RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN024L.rwl.conv LOG FILE PROCESSED: FRAN024L.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 WIDTH_LATE 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 0.326 0.179 1.851 6.553 0.248 0.756 2 484012 1778 1977 200 0.263 0.214 2.189 7.250 0.239 0.862 3 484021 1766 1977 212 0.243 0.203 2.403 9.683 0.264 0.869 4 484022 1839 1977 139 0.307 0.303 2.351 8.296 0.272 0.861 5 484031 1759 1977 219 0.155 0.102 0.874 3.254 0.284 0.840 6 484032 1792 1977 186 0.240 0.243 3.391 18.593 0.307 0.830 7 484041 1793 1977 185 0.274 0.171 1.603 6.478 0.285 0.801 8 484042 1809 1977 169 0.175 0.088 0.884 3.189 0.201 0.834 9 484051 1841 1977 137 0.263 0.186 2.155 7.838 0.296 0.726 10 484052 1881 1977 97 0.208 0.084 1.107 3.712 0.207 0.781 11 484061 1781 1977 197 0.223 0.167 2.164 8.719 0.217 0.849 12 484062 1808 1977 170 0.295 0.155 0.995 3.531 0.259 0.768 13 484071 1742 1977 236 0.191 0.142 2.130 8.083 0.309 0.727 14 484072 1826 1977 152 0.447 0.160 0.778 3.222 0.258 0.578 15 484081 1801 1977 177 0.281 0.165 1.791 7.054 0.270 0.758 16 484082 1811 1977 167 0.293 0.161 1.523 5.419 0.248 0.778 17 484091 1860 1977 118 0.359 0.166 1.105 5.096 0.274 0.669 18 484092 1843 1977 135 0.337 0.143 0.743 3.072 0.306 0.558 19 484101 1800 1977 178 0.230 0.127 1.899 10.860 0.277 0.619 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 484102 1811 1977 167 0.345 0.280 2.588 11.374 0.312 0.673 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 0.273 0.172 1.726 7.064 0.267 0.757 STANDARD DEVIATION 35 0.070 0.057 0.719 3.769 0.033 0.095 MEDIAN (50TH QUANTILE) 173 0.269 0.165 1.821 6.804 0.271 0.773 INTERQUARTILE RANGE 53 0.090 0.052 1.126 4.886 0.042 0.138 MINIMUM VALUE 97 0.155 0.084 0.743 3.072 0.201 0.558 LOWER HINGE (25TH QUANTILE) 138 0.226 0.143 1.050 3.621 0.248 0.699 UPPER HINGE (75TH QUANTILE) 191 0.316 0.194 2.176 8.508 0.291 0.837 MAXIMUM VALUE 236 0.447 0.303 3.391 18.593 0.312 0.869 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.273 0.273 0.020 -0.101 2.351 -0.407 0.811 MINIMUM CORRELATION: -0.407 SERIES 484052 AND 484091 97 YEARS MAXIMUM CORRELATION: 0.811 SERIES 484052 AND 484061 97 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 -0.089 0.298 0.312 0.363 0.407 0.307 0.211 SDEV 0.275 0.184 0.246 0.205 0.266 0.325 0.359 SERR 0.159 0.031 0.026 0.017 0.020 0.024 0.026 EPS -2.720 0.858 0.887 0.916 0.932 0.899 0.843 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 0.246 0.105 2.039 10.896 0.194 0.703 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.374 0.229 0.062 121 115 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.99 2.01 1.01 1.35 3.36 22.88 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.16 0.00 0.84 1.00 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 0.700 0.573 0.451 0.403 0.470 0.420 0.409 0.308 0.247 0.216 PACF 0.700 0.162 0.003 0.089 0.272 -0.039 0.044 -0.098 -0.020 -0.025 95% C.L. 0.130 0.183 0.211 0.227 0.239 0.254 0.266 0.276 0.282 0.286 |------------------ RAW DATA CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 3 0.562 0.522 0.188 0.105 |================== 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 0.49365896 0.02705499 0.00000000 0.22861867 2 484012 1 0.53824919 0.01342683 0.00000000 0.07734316 3 484021 1 0.37649187 0.00871613 0.00000000 0.07190017 4 484022 1 1.43403208 0.08495585 0.00000000 0.19026940 5 484031 1 0.17862217 0.03754888 0.00000000 0.13384964 6 484032 3 0.00000000 0.00000000 0.00140160 0.10905783 7 484041 3 0.00000000 0.00000000 0.00079303 0.20073444 8 484042 3 0.00000000 0.00000000 0.00060832 0.12326289 9 484051 3 0.00000000 0.00000000 0.00213326 0.11565157 10 484052 3 0.00000000 0.00000000 0.00182096 0.11871134 11 484061 3 0.00000000 0.00000000 0.00050496 0.17259765 12 484062 3 0.00000000 0.00000000 0.00029376 0.26866367 13 484071 3 0.00000000 0.00000000 0.00001087 0.18981320 14 484072 1 0.27712727 0.05488086 0.00000000 0.40073383 15 484081 3 0.00000000 0.00000000 0.00138954 0.15757383 16 484082 1 0.15442094 0.06136638 0.00000000 0.27886331 17 484091 3 0.00000000 0.00000000 -0.00082569 0.40785745 18 484092 3 0.00000000 0.00000000 -0.00036523 0.36172470 19 484101 1 0.33480734 0.05022346 0.00000000 0.19359905 SERIES IDENT OPTION A B C D 20 484102 3 0.00000000 0.00000000 0.00034246 0.31632349 |-------------------- 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 0.357 0.704 3.476 0.247 0.534 2 484012 1778 1977 200 1.013 0.497 1.029 3.954 0.238 0.788 3 484021 1766 1977 212 1.007 0.730 2.127 8.124 0.264 0.817 4 484022 1839 1977 139 1.003 0.672 2.661 10.649 0.267 0.642 5 484031 1759 1977 219 0.998 0.661 1.235 4.593 0.283 0.835 6 484032 1792 1977 186 1.050 1.030 3.124 16.309 0.306 0.702 7 484041 1793 1977 185 1.007 0.652 2.341 10.734 0.284 0.804 8 484042 1809 1977 169 1.009 0.512 1.047 3.391 0.200 0.835 9 484051 1841 1977 137 1.035 0.656 1.796 6.088 0.293 0.709 10 484052 1881 1977 97 1.005 0.299 0.414 3.417 0.205 0.605 11 484061 1781 1977 197 1.006 0.700 1.623 6.483 0.216 0.825 12 484062 1808 1977 170 1.001 0.517 0.926 3.226 0.254 0.748 13 484071 1742 1977 236 1.000 0.746 2.148 8.193 0.308 0.724 14 484072 1826 1977 152 1.000 0.331 1.081 4.362 0.247 0.537 15 484081 1801 1977 177 1.014 0.494 0.824 3.698 0.269 0.686 16 484082 1811 1977 167 1.000 0.542 1.508 5.091 0.246 0.786 17 484091 1860 1977 118 0.998 0.467 1.285 5.198 0.272 0.672 18 484092 1843 1977 135 1.000 0.422 0.737 3.052 0.304 0.548 19 484101 1800 1977 178 0.999 0.465 0.974 3.458 0.274 0.619 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 484102 1811 1977 167 1.000 0.790 2.343 9.663 0.310 0.664 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 1.007 0.577 1.496 6.158 0.264 0.704 STANDARD DEVIATION 34 0.013 0.178 0.743 3.487 0.033 0.101 MEDIAN (50TH QUANTILE) 173 1.002 0.529 1.260 4.842 0.268 0.706 INTERQUARTILE RANGE 46 0.008 0.220 1.188 4.691 0.042 0.165 MINIMUM VALUE 97 0.998 0.299 0.414 3.052 0.200 0.534 LOWER HINGE (25TH QUANTILE) 145 1.000 0.466 0.950 3.467 0.247 0.630 UPPER HINGE (75TH QUANTILE) 191 1.008 0.686 2.138 8.158 0.289 0.796 MAXIMUM