RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN024W.rwl.conv LOG FILE PROCESSED: FRAN024W.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_RING 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 1.447 0.557 1.219 4.968 0.169 0.829 2 484012 1778 1977 200 1.056 0.571 1.736 5.706 0.179 0.878 3 484021 1766 1977 212 0.949 0.564 1.370 4.941 0.201 0.882 4 484022 1839 1977 139 0.932 0.605 1.397 4.359 0.198 0.881 5 484031 1759 1977 219 0.600 0.384 0.679 2.781 0.230 0.900 6 484032 1792 1977 186 0.846 0.654 1.609 5.666 0.211 0.913 7 484041 1793 1977 185 1.000 0.516 0.722 2.828 0.192 0.917 8 484042 1809 1977 169 0.628 0.338 1.150 4.837 0.178 0.912 9 484051 1841 1977 137 0.981 0.432 1.669 5.775 0.154 0.846 10 484052 1881 1977 97 0.938 0.251 1.430 6.164 0.141 0.694 11 484061 1781 1977 197 0.712 0.484 1.387 4.582 0.202 0.917 12 484062 1808 1977 170 0.983 0.517 0.558 2.079 0.195 0.888 13 484071 1742 1977 236 0.693 0.353 0.791 3.680 0.198 0.881 14 484072 1826 1977 152 1.218 0.386 0.828 3.085 0.169 0.721 15 484081 1801 1977 177 0.915 0.396 0.531 3.052 0.226 0.802 16 484082 1811 1977 167 0.784 0.431 1.200 3.880 0.182 0.908 17 484091 1860 1977 118 1.691 0.457 0.595 3.539 0.125 0.810 18 484092 1843 1977 135 1.644 0.466 0.477 2.431 0.136 0.787 19 484101 1800 1977 178 0.911 0.460 0.776 2.539 0.168 0.913 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 484102 1811 1977 167 1.155 0.602 1.237 4.232 0.188 0.818 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 1.004 0.471 1.068 4.056 0.182 0.855 STANDARD DEVIATION 35 0.303 0.103 0.412 1.250 0.028 0.066 MEDIAN (50TH QUANTILE) 173 0.943 0.463 1.175 4.056 0.185 0.881 INTERQUARTILE RANGE 53 0.290 0.170 0.691 2.015 0.031 0.096 MINIMUM VALUE 97 0.600 0.251 0.477 2.079 0.125 0.694 LOWER HINGE (25TH QUANTILE) 138 0.815 0.391 0.700 2.940 0.168 0.814 UPPER HINGE (75TH QUANTILE) 191 1.105 0.561 1.392 4.955 0.199 0.910 MAXIMUM VALUE 236 1.691 0.654 1.736 6.164 0.230 0.917 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.334 0.295 0.021 -0.567 2.899 -0.444 0.869 MINIMUM CORRELATION: -0.444 SERIES 484061 AND 484091 118 YEARS MAXIMUM CORRELATION: 0.869 SERIES 484061 AND 484062 170 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 0.041 0.338 0.336 0.308 0.398 0.348 0.281 SDEV 0.296 0.264 0.289 0.261 0.337 0.326 0.392 SERR 0.171 0.044 0.030 0.021 0.026 0.024 0.028 EPS 0.277 0.879 0.897 0.895 0.929 0.915 0.887 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 0.881 0.313 0.399 2.689 0.140 0.881 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.588 0.347 0.111 91 145 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.42 1.03 1.01 1.18 2.21 8.95 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.12 0.00 0.85 0.97 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 0.877 0.808 0.771 0.747 0.706 0.670 0.668 0.628 0.567 0.525 PACF 0.877 0.167 0.152 0.113 -0.018 0.015 0.143 -0.104 -0.125 -0.022 95% C.L. 0.130 0.207 0.255 0.292 0.323 0.348 0.369 0.389 0.406 0.419 |------------------ 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 