.525 LOWER HINGE (25TH QUANTILE) 129 0.996 0.347 0.524 3.088 0.194 0.692 UPPER HINGE (75TH QUANTILE) 176 1.000 0.569 1.790 6.812 0.220 0.845 MAXIMUM VALUE 229 1.245 1.281 6.002 42.194 0.279 0.922 |------------------------ 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 490011 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 490012 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 490021 -67 49 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 490022 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 490031 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 490032 -67 115 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 490041 -67 137 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 490042 -67 153 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 490051 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 490052 -67 123 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 490061 -67 90 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 490062 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 490071 -67 118 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 490072 -67 117 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 490081 -67 109 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 490082 -67 138 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 490091 -67 100 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 490092 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 490101 -67 96 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 490102 -67 94 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 490011 1855 1977 123 0.989 0.411 0.857 3.652 0.247 0.674 2 490012 1855 1976 122 0.995 0.341 2.129 11.722 0.226 0.492 3 490021 1904 1977 74 0.996 0.260 0.033 3.333 0.196 0.558 4 490022 1900 1977 78 0.994 0.307 0.443 3.189 0.205 0.673 5 490031 1837 1972 136 0.980 0.313 0.342 3.675 0.196 0.717 6 490032 1795 1966 172 0.987 0.500 2.476 12.808 0.250 0.690 7 490041 1763 1967 205 0.998 0.265 0.238 3.000 0.208 0.432 8 490042 1743 1971 229 0.998 0.332 0.516 3.236 0.206 0.639 9 490051 1855 1977 123 0.970 0.352 0.581 3.024 0.199 0.771 10 490052 1793 1977 185 0.983 0.380 1.245 4.709 0.199 0.784 11 490061 1843 1977 135 0.953 0.492 1.357 4.886 0.231 0.833 12 490062 1832 1977 146 0.935 0.420 -0.013 2.436 0.203 0.858 13 490071 1800 1976 177 0.973 0.380 0.893 3.866 0.277 0.482 14 490072 1799 1974 176 0.969 0.369 0.816 3.167 0.212 0.687 15 490081 1798 1961 164 0.989 0.317 1.883 8.640 0.192 0.591 16 490082 1771 1977 207 0.977 0.341 1.387 6.073 0.173 0.747 17 490091 1828 1977 150 0.999 0.360 1.570 7.981 0.184 0.672 18 490092 1833 1977 145 0.995 0.260 0.390 3.132 0.175 0.623 19 490101 1834 1977 144 0.988 0.319 0.648 3.287 0.195 0.686 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 490102 1825 1965 141 0.993 0.257 0.454 2.849 0.183 0.592 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 152 0.983 0.349 0.912 4.933 0.208 0.660 STANDARD DEVIATION 39 0.017 0.069 0.699 3.012 0.027 0.113 MEDIAN (50TH QUANTILE) 145 0.988 0.341 0.732 3.493 0.201 0.673 INTERQUARTILE RANGE 47 0.020 0.069 0.955 2.330 0.025 0.141 MINIMUM VALUE 74 0.935 0.257 -0.013 2.436 0.173 0.432 LOWER HINGE (25TH QUANTILE) 129 0.975 0.310 0.417 3.150 0.194 0.591 UPPER HINGE (75TH QUANTILE) 176 0.995 0.380 1.372 5.480 0.219 0.732 MAXIMUM VALUE 229 0.999 0.500 2.476 12.808 0.277 0.858 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.314 0.212 0.015 -0.521 3.512 -0.413 0.783 MINIMUM CORRELATION: -0.413 SERIES 490062 AND 490081 130 YEARS MAXIMUM CORRELATION: 0.783 SERIES 490051 AND 490052 123 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.40 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1825. 