RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN025W.rwl.conv LOG FILE PROCESSED: FRAN025W.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: 482 1 Miraules Refuge WIDTH_RING ABAL - 482 2 France silver fir, European fir 1720 4228-224 1831 1977 - 482 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES --- NO GAPS IN DATA FOUND --- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 482011 1838 1977 140 1.880 1.029 0.606 2.405 0.191 0.913 2 482012 1846 1977 132 1.565 0.958 0.874 3.473 0.218 0.865 3 482021 1891 1977 87 2.031 0.734 0.775 3.110 0.164 0.832 4 482022 1889 1977 89 2.288 0.895 0.593 3.722 0.180 0.810 5 482031 1849 1977 129 2.003 0.663 0.129 2.440 0.195 0.747 6 482032 1863 1977 115 2.095 0.715 0.600 3.205 0.200 0.757 7 482041 1831 1977 147 1.770 0.427 0.059 3.051 0.164 0.657 8 482042 1855 1977 123 1.850 0.589 0.399 2.195 0.154 0.854 9 482051 1883 1977 95 2.857 1.179 0.068 2.051 0.148 0.901 10 482052 1888 1977 90 3.163 1.213 -0.061 2.160 0.136 0.898 11 482061 1836 1977 142 1.957 0.936 0.242 1.902 0.187 0.899 12 482062 1842 1977 136 2.008 0.947 0.189 2.099 0.189 0.899 13 482071 1879 1977 99 2.477 0.912 0.650 2.471 0.166 0.860 14 482072 1875 1977 103 2.378 0.883 0.535 2.413 0.178 0.844 15 482081 1853 1977 125 2.019 0.791 0.461 2.142 0.145 0.914 16 482082 1849 1977 129 1.950 0.637 0.286 2.615 0.151 0.852 17 482091 1846 1977 132 1.672 0.881 0.716 2.378 0.193 0.853 18 482092 1852 1977 126 1.545 0.966 0.852 2.757 0.210 0.917 19 482101 1838 1977 140 1.587 1.152 0.832 2.427 0.171 0.956 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 1.648 1.136 0.562 1.977 0.169 0.951 21 482111 1896 1977 82 2.671 0.832 0.888 2.686 0.170 0.790 22 482112 1889 1977 89 2.462 0.895 0.328 2.133 0.191 0.801 23 482121 1861 1977 117 1.497 0.936 0.782 2.270 0.138 0.967 24 482122 1842 1977 136 1.631 0.986 0.283 1.663 0.142 0.942 NUMBER OF SERIES READ IN: 24 FROM 1831 TO 1977 147 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 2.042 0.887 0.485 2.489 0.173 0.862 STANDARD DEVIATION 20 0.440 0.192 0.288 0.510 0.023 0.074 MEDIAN (50TH QUANTILE) 125 1.980 0.904 0.548 2.409 0.170 0.862 INTERQUARTILE RANGE 39 0.673 0.213 0.483 0.584 0.038 0.092 MINIMUM VALUE 82 1.497 0.427 -0.061 1.663 0.136 0.657 LOWER HINGE (25TH QUANTILE) 97 1.660 0.762 0.262 2.137 0.153 0.821 UPPER HINGE (75TH QUANTILE) 136 2.333 0.976 0.745 2.721 0.191 0.914 MAXIMUM VALUE 147 3.163 1.213 0.888 3.722 0.218 0.967 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.704 0.139 0.008 -0.745 3.931 0.128 0.962 MINIMUM CORRELATION: 0.128 SERIES 482052 AND 482091 90 YEARS MAXIMUM CORRELATION: 0.962 SERIES 482101 AND 482102 138 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.39 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 120. 231. 276. RBAR 0.482 0.665 0.688 SDEV 0.263 0.210 0.157 SERR 0.024 0.014 0.009 EPS 0.950 0.979 0.981 NSS 20.6 23.9 24.0 |======================== 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 1831 1977 147 2.016 0.694 0.202 1.884 0.155 0.853 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.218 0.075 0.507 34 113 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.13 0.24 1.00 1.05 1.29 8.47 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.07 0.00 0.87 0.94 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 126. 39. 82. 97. 136. 