RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN024N.rwl.conv LOG FILE PROCESSED: FRAN024N.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_MINIMUM 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 1 484011 MISSING VALUES FOUND: 5 IN 1 GAPS / 1960 1964 / -------------------------------------------------------------------- 6 484032 MISSING VALUES FOUND: 5 IN 1 GAPS / 1915 1919 / -------------------------------------------------------------------- 10 484052 MISSING VALUES FOUND: 7 IN 1 GAPS / 1934 1940 / -------------------------------------------------------------------- 12 484062 MISSING VALUES FOUND: 4 IN 1 GAPS / 1870 1873 / -------------------------------------------------------------------- 14 484072 MISSING VALUES FOUND: 27 IN 1 GAPS / 1870 1896 / -------------------------------------------------------------------- 17 484091 MISSING VALUES FOUND: 6 IN 1 GAPS / 1963 1968 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 484011 1795 1977 183 0.294 0.024 0.234 3.255 0.061 0.501 2 484012 1778 1977 200 0.304 0.030 1.019 3.571 0.055 0.715 3 484021 1766 1977 212 0.313 0.034 1.303 5.033 0.058 0.747 4 484022 1839 1977 139 0.320 0.035 0.568 3.543 0.059 0.738 5 484031 1759 1977 219 0.344 0.038 0.558 2.977 0.059 0.738 6 484032 1792 1977 186 0.337 0.032 -0.214 2.388 0.052 0.777 7 484041 1793 1977 185 0.315 0.037 0.578 3.618 0.061 0.751 8 484042 1809 1977 169 0.348 0.038 0.844 3.129 0.062 0.699 9 484051 1841 1977 137 0.299 0.023 0.541 3.415 0.053 0.558 10 484052 1881 1977 97 0.283 0.017 0.755 3.243 0.051 0.440 11 484061 1781 1977 197 0.337 0.029 0.520 3.341 0.059 0.549 12 484062 1808 1977 170 0.330 0.039 0.988 4.418 0.055 0.800 13 484071 1742 1977 236 0.325 0.057 0.847 3.113 0.064 0.865 14 484072 1826 1977 152 0.309 0.044 1.512 4.926 0.064 0.801 15 484081 1801 1977 177 0.329 0.035 2.340 10.531 0.055 0.626 16 484082 1811 1977 167 0.363 0.040 0.753 4.216 0.057 0.679 17 484091 1860 1977 118 0.266 0.017 0.241 3.132 0.059 0.258 18 484092 1843 1977 135 0.260 0.021 0.230 3.190 0.068 0.454 19 484101 1800 1977 178 0.313 0.026 0.284 3.868 0.062 0.529 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 484102 1811 1977 167 0.323 0.032 1.133 5.610 0.051 0.775 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 169 0.316 0.032 0.752 4.026 0.058 0.650 STANDARD DEVIATION 36 0.026 0.010 0.555 1.723 0.005 0.155 MEDIAN (50TH QUANTILE) 173 0.318 0.033 0.666 3.479 0.059 0.707 INTERQUARTILE RANGE 53 0.032 0.013 0.601 1.156 0.006 0.224 MINIMUM VALUE 90 0.260 0.017 -0.214 2.388 0.051 0.258 LOWER HINGE (25TH QUANTILE) 138 0.301 0.025 0.402 3.161 0.055 0.539 UPPER HINGE (75TH QUANTILE) 191 0.333 0.038 1.003 4.317 0.061 0.763 MAXIMUM VALUE 236 0.363 0.057 2.340 10.531 0.068 0.865 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.323 0.227 0.016 -0.651 3.236 -0.344 0.783 MINIMUM CORRELATION: -0.344 SERIES 484022 AND 484102 139 YEARS MAXIMUM CORRELATION: 0.783 SERIES 484012 AND 484071 200 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 0.268 0.204 0.243 0.272 0.328 0.287 0.258 SDEV 0.299 0.252 0.232 0.233 0.213 0.234 0.270 SERR 0.173 0.042 0.024 0.019 0.016 0.017 0.020 EPS 0.766 0.785 0.848 0.878 0.906 0.890 0.874 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 0.333 0.040 1.379 5.552 0.044 0.859 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.463 -0.149 0.078 63 173 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.28 1.07 1.01 1.08 2.15 6.51 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.11 0.00 0.85 0.96 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 0.855 0.796 0.732 0.711 0.700 0.691 0.694 0.689 0.671 0.644 PACF 0.855 0.242 0.034 0.151 0.133 0.078 0.119 0.073 -0.002 -0.018 95% C.L. 0.130 0.204 