RUN: me FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: me026e.rwl LOG FILE PROCESSED: me026e.rwl_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: 400 1 Elephant Mountain ME WIDTH_EARLY PCRU - 400 2 United States of America red spruce -999 4449-7047 1667 1977 - 400 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 19 401101 MISSING VALUES FOUND: 1 IN 1 GAPS / 1808 1808 / -------------------------------------------------------------------- 20 401102 MISSING VALUES FOUND: 1 IN 1 GAPS / 1808 1808 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 400011 1743 1976 234 0.569 0.345 1.032 3.642 0.294 0.794 2 400012 1671 1976 306 0.459 0.311 1.448 5.203 0.281 0.866 3 400021 1691 1976 286 0.578 0.390 0.940 3.434 0.281 0.827 4 400022 1690 1976 287 0.435 0.213 1.312 7.214 0.245 0.735 5 400031 1739 1976 238 0.709 0.342 0.262 3.221 0.233 0.841 6 400032 1681 1976 296 0.541 0.386 0.360 2.102 0.269 0.924 7 400041 1808 1976 169 0.954 0.439 0.492 2.319 0.185 0.848 8 400042 1791 1976 186 0.645 0.353 1.037 4.059 0.241 0.845 9 400051 1777 1976 200 0.936 0.554 0.940 2.920 0.241 0.869 10 400052 1747 1976 230 0.889 0.577 0.998 3.145 0.250 0.893 11 401061 1700 1976 277 0.530 0.282 0.951 3.608 0.232 0.852 12 401062 1696 1976 281 0.679 0.379 1.321 4.974 0.242 0.829 13 401071 1825 1976 152 0.781 0.300 1.086 7.127 0.207 0.685 14 401072 1825 1976 152 0.862 0.296 1.669 11.584 0.194 0.620 15 401081 1820 1976 157 0.814 0.353 1.355 6.917 0.231 0.776 16 401082 1818 1976 159 1.254 0.469 0.797 3.943 0.210 0.777 17 401091 1667 1976 310 0.544 0.234 0.992 4.462 0.212 0.815 18 401092 1717 1952 236 0.545 0.235 0.555 3.099 0.223 0.779 19 401101 1747 1976 230 0.511 0.283 1.285 4.921 0.262 0.763 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 401102 1744 1976 233 0.423 0.257 1.710 7.478 0.259 0.787 21 401111 1826 1976 151 0.823 0.334 0.962 4.317 0.198 0.757 22 401112 1837 1976 140 0.794 0.237 1.291 8.236 0.201 0.567 23 401121 1834 1976 143 0.814 0.285 0.621 4.011 0.224 0.670 24 402122 1827 1975 149 0.954 0.375 1.421 6.283 0.166 0.782 25 402131 1692 1937 246 0.719 0.430 0.608 2.511 0.214 0.887 26 402132 1715 1937 223 0.450 0.336 0.987 3.096 0.234 0.915 27 402141 1749 1976 228 0.783 0.405 0.516 2.544 0.184 0.872 28 402142 1776 1976 201 0.777 0.486 1.057 3.229 0.199 0.917 29 402151 1828 1976 149 1.290 0.448 0.743 3.170 0.166 0.783 30 402152 1811 1976 166 0.738 0.390 1.377 3.909 0.179 0.882 31 402161 1818 1976 159 0.842 0.391 0.396 2.864 0.263 0.753 32 402162 1801 1976 176 1.057 0.404 0.318 3.063 0.272 0.631 33 402171 1829 1976 148 0.758 0.346 1.042 4.534 0.166 0.875 34 402172 1823 1976 154 0.741 0.361 0.573 2.547 0.198 0.870 NUMBER OF SERIES READ IN: 34 FROM 1667 TO 1976 310 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 207 0.741 0.360 0.955 4.403 0.225 0.802 STANDARD DEVIATION 55 0.214 0.087 0.388 2.066 0.035 0.088 MEDIAN (50TH QUANTILE) 200 0.750 0.353 0.990 3.776 0.227 0.821 INTERQUARTILE RANGE 84 0.297 0.108 0.683 1.878 0.051 0.107 MINIMUM VALUE 140 0.423 0.213 0.262 2.102 0.166 0.567 LOWER HINGE (25TH QUANTILE) 154 0.545 0.296 0.608 3.096 0.198 0.763 UPPER HINGE (75TH QUANTILE) 238 0.842 0.404 1.291 4.974 0.250 0.870 MAXIMUM VALUE 310 1.290 0.577 1.710 11.584 0.294 0.924 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 561 0.381 0.280 0.012 -0.768 3.472 -0.617 0.982 MINIMUM CORRELATION: -0.617 SERIES 400032 AND 402132 223 YEARS MAXIMUM CORRELATION: 0.982 SERIES 400051 AND 400052 200 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 55.37 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1720. 