0.787 0.674 0.051 0.080 0.122 |================== 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 1.55150437 0.03861552 0.00000000 1.23156905 2 484012 1 1.33967793 0.01080957 0.00000000 0.51034909 3 484021 3 0.00000000 0.00000000 -0.00423952 1.40018821 4 484022 1 2.58543038 0.10146406 0.00000000 0.75762677 5 484031 3 0.00000000 0.00000000 0.00151127 0.43357757 6 484032 3 0.00000000 0.00000000 0.00539852 0.34147456 7 484041 3 0.00000000 0.00000000 0.00342802 0.68124855 8 484042 3 0.00000000 0.00000000 0.00338365 0.34020075 9 484051 3 0.00000000 0.00000000 0.00505367 0.63202661 10 484052 3 0.00000000 0.00000000 0.00306214 0.78758377 11 484061 3 0.00000000 0.00000000 0.00168597 0.54471302 12 484062 3 0.00000000 0.00000000 0.00229068 0.78048581 13 484071 3 0.00000000 0.00000000 0.00268299 0.37490442 14 484072 3 0.00000000 0.00000000 0.00159336 1.03443825 15 484081 3 0.00000000 0.00000000 0.00176921 0.75739920 16 484082 3 0.00000000 0.00000000 0.00253486 0.57150280 17 484091 3 0.00000000 0.00000000 -0.00326179 1.88509345 18 484092 3 0.00000000 0.00000000 0.00343786 1.40992928 19 484101 1 1.34740460 0.04946029 0.00000000 0.76157600 SERIES IDENT OPTION A B C D 20 484102 1 0.65194005 0.07363966 0.00000000 1.10376585 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 484011 1795 1977 183 0.999 0.293 0.391 3.144 0.169 0.736 2 484012 1778 1977 200 1.002 0.378 0.702 3.740 0.178 0.813 3 484021 1766 1977 212 1.011 0.535 1.111 3.978 0.200 0.866 4 484022 1839 1977 139 1.000 0.538 1.599 5.658 0.194 0.864 5 484031 1759 1977 219 1.010 0.643 0.829 3.618 0.228 0.887 6 484032 1792 1977 186 1.064 0.879 2.643 13.169 0.210 0.782 7 484041 1793 1977 185 1.010 0.527 1.387 6.195 0.191 0.898 8 484042 1809 1977 169 1.019 0.509 0.858 3.455 0.177 0.884 9 484051 1841 1977 137 1.008 0.382 1.166 4.084 0.153 0.806 10 484052 1881 1977 97 1.000 0.243 1.084 5.591 0.140 0.647 11 484061 1781 1977 197 1.007 0.639 0.869 2.966 0.201 0.901 12 484062 1808 1977 170 1.004 0.521 0.613 2.471 0.190 0.861 13 484071 1742 1977 236 1.010 0.503 1.093 4.239 0.197 0.850 14 484072 1826 1977 152 1.001 0.321 0.975 3.581 0.169 0.712 15 484081 1801 1977 177 1.002 0.416 0.326 2.668 0.224 0.769 16 484082 1811 1977 167 1.002 0.507 0.867 3.284 0.181 0.871 17 484091 1860 1977 118 0.999 0.267 0.891 3.703 0.124 0.808 18 484092 1843 1977 135 1.000 0.267 0.357 2.464 0.135 0.760 19 484101 1800 1977 178 0.999 0.439 0.961 3.143 0.167 0.873 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 484102 1811 1977 167 1.000 0.528 1.488 5.026 0.187 0.815 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 1.007 0.467 1.011 4.309 0.181 0.820 STANDARD DEVIATION 34 0.015 0.155 0.517 2.336 0.028 0.069 MEDIAN (50TH QUANTILE) 173 1.002 0.505 0.926 3.660 0.184 0.833 INTERQUARTILE RANGE 46 0.010 0.182 0.373 1.489 0.031 0.096 MINIMUM VALUE 97 0.999 0.243 0.326 2.464 0.124 0.647 LOWER HINGE (25TH QUANTILE) 145 1.000 0.349 0.766 3.144 0.168 0.776 UPPER HINGE (75TH QUANTILE) 191 1.010 0.531 1.138 4.632 0.199 0.872 MAXIMUM VALUE 236 1.064 0.879 