147. |----------- 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 0.847 0.814 0.794 0.743 0.747 0.696 0.652 0.625 0.592 0.553 PACF 0.847 0.342 0.201 -0.010 0.165 -0.077 -0.070 -0.028 0.014 -0.065 95% C.L. 0.165 0.257 0.320 0.370 0.408 0.444 0.473 0.497 0.518 0.536 |------------------ 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 0.765 0.480 0.228 0.214 |================== 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 482011 3 0.00000000 0.00000000 -0.01633017 3.03149128 2 482012 3 0.00000000 0.00000000 -0.01884758 2.81813669 3 482021 1 2.54105830 0.02633873 0.00000000 1.04722738 4 482022 3 0.00000000 0.00000000 -0.03020191 3.64672637 5 482031 3 0.00000000 0.00000000 -0.00701789 2.45903111 6 482032 1 2.09425807 0.02723454 0.00000000 1.46467113 7 482041 3 0.00000000 0.00000000 -0.00606412 2.21860862 8 482042 3 0.00000000 0.00000000 -0.00871684 2.39068770 9 482051 3 0.00000000 0.00000000 -0.03438438 4.50708199 10 482052 3 0.00000000 0.00000000 -0.03755402 4.87126350 11 482061 3 0.00000000 0.00000000 -0.01527862 3.04946351 12 482062 3 0.00000000 0.00000000 -0.01706130 3.17664051 13 482071 1 3.52967572 0.01275070 0.00000000 0.48541182 14 482072 1 2.27223659 0.01546485 0.00000000 1.25072372 15 482081 3 0.00000000 0.00000000 -0.01414943 2.91021419 16 482082 3 0.00000000 0.00000000 -0.01007033 2.60488129 17 482091 1 2.51031828 0.00895119 0.00000000 0.20579290 18 482092 3 0.00000000 0.00000000 -0.01919277 2.76358223 19 482101 3 0.00000000 0.00000000 -0.02113623 3.07688999 SERIES IDENT OPTION A B C D 20 482102 -67 92 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 482111 1 3.02506208 0.01658634 0.00000000 1.03091764 22 482112 3 0.00000000 0.00000000 -0.02627409 3.64480591 23 482121 3 0.00000000 0.00000000 -0.02189678 2.78900385 24 482122 3 0.00000000 0.00000000 -0.02210185 3.14471245 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 482011 1838 1977 140 0.989 0.388 0.615 3.064 0.189 0.797 2 482012 1846 1977 132 1.075 0.636 2.405 11.502 0.218 0.782 3 482021 1891 1977 87 1.000 0.188 -0.197 2.815 0.161 0.411 4 482022 1889 1977 89 1.002 0.190 0.252 3.088 0.177 0.290 5 482031 1849 1977 129 0.998 0.294 -0.067 2.900 0.193 0.680 6 482032 1863 1977 115 1.000 0.244 0.423 3.161 0.198 0.529 7 482041 1831 1977 147 0.999 0.191 -0.037 3.723 0.163 0.465 8 482042 1855 1977 123 0.998 0.257 0.040 2.389 0.153 0.743 9 482051 1883 1977 95 0.993 0.246 0.330 2.393 0.146 0.731 10 482052 1888 1977 90 0.989 0.217 0.250 2.723 0.132 0.702 11 482061 1836 1977 142 0.985 0.338 0.429 2.489 0.186 0.812 12 482062 1842 1977 136 0.986 0.325 0.252 2.303 0.188 0.784 13 482071 1879 1977 99 1.001 0.222 0.013 2.902 0.164 0.622 14 482072 1875 1977 103 1.000 0.308 0.565 3.266 0.177 0.737 15 482081 1853 1977 125 0.997 0.275 -0.069 2.117 0.144 0.798 16 482082 1849 1977 129 1.001 0.272 0.281 2.767 0.150 0.773 17 482091 1846 1977 132 1.003 0.467 1.567 6.539 0.192 0.832 18 482092 1852 1977 126 1.034 0.481 1.281 5.472 0.209 0.807 19 482101 1838 1977 140 1.270 1.464 4.086 20.325 0.173 0.839 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 0.996 0.233 0.644 4.668 0.166 0.536 21 482111 1896 1977 82 1.000 0.182 -0.001 2.900 0.167 0.413 22 482112 1889 1977 89 1.003 0.244 0.006 2.607 0.190 0.538 23 482121 1861 1977 117 1.142 0.806 2.729 10.304 0.136 0.866 24 482122 1842 1977 136 1.175 1.031 4.663 26.311 0.146 0.785 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.027 0.396 0.853 5.530 0.172 0.678 STANDARD DEVIATION 20 0.070 0.309 1.322 6.044 0.023 0.162 MEDIAN (50TH QUANTILE) 125 1.000 0.273 0.306 2.983 0.170 0.740 INTERQUARTILE RANGE 39 0.006 0.200 0.953 2.405 0.038 0.261 MINIMUM VALUE 82 0.985 0.182 -0.197 2.117 0.132 0.290 LOWER HINGE (25TH QUANTILE) 97 0.997 0.228 0.010 2.665 0.151 0.537 UPPER HINGE (75TH QUANTILE) 136 1.003 0.428 0.963 5.070 0.189 0.798 MAXIMUM VALUE 147 1.270 1.464 4.663 26.311 0.218 0.866 |------------------------ 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 482011 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 482012 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 482021 