VALUE 236 1.050 1.030 3.124 16.309 0.310 0.835 |------------------------ 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 0.995 0.315 0.855 4.965 0.247 0.385 2 484012 1778 1977 200 0.984 0.407 1.161 4.911 0.238 0.695 3 484021 1766 1977 212 0.957 0.495 2.362 9.926 0.264 0.722 4 484022 1839 1977 139 0.986 0.413 1.400 5.360 0.266 0.478 5 484031 1759 1977 219 0.965 0.437 1.118 4.437 0.284 0.666 6 484032 1792 1977 186 0.967 0.591 2.300 11.735 0.306 0.718 7 484041 1793 1977 185 0.982 0.447 0.853 4.568 0.284 0.721 8 484042 1809 1977 169 0.980 0.281 0.828 3.507 0.200 0.604 9 484051 1841 1977 137 0.985 0.438 1.560 5.956 0.294 0.500 10 484052 1881 1977 97 0.993 0.258 0.652 4.502 0.205 0.490 11 484061 1781 1977 197 0.961 0.421 2.357 10.980 0.217 0.684 12 484062 1808 1977 170 0.982 0.372 0.802 3.203 0.254 0.616 13 484071 1742 1977 236 0.979 0.578 1.881 7.658 0.309 0.678 14 484072 1826 1977 152 0.996 0.294 0.685 3.778 0.247 0.440 15 484081 1801 1977 177 0.984 0.395 1.021 4.915 0.268 0.578 16 484082 1811 1977 167 0.971 0.389 1.205 5.000 0.246 0.617 17 484091 1860 1977 118 0.996 0.307 1.045 4.763 0.271 0.340 18 484092 1843 1977 135 0.984 0.330 0.776 3.282 0.303 0.316 19 484101 1800 1977 178 0.992 0.362 1.126 5.537 0.275 0.387 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 484102 1811 1977 167 0.993 0.772 2.339 8.809 0.310 0.656 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 0.982 0.415 1.316 5.890 0.264 0.565 STANDARD DEVIATION 34 0.012 0.122 0.603 2.546 0.033 0.136 MEDIAN (50TH QUANTILE) 173 0.984 0.401 1.122 4.940 0.267 0.610 INTERQUARTILE RANGE 46 0.018 0.120 0.881 2.338 0.042 0.222 MINIMUM VALUE 97 0.957 0.258 0.652 3.203 0.200 0.316 LOWER HINGE (25TH QUANTILE) 145 0.975 0.322 0.840 4.469 0.247 0.459 UPPER HINGE (75TH QUANTILE) 191 0.993 0.442 1.721 6.807 0.289 0.681 MAXIMUM VALUE 236 0.996 0.772 2.362 11.735 0.310 0.722 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.222 0.164 0.012 0.005 2.909 -0.235 0.636 MINIMUM CORRELATION: -0.235 SERIES 484032 AND 484091 118 YEARS MAXIMUM CORRELATION: 0.636 SERIES 484021 AND 484052 97 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 0.046 0.174 0.165 0.254 0.327 0.218 0.232 SDEV 0.333 0.226 0.212 0.190 0.230 0.276 0.285 SERR 0.192 0.038 0.022 0.015 0.018 0.020 0.021 EPS 0.301 0.750 0.774 0.867 0.906 0.848 0.858 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 0.946 0.331 1.512 7.182 0.232 0.582 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.325 0.162 0.143 86 150 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.44 1.14 1.01 1.13 2.27 13.93 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 0.580 0.419 0.334 0.254 0.275 0.210 0.228 0.127 0.052 0.001 PACF 0.580 0.124 0.076 0.011 0.130 -0.029 0.096 -0.115 -0.057 -0.072 95% C.L. 0.130 0.168 0.185 0.195 0.201 0.207 0.211 0.215 0.216 0.216 |------------------ STANDARD CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 3 0.386 0.477 0.100 0.132 |======================= 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 0.507 0.343 0.362 