2.643 13.169 0.228 0.901 |------------------------ 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 0.997 0.216 -0.287 2.901 0.168 0.507 2 484012 1778 1977 200 0.991 0.324 0.509 3.339 0.178 0.750 3 484021 1766 1977 212 0.967 0.355 1.249 5.135 0.200 0.757 4 484022 1839 1977 139 0.987 0.295 0.665 3.072 0.194 0.654 5 484031 1759 1977 219 0.953 0.411 1.176 4.243 0.227 0.769 6 484032 1792 1977 186 0.968 0.427 0.963 3.955 0.209 0.785 7 484041 1793 1977 185 0.982 0.330 0.478 3.304 0.191 0.792 8 484042 1809 1977 169 0.970 0.301 1.016 4.412 0.176 0.738 9 484051 1841 1977 137 0.993 0.279 0.893 4.257 0.153 0.687 10 484052 1881 1977 97 0.995 0.211 1.161 6.293 0.140 0.563 11 484061 1781 1977 197 0.967 0.346 1.106 4.418 0.199 0.738 12 484062 1808 1977 170 0.976 0.288 0.361 2.915 0.189 0.657 13 484071 1742 1977 236 0.988 0.409 0.562 3.252 0.197 0.815 14 484072 1826 1977 152 0.996 0.252 0.752 3.790 0.169 0.589 15 484081 1801 1977 177 0.988 0.333 0.241 3.509 0.224 0.689 16 484082 1811 1977 167 0.963 0.343 0.839 3.476 0.179 0.767 17 484091 1860 1977 118 0.996 0.176 0.740 3.450 0.124 0.575 18 484092 1843 1977 135 0.993 0.205 0.415 2.788 0.134 0.636 19 484101 1800 1977 178 0.992 0.266 0.441 3.716 0.166 0.660 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 484102 1811 1977 167 0.995 0.514 1.517 5.161 0.187 0.814 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 0.983 0.314 0.740 3.869 0.180 0.697 STANDARD DEVIATION 34 0.014 0.084 0.418 0.893 0.028 0.090 MEDIAN (50TH QUANTILE) 173 0.988 0.313 0.746 3.613 0.183 0.714 INTERQUARTILE RANGE 46 0.025 0.091 0.602 1.056 0.031 0.123 MINIMUM VALUE 97 0.953 0.176 -0.287 2.788 0.124 0.507 LOWER HINGE (25TH QUANTILE) 145 0.969 0.259 0.459 3.278 0.167 0.645 UPPER HINGE (75TH QUANTILE) 191 0.994 0.350 1.061 4.335 0.198 0.768 MAXIMUM VALUE 236 0.997 0.514 1.517 6.293 0.227 0.815 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.236 0.182 0.013 0.083 2.740 -0.193 0.680 MINIMUM CORRELATION: -0.193 SERIES 484092 AND 484102 135 YEARS MAXIMUM CORRELATION: 0.680 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 0.104 0.228 0.157 0.184 0.332 0.255 0.292 SDEV 0.227 0.243 0.275 0.251 0.287 0.306 0.293 SERR 0.131 0.041 0.029 0.020 0.022 0.022 0.021 EPS 0.509 0.808 0.764 0.812 0.908 0.873 0.892 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 0.972 0.265 0.728 3.518 0.165 0.700 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.115 0.052 0.197 78 158 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.21 0.93 1.00 1.06 1.98 5.82 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.13 0.00 0.85 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 0.697 0.545 0.486 0.442 0.349 0.234 0.237 0.148 0.032 -0.034 PACF 0.697 0.115 0.137 0.076 -0.057 -0.109 0.111 -0.135 -0.129 -0.041 95% C.L. 0.130 0.183 0.209 0.227 0.241 0.250 0.253 0.257 0.258 0.258 |------------------ 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 0.531 0.575 0.023 0.115 0.097 |======================= 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 0.636 0.468 