1850. 1875. 1900. 1925. 1950. CORR 3. 28. 36. 105. 153. 171. 91. RBAR 0.190 0.492 0.451 0.284 0.297 0.330 0.437 SDEV 0.247 0.214 0.200 0.309 0.328 0.247 0.209 SERR 0.143 0.040 0.033 0.030 0.027 0.019 0.022 EPS 0.577 0.909 0.925 0.875 0.889 0.908 0.937 NSS 5.8 10.4 15.1 17.7 18.9 19.9 19.2 |======================== 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 1743 1977 235 0.967 0.212 0.333 3.532 0.168 0.459 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.278 0.159 0.073 65 170 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.27 0.91 1.00 1.11 2.02 9.89 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.12 0.00 0.85 0.97 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 0.457 0.338 0.175 0.116 0.028 0.062 -0.059 -0.207 -0.234 -0.169 PACF 0.457 0.163 -0.037 0.006 -0.049 0.065 -0.120 -0.222 -0.070 0.052 95% C.L. 0.130 0.155 0.167 0.170 0.172 0.172 0.172 0.173 0.177 0.182 |------------------ 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 2 0.232 0.383 0.164 |======================= 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 0.522 0.358 0.199 0.114 0.043 0.043 -0.090 -0.181 -0.180 -0.093 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 0.522 2 0.460 0.119 3 0.464 0.136 -0.038 4 0.464 0.138 -0.033 -0.010 5 0.464 0.137 -0.030 0.003 -0.027 6 0.465 0.137 -0.028 -0.003 -0.045 0.038 7 0.471 0.129 -0.029 -0.007 -0.023 0.113 -0.161 8 0.449 0.145 -0.032 -0.008 -0.027 0.130 -0.098 -0.136 9 0.449 0.145 -0.032 -0.008 -0.027 0.130 -0.097 -0.135 -0.001 10 0.449 0.157 -0.023 -0.021 -0.024 0.131 -0.094 -0.149 -0.044 0.096 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) 1811.65 1739.05 1737.72 1739.37 1741.35 1743.17 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1744.84 1740.63 1738.26 1740.26 1740.10 SELECTED AUTOREGRESSION ORDER: 2 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 0.460 0.119 R-SQUARED DUE TO POOLED AUTOREGRESSION: 28.23 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 139.32 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.460 0.330 0.206 0.134 0.086 0.055 0.036 0.023 0.015 0.0095 0.006 0.004 0.003 0.002 0.001 0.001 0.000 0.000 0.000 0.0001 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 490011 2 0.458 0.717 -0.063 2 490012 2 0.271 0.411 0.167 3 490021 2 0.313 0.558 0.002 4 490022 2 0.465 0.702 -0.034 5 490031 2 0.529 0.766 -0.055 6 490032 2 0.504 0.568 0.182 7 490041 2 0.226 0.350 0.201 8 490042 2 0.445 0.510 0.209 9 490051 2 0.612 0.628 0.186 10 490052 2 0.630 0.653 0.170 11 490061 2 0.701 0.821 0.016 12 490062 2 0.749 0.678 0.210 13 490071 2 0.263 0.419 0.144 14 490072 2 0.492 0.591 0.146 15 490081 2 0.381 0.466 0.214 16 490082 2 0.599 0.554 0.261 17 490091 2 0.551 0.709 0.044 18 490092 2 0.400 0.548 0.122 19 490101 2 0.474 0.635 0.074 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 490102 2 0.369 0.501 0.156 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.472 0.589 0.118 STANDARD DEVIATION 0 0.144 0.125 0.099 MEDIAN 2 0.469 0.580 0.151 INTERQUARTILE RANGE 0 0.200 0.184 0.164 MINIMUM VALUE 2 0.226 0.350 -0.063 LOWER HINGE 2 0.375 0.506 0.030 UPPER HINGE 2 0.575 0.690 0.194 MAXIMUM VALUE 2 0.749 0.821 0.261 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 490011 1855 1977 123 1.000 0.303 0.732 5.481 0.330 -0.001 2 490012 1855 1976 122 1.000 0.292 3.050 23.614 0.271 0.016 3 490021 1904 1977 74 1.000 0.215 0.484 4.640 0.242 0.000 4 490022 1900 1977 78 1.000 0.225 0.623 3.140 0.259 0.002 5 490031 1837 1972 136 1.000 0.214 0.670 4.105 0.232 -0.008 6 490032 1795 1966 172 1.000 0.354 3.258 26.273 0.307 0.020 7 490041 1763 1967 205 1.000 