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 482022 -67 59 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 482031 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 482032 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 482041 -67 98 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 482042 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 482051 -67 63 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 482052 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 482061 -67 95 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 482062 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 482071 -67 66 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 482072 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 482081 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 482082 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 482091 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 482092 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 482101 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 482102 -67 92 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 482111 -67 54 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 482112 -67 59 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 482121 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 482122 -67 91 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 482011 1838 1977 140 0.987 0.313 0.544 3.031 0.188 0.693 2 482012 1846 1977 132 0.974 0.319 0.412 2.776 0.217 0.669 3 482021 1891 1977 87 0.999 0.183 -0.116 2.729 0.161 0.377 4 482022 1889 1977 89 0.999 0.184 0.109 2.965 0.177 0.259 5 482031 1849 1977 129 0.995 0.254 -0.224 2.607 0.193 0.556 6 482032 1863 1977 115 0.997 0.219 0.207 3.017 0.198 0.433 7 482041 1831 1977 147 0.999 0.182 0.165 3.820 0.162 0.389 8 482042 1855 1977 123 0.992 0.180 -0.007 3.189 0.152 0.491 9 482051 1883 1977 95 0.995 0.211 0.079 2.500 0.146 0.637 10 482052 1888 1977 90 0.998 0.164 -0.178 2.749 0.133 0.494 11 482061 1836 1977 142 0.991 0.256 0.340 3.472 0.186 0.623 12 482062 1842 1977 136 0.994 0.272 0.529 3.945 0.188 0.641 13 482071 1879 1977 99 0.996 0.179 -0.208 3.267 0.163 0.439 14 482072 1875 1977 103 0.990 0.214 0.146 2.922 0.176 0.511 15 482081 1853 1977 125 0.988 0.172 -0.397 2.885 0.142 0.521 16 482082 1849 1977 129 0.993 0.221 0.008 2.657 0.149 0.680 17 482091 1846 1977 132 0.982 0.290 0.041 3.444 0.192 0.626 18 482092 1852 1977 126 0.972 0.248 0.087 3.076 0.210 0.538 19 482101 1838 1977 140 0.993 0.333 -0.012 3.001 0.170 0.784 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 0.997 0.207 0.521 4.899 0.166 0.438 21 482111 1896 1977 82 0.999 0.174 -0.096 3.110 0.167 0.359 22 482112 1889 1977 89 0.996 0.213 0.104 2.661 0.189 0.384 23 482121 1861 1977 117 0.979 0.213 0.066 2.372 0.137 0.687 24 482122 1842 1977 136 0.980 0.268 0.887 5.880 0.143 0.710 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 0.991 0.228 0.125 3.207 0.171 0.539 STANDARD DEVIATION 20 0.008 0.050 0.294 0.786 0.023 0.136 MEDIAN (50TH QUANTILE) 125 0.994 0.214 0.083 3.009 0.169 0.529 INTERQUARTILE RANGE 39 0.010 0.080 0.327 0.616 0.038 0.219 MINIMUM VALUE 82 0.972 0.164 -0.397 2.372 0.133 0.259 LOWER HINGE (25TH QUANTILE) 97 0.987 0.182 -0.054 2.739 0.151 0.436 UPPER HINGE (75TH QUANTILE) 136 0.997 0.262 0.273 3.355 0.189 0.655 MAXIMUM VALUE 147 0.999 0.333 0.887 5.880 0.217 0.784 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.455 0.151 0.009 -0.335 2.680 0.057 0.777 MINIMUM CORRELATION: 0.057 SERIES 482071 AND 482101 99 YEARS MAXIMUM CORRELATION: 0.777 SERIES 482061 AND 482062 136 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.39 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 120. 231. 