0.251 0.285 0.314 0.339 0.362 0.384 0.405 0.423 |------------------ 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 0.801 0.462 0.228 0.108 0.144 |================== 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 3 0.00000000 0.00000000 -0.00019472 0.31110129 2 484012 1 0.08984020 0.02484497 0.00000000 0.28596899 3 484021 1 0.12916186 0.04245730 0.00000000 0.29883176 4 484022 3 0.00000000 0.00000000 -0.00067309 0.36747578 5 484031 3 0.00000000 0.00000000 -0.00043505 0.39150894 6 484032 3 0.00000000 0.00000000 -0.00040380 0.37359798 7 484041 3 0.00000000 0.00000000 -0.00041257 0.35334197 8 484042 1 0.10197181 0.01303782 0.00000000 0.30714846 9 484051 1 0.06621760 0.05604797 0.00000000 0.29081684 10 484052 1 0.01920059 0.00666174 0.00000000 0.26859203 11 484061 3 0.00000000 0.00000000 -0.00025571 0.36252305 12 484062 3 0.00000000 0.00000000 -0.00051194 0.37327147 13 484071 1 0.19796857 0.00840605 0.00000000 0.23934469 14 484072 1 0.12750617 0.01992636 0.00000000 0.27205023 15 484081 1 0.01165437 0.15717220 0.00000000 0.32831371 16 484082 1 0.24784911 0.00268752 0.00000000 0.16370209 17 484091 1 0.01986269 0.06590576 0.00000000 0.26342332 18 484092 1 0.04939559 0.04051271 0.00000000 0.25155783 19 484101 3 0.00000000 0.00000000 -0.00020763 0.33172920 SERIES IDENT OPTION A B C D 20 484102 3 0.00000000 0.00000000 0.00018490 0.30752254 |-------------------- 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 0.078 0.475 2.970 0.060 0.470 2 484012 1778 1977 200 1.000 0.067 0.452 3.679 0.055 0.380 3 484021 1766 1977 212 1.000 0.066 0.265 2.712 0.058 0.367 4 484022 1839 1977 139 1.000 0.064 0.234 3.186 0.059 0.363 5 484031 1759 1977 219 1.000 0.076 0.600 3.100 0.059 0.449 6 484032 1792 1977 186 1.000 0.072 0.210 2.721 0.052 0.608 7 484041 1793 1977 185 1.000 0.096 1.098 4.965 0.061 0.642 8 484042 1809 1977 169 1.000 0.080 0.659 3.493 0.062 0.457 9 484051 1841 1977 137 1.000 0.059 0.296 3.107 0.052 0.345 10 484052 1881 1977 97 1.000 0.059 0.666 3.389 0.050 0.419 11 484061 1781 1977 197 1.000 0.074 0.686 3.737 0.059 0.397 12 484062 1808 1977 170 1.000 0.086 0.500 3.775 0.054 0.661 13 484071 1742 1977 236 1.000 0.091 0.861 3.862 0.064 0.580 14 484072 1826 1977 152 1.000 0.079 0.382 3.232 0.062 0.506 15 484081 1801 1977 177 1.000 0.105 2.341 10.588 0.055 0.621 16 484082 1811 1977 167 1.000 0.084 1.399 7.500 0.057 0.469 17 484091 1860 1977 118 1.000 0.061 0.219 2.911 0.058 0.195 18 484092 1843 1977 135 1.000 0.066 0.144 3.744 0.068 0.209 19 484101 1800 1977 178 1.000 0.076 0.487 3.486 0.061 0.443 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 484102 1811 1977 167 1.000 0.095 0.843 4.366 0.050 0.743 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 1.000 0.077 0.641 4.026 0.058 0.466 STANDARD DEVIATION 34 0.000 0.013 0.512 1.868 0.005 0.144 MEDIAN (50TH QUANTILE) 173 1.000 0.076 0.494 3.490 0.058 0.453 INTERQUARTILE RANGE 46 0.000 0.019 0.484 0.715 0.006 0.221 MINIMUM VALUE 97 1.000 0.059 0.144 2.712 0.050 0.195 LOWER HINGE (25TH QUANTILE) 145 1.000 0.066 0.280 3.103 0.055 0.374 UPPER HINGE (75TH QUANTILE) 191 1.000 0.085 0.764 3.819 0.061 0.594 MAXIMUM VALUE 236 1.000 0.105 2.341 10.588 0.068 0.743 |------------------------ 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 0.071 0.478 3.158 0.060 0.371 2 484012 1778 1977 200 1.000 0.065 0.460 3.638 0.055 0.341 3 484021 1766 1977 212 1.000 0.062 0.307 2.765 0.058 0.281 4 484022 1839 1977 139 1.000 0.058 0.136 3.015 0.059 0.216 5 484031 1759 1977 219 1.000 0.069 0.591 3.158 0.059 0.339 6 484032 1792 1977 186 1.000 0.062 0.210 2.824 0.052 0.476 7 484041 1793 1977 185 0.999 0.082 0.814 4.497 0.060 0.517 8 484042 1809 1977 169 1.000 0.072 0.603 3.670 0.062 0.348 