0.395 0.342 0.260 0.169 0.175 0.160 0.056 -0.022 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 0.636 2 0.568 0.106 3 0.557 0.047 0.104 4 0.551 0.045 0.072 0.058 5 0.553 0.047 0.073 0.073 -0.028 6 0.551 0.051 0.078 0.076 0.006 -0.061 7 0.556 0.051 0.071 0.069 0.001 -0.107 0.084 8 0.555 0.052 0.071 0.068 0.000 -0.108 0.077 0.013 9 0.557 0.062 0.057 0.069 0.009 -0.099 0.083 0.085 -0.129 10 0.547 0.068 0.064 0.061 0.010 -0.094 0.088 0.089 -0.085 -0.078 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) 1751.54 1631.17 1630.48 1629.91 1631.13 1632.94 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1634.06 1634.39 1636.35 1634.41 1634.97 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 0.557 0.047 0.104 R-SQUARED DUE TO POOLED AUTOREGRESSION: 41.77 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 171.74 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.557 0.358 0.330 0.259 0.197 0.156 0.123 0.097 0.076 0.0597 0.047 0.037 0.029 0.023 0.018 0.014 0.011 0.009 0.007 0.0054 0.004 0.003 0.003 0.002 0.002 0.001 0.001 0.001 0.001 0.0005 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 0.287 0.540 -0.083 0.076 2 484012 3 0.573 0.687 0.015 0.091 3 484021 3 0.584 0.841 -0.123 0.023 4 484022 3 0.443 0.584 0.132 -0.025 5 484031 3 0.601 0.680 0.034 0.099 6 484032 3 0.661 0.712 0.102 0.021 7 484041 3 0.645 0.657 0.169 0.005 8 484042 3 0.608 0.464 0.335 0.039 9 484051 3 0.512 0.573 0.238 -0.079 10 484052 3 0.342 0.488 0.169 -0.033 11 484061 3 0.562 0.649 0.084 0.048 12 484062 3 0.465 0.541 0.041 0.178 13 484071 3 0.689 0.685 0.069 0.112 14 484072 3 0.371 0.552 -0.036 0.159 15 484081 3 0.498 0.557 0.167 0.030 16 484082 3 0.596 0.668 0.106 0.029 17 484091 3 0.357 0.544 0.126 -0.069 18 484092 3 0.428 0.668 -0.029 -0.014 19 484101 3 0.454 0.644 -0.036 0.105 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 484102 3 0.668 0.813 0.088 -0.106 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.517 0.627 0.078 0.034 STANDARD DEVIATION 0 0.120 0.099 0.111 0.077 MEDIAN 3 0.537 0.647 0.086 0.029 INTERQUARTILE RANGE 0 0.169 0.135 0.157 0.114 MINIMUM VALUE 3 0.287 0.464 -0.123 -0.106 LOWER HINGE 3 0.436 0.548 -0.007 -0.020 UPPER HINGE 3 0.605 0.683 0.150 0.095 MAXIMUM VALUE 3 0.689 0.841 0.335 0.178 |------------------- 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 0.184 -0.062 2.925 0.208 -0.019 2 484012 1778 1977 200 1.000 0.212 0.153 4.293 0.234 -0.002 3 484021 1766 1977 212 1.000 0.229 0.725 4.406 0.250 0.002 4 484022 1839 1977 139 1.000 0.220 1.096 4.647 0.234 0.002 5 484031 1759 1977 219 1.000 0.260 0.307 3.828 0.282 -0.006 6 484032 1792 1977 186 1.000 0.245 0.215 5.048 0.263 -0.026 7 484041 1793 1977 185 1.000 0.197 0.195 4.407 0.223 0.001 8 484042 1809 1977 169 1.000 0.190 -0.126 4.071 0.212 0.001 9 484051 1841 1977 137 1.000 0.197 0.869 4.688 0.197 0.014 10 484052 1881 1977 97 1.000 0.172 0.967 6.581 0.172 -0.001 11 484061 1781 1977 197 1.000 0.231 0.627 3.872 0.252 -0.007 12 484062 1808 1977 170 1.000 0.210 0.531 4.544 0.219 -0.011 13 484071 1742 1977 