0.238 0.239 0.214 0.202 0.177 0.130 0.061 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 0.507 2 0.449 0.115 3 0.425 0.024 0.204 4 0.434 0.025 0.221 -0.040 5 0.438 0.002 0.219 -0.084 0.102 6 0.437 0.003 0.217 -0.084 0.098 0.009 7 0.436 -0.004 0.222 -0.099 0.098 -0.021 0.070 8 0.436 -0.004 0.223 -0.100 0.099 -0.021 0.072 -0.005 9 0.436 -0.003 0.223 -0.099 0.098 -0.018 0.072 0.000 -0.012 10 0.435 -0.003 0.229 -0.100 0.106 -0.027 0.090 0.000 0.025 -0.084 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) 1868.52 1800.26 1799.09 1791.05 1792.67 1792.20 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1794.17 1795.03 1797.02 1798.99 1799.33 SELECTED AUTOREGRESSION ORDER: 3 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 0.425 0.024 0.204 R-SQUARED DUE TO POOLED AUTOREGRESSION: 29.79 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 142.43 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.425 0.205 0.301 0.220 0.142 0.127 0.102 0.076 0.061 0.0485 0.038 0.029 0.023 0.018 0.014 0.011 0.009 0.007 0.005 0.0043 0.003 0.003 0.002 0.002 0.001 0.001 0.001 0.001 0.000 0.0004 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 484011 3 0.165 0.422 -0.075 -0.044 2 484012 3 0.511 0.621 -0.005 0.156 3 484021 3 0.538 0.703 0.041 -0.019 4 484022 3 0.321 0.333 0.100 0.262 5 484031 3 0.473 0.587 -0.026 0.198 6 484032 3 0.555 0.712 -0.030 0.093 7 484041 3 0.543 0.583 0.115 0.096 8 484042 3 0.384 0.562 -0.026 0.148 9 484051 3 0.295 0.405 0.246 -0.063 10 484052 3 0.253 0.487 0.049 -0.040 11 484061 3 0.482 0.598 0.129 0.001 12 484062 3 0.393 0.548 0.054 0.085 13 484071 3 0.508 0.508 0.159 0.121 14 484072 3 0.237 0.426 -0.073 0.225 15 484081 3 0.395 0.401 0.195 0.129 16 484082 3 0.412 0.495 0.140 0.073 17 484091 3 0.148 0.276 0.166 0.030 18 484092 3 0.116 0.292 0.034 0.105 19 484101 3 0.161 0.360 0.040 0.073 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 484102 3 0.442 0.583 0.138 -0.036 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.367 0.495 0.069 0.080 STANDARD DEVIATION 0 0.145 0.128 0.092 0.093 MEDIAN 3 0.394 0.501 0.052 0.089 INTERQUARTILE RANGE 0 0.250 0.183 0.155 0.147 MINIMUM VALUE 3 0.116 0.276 -0.075 -0.063 LOWER HINGE 3 0.245 0.403 -0.015 -0.009 UPPER HINGE 3 0.495 0.585 0.139 0.139 MAXIMUM VALUE 3 0.555 0.712 0.246 0.262 |------------------- 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 0.288 1.163 6.996 0.288 -0.001 2 484012 1778 1977 200 1.000 0.285 0.858 6.448 0.305 0.011 3 484021 1766 1977 212 1.000 0.341 0.895 6.417 0.353 -0.003 4 484022 1839 1977 139 1.000 0.342 1.262 6.551 0.320 0.030 5 484031 1759 1977 219 1.000 0.317 0.744 5.467 0.355 -0.003 6 484032 1792 1977 186 1.002 0.381 1.792 11.365 0.365 -0.013 7 484041 1793 1977 185 1.000 0.302 0.595 4.536 0.335 0.003 8 484042 1809 1977 169 1.000 0.220 0.617 3.804 0.246 0.002 9 484051 1841 1977 137 1.000 0.368 1.670 7.202 0.335 0.006 10 484052 1881 1977 97 1.000 0.223 0.456 3.647 0.238 0.011 11 484061 1781 1977 197 1.000 0.303 2.059 12.480 0.277 0.002 12 484062 1808 1977 170 1.000 