9 484051 1841 1977 137 1.000 0.058 0.241 3.013 0.052 0.308 10 484052 1881 1977 97 1.000 0.056 0.753 3.622 0.050 0.338 11 484061 1781 1977 197 1.000 0.069 0.588 3.521 0.059 0.321 12 484062 1808 1977 170 1.000 0.077 0.501 3.678 0.054 0.577 13 484071 1742 1977 236 0.999 0.083 0.866 4.016 0.064 0.497 14 484072 1826 1977 152 1.000 0.075 0.374 3.175 0.062 0.456 15 484081 1801 1977 177 1.000 0.101 2.359 10.585 0.055 0.597 16 484082 1811 1977 167 1.000 0.075 1.370 8.118 0.057 0.354 17 484091 1860 1977 118 1.000 0.057 0.434 3.437 0.058 0.103 18 484092 1843 1977 135 1.000 0.064 0.142 3.541 0.068 0.175 19 484101 1800 1977 178 1.000 0.064 0.662 4.804 0.062 0.223 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 484102 1811 1977 167 1.000 0.075 0.822 4.610 0.050 0.593 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 1.000 0.070 0.635 4.142 0.058 0.372 STANDARD DEVIATION 34 0.000 0.011 0.501 1.911 0.005 0.140 MEDIAN (50TH QUANTILE) 173 1.000 0.069 0.545 3.581 0.059 0.345 INTERQUARTILE RANGE 46 0.000 0.013 0.443 1.099 0.006 0.192 MINIMUM VALUE 97 0.999 0.056 0.136 2.765 0.050 0.103 LOWER HINGE (25TH QUANTILE) 145 1.000 0.062 0.341 3.158 0.055 0.294 UPPER HINGE (75TH QUANTILE) 191 1.000 0.075 0.783 4.257 0.061 0.487 MAXIMUM VALUE 236 1.000 0.101 2.359 10.585 0.068 0.597 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.260 0.130 0.009 -0.097 2.820 -0.052 0.620 MINIMUM CORRELATION: -0.052 SERIES 484051 AND 484081 137 YEARS MAXIMUM CORRELATION: 0.620 SERIES 484042 AND 484072 152 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 0.130 0.215 0.256 0.313 0.331 0.311 0.270 SDEV 0.175 0.213 0.209 0.199 0.176 0.187 0.197 SERR 0.101 0.036 0.022 0.016 0.013 0.014 0.014 EPS 0.572 0.795 0.857 0.897 0.908 0.900 0.881 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 0.995 0.047 0.495 3.344 0.047 0.142 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.232 0.121 -0.067 59 177 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.36 0.97 1.01 1.10 2.07 15.21 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.11 0.00 0.87 0.98 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 0.141 0.075 -0.047 0.009 -0.072 -0.083 -0.027 0.033 -0.087 -0.114 PACF 0.141 0.056 -0.066 0.021 -0.070 -0.071 0.006 0.040 -0.105 -0.101 95% C.L. 0.130 0.133 0.133 0.134 0.134 0.134 0.135 0.135 0.135 0.136 |------------------ 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 0.023 0.141 |======================= 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 0.050 0.064 -0.120 0.068 -0.062 -0.103 -0.007 0.022 -0.110 -0.146 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 0.050 2 0.047 0.061 3 0.055 0.067 -0.127 4 0.065 0.062 -0.131 0.078 5 0.069 0.055 -0.128 0.082 -0.056 6 0.062 0.065 -0.144 0.089 -0.047 -0.124 7 0.067 0.067 -0.147 0.094 -0.049 -0.126 0.035 8 0.066 0.068 -0.146 0.092 -0.047 -0.127 0.034 0.015 9 0.068 0.073 -0.164 0.086 -0.034 -0.148 0.044 0.024 -0.142 10 0.051 0.076 -0.159 0.068 -0.038 -0.137 0.024 0.033 -0.134 -0.122 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) 1052.92 1054.33 1055.44 1053.59 1054.14 1055.41 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1053.76 1055.47 1057.42 1054.60 1053.07 SELECTED AUTOREGRESSION ORDER: 0 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 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 484011 0 0.141 2 484012 0 0.119 3 484021 0 0.082 4 484022 0 0.048 5 484031 0 0.115 6 484032 0 0.227 7 484041 0 0.282 8 484042 0 0.122 9 484051 0 0.095 10 484052 0 0.115 11 484061 0 0.105 12 484062 0 0.347 13 484071 0 0.247 14 484072 0 0.215 15 484081 0 0.359 16 484082 0 0.126 17 484091 0 0.011 18 484092 0 0.031 19 484101 0 0.050 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 