0.233 0.474 3.993 0.249 -0.001 8 490042 1743 1971 229 1.000 0.248 0.880 4.927 0.256 -0.010 9 490051 1855 1977 123 1.000 0.220 0.863 4.285 0.224 0.012 10 490052 1793 1977 185 1.000 0.231 0.288 3.852 0.261 0.004 11 490061 1843 1977 135 1.000 0.272 0.693 5.438 0.287 0.002 12 490062 1832 1977 146 1.000 0.210 0.509 3.332 0.224 0.004 13 490071 1800 1976 177 1.000 0.327 1.384 6.487 0.314 0.010 14 490072 1799 1974 176 1.000 0.264 1.176 5.313 0.263 -0.004 15 490081 1798 1961 164 1.000 0.250 1.874 10.320 0.236 -0.007 16 490082 1771 1977 207 1.000 0.218 1.321 6.122 0.218 -0.035 17 490091 1828 1977 150 1.000 0.241 1.551 7.007 0.242 0.069 18 490092 1833 1977 145 1.000 0.201 -0.034 3.192 0.223 0.005 19 490101 1834 1977 144 1.000 0.232 0.778 5.339 0.242 0.002 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 490102 1825 1965 141 1.000 0.204 0.139 3.586 0.231 -0.012 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 152 1.000 0.248 1.036 7.022 0.256 0.003 STANDARD DEVIATION 39 0.000 0.042 0.865 6.362 0.032 0.019 MEDIAN (50TH QUANTILE) 145 1.000 0.232 0.755 5.120 0.246 0.002 INTERQUARTILE RANGE 47 0.000 0.051 0.856 2.382 0.035 0.012 MINIMUM VALUE 74 1.000 0.201 -0.034 3.140 0.218 -0.035 LOWER HINGE (25TH QUANTILE) 129 1.000 0.217 0.496 3.923 0.232 -0.005 UPPER HINGE (75TH QUANTILE) 176 1.000 0.268 1.353 6.304 0.267 0.007 MAXIMUM VALUE 229 1.000 0.354 3.258 26.273 0.330 0.069 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.460 0.107 0.008 0.125 2.595 0.218 0.718 MINIMUM CORRELATION: 0.218 SERIES 490051 AND 490071 122 YEARS MAXIMUM CORRELATION: 0.718 SERIES 490021 AND 490031 69 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.40 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1825. 1850. 1875. 1900. 1925. 1950. CORR 3. 28. 36. 105. 153. 171. 91. RBAR 0.551 0.691 0.629 0.404 0.438 0.490 0.543 SDEV 0.057 0.099 0.115 0.144 0.147 0.126 0.109 SERR 0.033 0.019 0.019 0.014 0.012 0.010 0.011 EPS 0.877 0.959 0.962 0.923 0.936 0.950 0.958 NSS 5.8 10.4 15.1 17.7 18.9 19.9 19.2 |======================== 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 1743 1977 235 0.988 0.181 0.501 5.020 0.208 -0.151 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.331 0.141 -0.002 81 154 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.33 1.07 1.00 1.12 2.19 14.71 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.12 0.00 0.85 0.98 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 -0.150 -0.039 -0.050 -0.037 -0.072 0.165 0.021 -0.132 -0.160 -0.054 PACF -0.150 -0.063 -0.067 -0.060 -0.097 0.134 0.056 -0.121 -0.200 -0.126 95% C.L. 0.130 0.133 0.134 0.134 0.134 0.135 0.138 0.138 0.140 0.143 |------------------ 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 0.027 -0.151 |---------- 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 -0.005 -0.014 -0.081 -0.052 -0.055 0.156 0.013 -0.156 -0.194 -0.079 PACF -0.005 -0.014 -0.081 -0.054 -0.059 0.148 0.006 -0.169 -0.190 -0.080 95% C.L. 0.130 0.130 0.130 0.131 0.132 0.132 0.135 0.135 0.138 0.143 |----------------- 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 2 0.007 -0.005 -0.014 |========================= 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 1743 1977 235 0.989 0.203 0.282 3.241 0.157 0.476 |------------ 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 0.474 0.280 0.095 0.030 -0.004 0.055 -0.072 -0.222 -0.271 -0.187 PACF 0.474 0.071 -0.080 -0.007 -0.004 0.084 -0.159 -0.216 -0.084 0.055 95% C.L. 0.130 0.157 0.165 0.166 0.166 0.166 0.167 0.167 0.172 0.179 |------------------- 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 0.230 0.475 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.62 MINUTES