276. RBAR 0.360 0.525 0.538 SDEV 0.206 0.169 0.187 SERR 0.019 0.011 0.011 EPS 0.921 0.963 0.965 NSS 20.6 23.9 24.0 |======================== 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 1831 1977 147 0.982 0.178 -0.189 2.545 0.152 0.492 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.180 0.069 0.099 55 92 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.17 0.40 1.00 1.04 1.45 9.74 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.08 0.00 0.87 0.96 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 0.489 0.359 0.340 0.200 0.167 0.052 0.037 -0.071 -0.135 -0.212 PACF 0.489 0.158 0.155 -0.057 0.025 -0.112 0.017 -0.139 -0.070 -0.154 95% C.L. 0.165 0.201 0.217 0.231 0.236 0.239 0.240 0.240 0.240 0.242 |------------------ 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 0.290 0.382 0.105 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 0.485 0.354 0.369 0.252 0.149 0.061 0.107 0.002 -0.064 -0.144 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 0.485 2 0.410 0.156 3 0.379 0.074 0.199 4 0.382 0.075 0.204 -0.015 5 0.381 0.087 0.208 0.006 -0.056 6 0.375 0.087 0.229 0.015 -0.019 -0.097 7 0.384 0.089 0.227 -0.005 -0.026 -0.130 0.087 8 0.392 0.077 0.225 -0.006 -0.006 -0.122 0.123 -0.091 9 0.387 0.084 0.218 -0.006 -0.006 -0.110 0.127 -0.070 -0.055 10 0.378 0.073 0.238 -0.023 -0.007 -0.111 0.161 -0.057 0.006 -0.158 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) 1086.47 1049.04 1047.44 1043.52 1045.49 1047.03 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1047.63 1048.51 1049.27 1050.83 1049.13 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 0.379 0.074 0.199 R-SQUARED DUE TO POOLED AUTOREGRESSION: 28.32 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 139.51 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.379 0.218 0.309 0.208 0.145 0.132 0.102 0.077 0.063 0.0499 0.039 0.031 0.025 0.019 0.015 0.012 0.010 0.008 0.006 0.0047 0.004 0.003 0.002 0.002 0.001 0.001 0.001 0.001 0.001 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 482011 3 0.535 0.666 0.098 -0.036 2 482012 3 0.513 0.564 0.154 0.050 3 482021 3 0.177 0.372 -0.056 0.190 4 482022 3 0.068 0.263 -0.010 -0.015 5 482031 3 0.355 0.458 0.180 0.017 6 482032 3 0.220 0.358 0.090 0.130 7 482041 3 0.190 0.346 0.019 0.164 8 482042 3 0.291 0.363 0.143 0.149 9 482051 3 0.439 0.526 0.062 0.154 10 482052 3 0.281 0.538 -0.130 0.122 11 482061 3 0.439 0.584 0.037 0.086 12 482062 3 0.494 0.573 0.044 0.152 13 482071 3 0.203 0.394 0.107 -0.005 14 482072 3 0.288 0.470 0.050 0.084 15 482081 3 0.342 0.381 0.125 0.187 16 482082 3 0.514 0.588 0.084 0.092 17 482091 3 0.467 0.487 0.148 0.130 18 482092 3 0.365 0.368 0.193 0.157 19 482101 3 0.694 0.582 0.178 0.118 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 482102 3 0.254 0.334 0.095 0.202 21 482111 3 0.167 0.329 0.071 0.037 22 482112 3 0.253 0.271 0.166 0.156 23 482121 3 0.549 0.542 -0.006 0.286 24 482122 3 0.625 0.588 0.146 0.106 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.363 0.456 0.083 0.113 STANDARD DEVIATION 0 0.162 0.117 0.080 0.076 MEDIAN 3 0.348 0.464 0.092 0.126 INTERQUARTILE RANGE 0 0.267 0.208 0.106 0.089 MINIMUM VALUE 3 0.068 0.263 -0.130 -0.036 LOWER HINGE 3 0.236 0.360 0.041 0.067 UPPER HINGE 3 0.504 0.569 0.147 0.156 MAXIMUM VALUE 3 0.694 0.666 0.193 0.286 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 482011 1838 1977 140 1.000 0.216 0.253 5.012 0.251 0.006 2 482012 1846 1977 132 1.000 0.221 -0.098 2.955 0.273 0.001 3 482021 1891 1977 87 1.000 0.166 0.067 3.651 0.178 0.009 4 482022 1889 1977 89 1.000 0.178 0.164 3.337 0.195 0.001 5 482031 1849 1977 129 1.000 0.204 0.029 2.937 0.236 -0.006 6 482032 1863 1977 115 1.000 0.193 0.197 2.815 0.226 0.005 7 482041 1831 1977 