484102 0 0.359 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 0 0.160 STANDARD DEVIATION 0 0.110 MEDIAN 0 0.120 INTERQUARTILE RANGE 0 0.148 MINIMUM VALUE 0 0.011 LOWER HINGE 0 0.089 UPPER HINGE 0 0.237 MAXIMUM VALUE 0 0.359 |------------------- 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 0.071 0.478 3.158 0.060 0.371 2 484012 1778 1977 200 1.000 0.065 0.460 3.638 0.055 0.341 3 484021 1766 1977 212 1.000 0.062 0.307 2.765 0.058 0.281 4 484022 1839 1977 139 1.000 0.058 0.136 3.015 0.059 0.216 5 484031 1759 1977 219 1.000 0.069 0.591 3.158 0.059 0.339 6 484032 1792 1977 186 1.000 0.062 0.210 2.824 0.052 0.476 7 484041 1793 1977 185 1.000 0.082 0.814 4.497 0.060 0.517 8 484042 1809 1977 169 1.000 0.072 0.603 3.670 0.062 0.348 9 484051 1841 1977 137 1.000 0.058 0.241 3.013 0.052 0.308 10 484052 1881 1977 97 1.000 0.056 0.753 3.622 0.050 0.338 11 484061 1781 1977 197 1.000 0.069 0.588 3.521 0.059 0.321 12 484062 1808 1977 170 1.000 0.077 0.501 3.678 0.054 0.577 13 484071 1742 1977 236 1.000 0.083 0.866 4.016 0.064 0.497 14 484072 1826 1977 152 1.000 0.075 0.374 3.175 0.062 0.456 15 484081 1801 1977 177 1.000 0.101 2.359 10.585 0.055 0.597 16 484082 1811 1977 167 1.000 0.075 1.370 8.118 0.057 0.354 17 484091 1860 1977 118 1.000 0.057 0.434 3.437 0.058 0.103 18 484092 1843 1977 135 1.000 0.064 0.142 3.541 0.068 0.175 19 484101 1800 1977 178 1.000 0.064 0.662 4.804 0.062 0.223 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 484102 1811 1977 167 1.000 0.075 0.822 4.610 0.050 0.593 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 1.000 0.070 0.635 4.142 0.058 0.372 STANDARD DEVIATION 34 0.000 0.011 0.501 1.911 0.005 0.140 MEDIAN (50TH QUANTILE) 173 1.000 0.069 0.544 3.581 0.059 0.345 INTERQUARTILE RANGE 46 0.000 0.013 0.443 1.099 0.006 0.192 MINIMUM VALUE 97 1.000 0.056 0.136 2.765 0.050 0.103 LOWER HINGE (25TH QUANTILE) 145 1.000 0.062 0.341 3.158 0.055 0.294 UPPER HINGE (75TH QUANTILE) 191 1.000 0.075 0.783 4.257 0.061 0.487 MAXIMUM VALUE 236 1.000 0.101 2.359 10.585 0.068 0.597 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.260 0.130 0.009 -0.097 2.820 -0.052 0.620 MINIMUM CORRELATION: -0.052 SERIES 484051 AND 484081 137 YEARS MAXIMUM CORRELATION: 0.620 SERIES 484042 AND 484072 152 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 0.130 0.215 0.256 0.313 0.331 0.311 0.270 SDEV 0.175 0.213 0.209 0.199 0.176 0.187 0.197 SERR 0.101 0.036 0.022 0.016 0.013 0.014 0.014 EPS 0.572 0.795 0.857 0.897 0.908 0.900 0.881 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 0.996 0.046 0.496 3.347 0.047 0.142 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.231 0.121 -0.067 59 177 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.36 1.02 1.01 1.10 2.12 14.99 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.11 0.00 0.87 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 0.141 0.075 -0.047 0.009 -0.072 -0.082 -0.027 0.033 -0.087 -0.114 PACF 0.141 0.056 -0.067 0.020 -0.070 -0.071 0.005 0.040 -0.105 -0.101 95% C.L. 0.130 0.133 0.133 0.134 0.134 0.134 0.135 0.135 0.136 0.136 |------------------ 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 0.023 0.141 |========================= 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 0.996 0.046 0.496 3.347 0.047 0.142 |------------ 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 0.141 0.075 -0.047 0.009 -0.072 -0.082 -0.027 0.033 -0.087 -0.114 PACF 0.141 0.056 -0.067 0.020 -0.070 -0.071 0.005 0.040 -0.105 -0.101 95% C.L. 0.130 0.133 0.133 0.134 0.134 0.134 0.135 0.135 0.136 0.136 |------------------- 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 0.023 0.141 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.25 MINUTES