236 1.000 0.226 0.156 4.369 0.240 -0.012 14 484072 1826 1977 152 1.000 0.200 0.975 4.623 0.205 0.004 15 484081 1801 1977 177 1.000 0.237 0.361 3.580 0.255 0.002 16 484082 1811 1977 167 1.000 0.218 0.585 5.436 0.226 0.000 17 484091 1860 1977 118 1.000 0.140 0.622 3.617 0.158 -0.014 18 484092 1843 1977 135 1.000 0.156 0.337 3.500 0.180 0.010 19 484101 1800 1977 178 1.000 0.196 0.487 4.473 0.213 0.000 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 484102 1811 1977 167 1.000 0.297 1.150 6.053 0.276 0.000 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 1.000 0.211 0.509 4.448 0.225 -0.003 STANDARD DEVIATION 34 0.000 0.036 0.373 0.863 0.033 0.009 MEDIAN (50TH QUANTILE) 173 1.000 0.211 0.509 4.407 0.225 0.000 INTERQUARTILE RANGE 46 0.000 0.037 0.592 0.818 0.045 0.011 MINIMUM VALUE 97 1.000 0.140 -0.126 2.925 0.158 -0.026 LOWER HINGE (25TH QUANTILE) 145 1.000 0.193 0.205 3.850 0.206 -0.009 UPPER HINGE (75TH QUANTILE) 191 1.000 0.230 0.797 4.668 0.251 0.002 MAXIMUM VALUE 236 1.000 0.297 1.150 6.581 0.282 0.014 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.314 0.099 0.007 0.327 3.714 0.038 0.630 MINIMUM CORRELATION: 0.038 SERIES 484092 AND 484102 135 YEARS MAXIMUM CORRELATION: 0.630 SERIES 484071 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 0.281 0.350 0.366 0.362 0.365 0.250 0.301 SDEV 0.075 0.107 0.132 0.147 0.161 0.156 0.151 SERR 0.044 0.018 0.014 0.012 0.012 0.011 0.011 EPS 0.777 0.885 0.909 0.916 0.920 0.869 0.896 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 0.989 0.146 0.247 3.503 0.168 -0.089 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.153 0.088 0.063 82 154 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.30 0.83 1.00 1.08 1.91 31.66 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.13 0.00 0.85 0.97 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 -0.089 -0.105 -0.005 0.105 0.017 -0.106 0.143 0.075 -0.092 -0.081 PACF -0.089 -0.114 -0.026 0.092 0.034 -0.083 0.136 0.077 -0.062 -0.066 95% C.L. 0.130 0.131 0.133 0.133 0.134 0.134 0.135 0.138 0.139 0.140 |------------------ 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 2 0.022 -0.100 -0.116 |---------- 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 0.002 0.012 0.013 0.088 0.035 -0.072 0.137 0.062 -0.080 -0.078 PACF 0.002 0.012 0.013 0.088 0.035 -0.075 0.136 0.056 -0.092 -0.072 95% C.L. 0.130 0.130 0.130 0.130 0.131 0.131 0.132 0.134 0.135 0.136 |----------------- 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 0.002 0.012 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 1742 1977 236 0.992 0.200 0.271 2.612 0.125 0.677 |------------ 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 0.674 0.529 0.470 0.416 0.322 0.232 0.246 0.169 0.055 0.013 PACF 0.674 0.137 0.131 0.058 -0.051 -0.062 0.111 -0.093 -0.133 -0.015 95% C.L. 0.130 0.180 0.204 0.222 0.235 0.242 0.246 0.250 0.252 0.252 |------------------- 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 0.482 0.562 0.055 0.145 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.25 MINUTES