147 1.000 0.164 0.037 4.271 0.184 0.020 8 482042 1855 1977 123 1.000 0.152 0.500 4.445 0.173 0.009 9 482051 1883 1977 95 1.000 0.158 0.499 3.291 0.179 0.004 10 482052 1888 1977 90 1.000 0.141 -0.111 3.216 0.156 0.022 11 482061 1836 1977 142 1.000 0.192 0.091 2.751 0.223 0.029 12 482062 1842 1977 136 1.000 0.193 0.181 3.097 0.225 0.038 13 482071 1879 1977 99 1.000 0.160 -0.176 3.125 0.189 0.001 14 482072 1875 1977 103 1.000 0.180 0.162 3.026 0.207 -0.010 15 482081 1853 1977 125 1.000 0.141 -0.352 3.510 0.166 0.027 16 482082 1849 1977 129 1.000 0.154 -0.268 3.168 0.180 0.009 17 482091 1846 1977 132 1.000 0.209 0.377 4.281 0.226 -0.014 18 482092 1852 1977 126 1.000 0.198 -0.007 3.371 0.234 0.013 19 482101 1838 1977 140 1.000 0.184 0.171 2.667 0.199 0.029 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 1.000 0.179 0.939 6.275 0.188 0.008 21 482111 1896 1977 82 1.000 0.162 0.155 3.317 0.192 0.004 22 482112 1889 1977 89 1.000 0.189 0.101 3.298 0.209 0.036 23 482121 1861 1977 117 1.000 0.142 0.490 4.122 0.161 -0.016 24 482122 1842 1977 136 1.000 0.164 0.721 4.396 0.176 0.061 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.000 0.177 0.172 3.597 0.201 0.012 STANDARD DEVIATION 20 0.000 0.024 0.302 0.841 0.030 0.018 MEDIAN (50TH QUANTILE) 125 1.000 0.178 0.158 3.307 0.193 0.008 INTERQUARTILE RANGE 39 0.000 0.034 0.305 1.135 0.047 0.023 MINIMUM VALUE 82 1.000 0.141 -0.352 2.667 0.156 -0.016 LOWER HINGE (25TH QUANTILE) 97 1.000 0.159 0.011 3.062 0.179 0.001 UPPER HINGE (75TH QUANTILE) 136 1.000 0.193 0.315 4.197 0.225 0.024 MAXIMUM VALUE 147 1.000 0.221 0.939 6.275 0.273 0.061 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.537 0.095 0.006 -0.275 2.992 0.240 0.783 MINIMUM CORRELATION: 0.240 SERIES 482112 AND 482122 89 YEARS MAXIMUM CORRELATION: 0.783 SERIES 482061 AND 482062 136 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.39 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 120. 231. 276. RBAR 0.512 0.596 0.623 SDEV 0.113 0.113 0.111 SERR 0.010 0.007 0.007 EPS 0.956 0.972 0.975 NSS 20.6 23.9 24.0 |======================== 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 1831 1977 147 0.997 0.141 -0.100 3.173 0.174 -0.129 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.138 0.040 0.076 40 107 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.18 0.72 1.00 1.08 1.80 3.86 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.08 0.00 0.86 0.94 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 -0.128 -0.036 0.138 -0.041 0.084 -0.054 0.069 -0.018 -0.048 -0.124 PACF -0.128 -0.053 0.129 -0.009 0.090 -0.054 0.071 -0.031 -0.030 -0.173 95% C.L. 0.165 0.168 0.168 0.171 0.171 0.172 0.173 0.173 0.174 0.174 |------------------ 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 0.019 -0.128 |---------- 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 0.001 -0.009 0.006 -0.006 0.089 -0.051 0.090 -0.025 -0.055 -0.137 PACF 0.001 -0.009 0.007 -0.007 0.089 -0.052 0.094 -0.030 -0.051 -0.150 95% C.L. 0.165 0.165 0.165 0.165 0.165 0.166 0.167 0.168 0.168 0.169 |----------------- 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 0.000 0.002 -0.010 0.007 |========================= 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 1831 1977 147 0.990 0.160 -0.166 2.759 0.140 0.457 |------------ 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 0.454 0.309 0.317 0.209 0.160 0.055 0.058 -0.049 -0.141 -0.216 PACF 0.454 0.129 0.174 -0.009 0.015 -0.099 0.026 -0.130 -0.110 -0.160 95% C.L. 0.165 0.196 0.209 0.222 0.227 0.230 0.230 0.231 0.231 0.233 |------------------- 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 0.254 0.369 0.067 0.187 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 2.15 MINUTES