0.290 0.778 3.132 0.303 -0.002 13 484071 1742 1977 236 1.002 0.394 1.327 8.031 0.384 -0.015 14 484072 1826 1977 152 1.000 0.257 0.731 3.436 0.273 0.001 15 484081 1801 1977 177 1.000 0.309 0.983 4.722 0.315 0.015 16 484082 1811 1977 167 1.000 0.301 1.124 7.169 0.299 0.008 17 484091 1860 1977 118 1.000 0.284 0.947 4.461 0.310 0.001 18 484092 1843 1977 135 1.000 0.310 0.805 3.448 0.335 0.001 19 484101 1800 1977 178 1.000 0.331 1.500 6.517 0.325 -0.001 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 484102 1811 1977 167 1.004 0.571 2.643 12.169 0.417 0.024 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 1.000 0.321 1.148 6.400 0.319 0.004 STANDARD DEVIATION 34 0.001 0.074 0.552 2.834 0.044 0.011 MEDIAN (50TH QUANTILE) 173 1.000 0.306 0.965 6.432 0.318 0.002 INTERQUARTILE RANGE 46 0.000 0.055 0.653 3.053 0.051 0.011 MINIMUM VALUE 97 1.000 0.220 0.456 3.132 0.238 -0.015 LOWER HINGE (25TH QUANTILE) 145 1.000 0.287 0.761 4.133 0.294 -0.002 UPPER HINGE (75TH QUANTILE) 191 1.000 0.342 1.414 7.185 0.344 0.009 MAXIMUM VALUE 236 1.004 0.571 2.643 12.480 0.417 0.030 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.262 0.103 0.007 0.431 3.473 0.027 0.613 MINIMUM CORRELATION: 0.027 SERIES 484032 AND 484052 97 YEARS MAXIMUM CORRELATION: 0.613 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 0.138 0.231 0.261 0.317 0.314 0.220 0.247 SDEV 0.199 0.173 0.138 0.137 0.148 0.163 0.168 SERR 0.115 0.029 0.014 0.011 0.011 0.012 0.012 EPS 0.588 0.810 0.859 0.899 0.901 0.850 0.868 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 0.975 0.224 0.501 4.389 0.248 -0.092 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.286 0.161 0.060 82 154 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.47 0.91 1.00 1.19 2.11 13.90 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.13 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 -0.091 -0.064 -0.042 -0.088 0.100 0.015 0.106 0.010 -0.001 0.016 PACF -0.091 -0.073 -0.056 -0.104 0.075 0.016 0.116 0.037 0.041 0.030 95% C.L. 0.130 0.131 0.132 0.132 0.133 0.134 0.134 0.136 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 0 0.000 |---------- 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 -0.008 0.001 0.008 -0.085 0.099 0.030 0.116 0.029 0.006 0.015 PACF -0.008 0.001 0.008 -0.085 0.099 0.031 0.119 0.021 0.024 0.008 95% C.L. 0.130 0.130 0.130 0.130 0.131 0.132 0.133 0.134 0.134 0.134 |----------------- 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 3 0.009 -0.008 0.001 0.009 |========================= 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 0.981 0.274 0.909 4.527 0.201 0.532 |------------ 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 0.530 0.383 0.384 0.271 0.290 0.249 0.236 0.151 0.092 0.051 PACF 0.530 0.142 0.192 -0.024 0.129 0.002 0.071 -0.097 -0.034 -0.073 95% C.L. 0.130 0.163 0.177 0.191 0.197 0.204 0.209 0.214 0.216 0.216 |------------------- 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 3 0.344 0.414 0.057 0.230 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.26 MINUTES