1745. 1770. 1795. 1820. 1845. 1870. 1895. 1920. 1945. CORR 15. 45. 78. 120. 171. 300. 561. 561. 496. 465. RBAR 0.420 0.413 0.245 0.472 0.553 0.626 0.477 0.401 0.398 0.305 SDEV 0.220 0.331 0.260 0.216 0.274 0.170 0.197 0.249 0.243 0.279 SERR 0.057 0.049 0.029 0.020 0.021 0.010 0.008 0.010 0.011 0.013 EPS 0.870 0.901 0.844 0.945 0.970 0.982 0.969 0.958 0.957 0.934 NSS 9.2 13.0 16.7 19.2 25.9 32.5 34.0 34.0 33.7 32.4 |======================== 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 1667 1976 310 0.626 0.226 1.067 5.531 0.178 0.810 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.632 0.354 0.120 89 221 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.32 0.64 1.00 1.09 1.72 13.16 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.08 0.00 0.86 0.93 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 200. 84. 140. 154. 238. 310. |----------- 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 0.808 0.725 0.656 0.603 0.528 0.493 0.445 0.413 0.363 0.351 PACF 0.808 0.210 0.072 0.050 -0.054 0.061 -0.009 0.024 -0.039 0.063 95% C.L. 0.114 0.172 0.208 0.233 0.253 0.266 0.278 0.287 0.295 0.300 |------------------ 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 2 0.676 0.656 0.194 |================== 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 400011 3 0.00000000 0.00000000 0.00373849 0.12965849 2 400012 3 0.00000000 0.00000000 0.00247326 0.07901404 3 400021 3 0.00000000 0.00000000 -0.00124476 0.75680459 4 400022 3 0.00000000 0.00000000 -0.00001929 0.43776101 5 400031 3 0.00000000 0.00000000 0.00299065 0.35135731 6 400032 3 0.00000000 0.00000000 0.00345143 0.02864521 7 400041 1 0.79467815 0.03618209 0.00000000 0.82686323 8 400042 3 0.00000000 0.00000000 -0.00205851 0.83720195 9 400051 3 0.00000000 0.00000000 -0.00338898 1.27634275 10 400052 3 0.00000000 0.00000000 -0.00026228 0.91916347 11 401061 3 0.00000000 0.00000000 -0.00121774 0.69908494 12 401062 3 0.00000000 0.00000000 -0.00112651 0.83798349 13 401071 1 1.51217782 0.17376049 0.00000000 0.72823417 14 401072 1 1.79420495 0.20036776 0.00000000 0.80870163 15 401081 1 0.96904683 0.01367187 0.00000000 0.41791967 16 401082 1 1.43014002 0.00609844 0.00000000 0.34115246 17 401091 1 0.64547426 0.00550802 0.00000000 0.23559910 18 401092 1 0.47570026 0.05499087 0.00000000 0.50900555 19 401101 3 0.00000000 0.00000000 0.00017429 0.48886827 SERIES IDENT OPTION A B C D 20 401102 3 0.00000000 0.00000000 -0.00203298 0.65994108 21 401111 3 0.00000000 0.00000000 0.00088390 0.75534040 22 401112 3 0.00000000 0.00000000 0.00050104 0.75831962 23 401121 1 1.44874883 0.26164261 0.00000000 0.78010988 24 402122 1 1.89285445 0.13538840 0.00000000 0.86680776 25 402131 3 0.00000000 0.00000000 -0.00426681 1.24617887 26 402132 -67 149 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 27 402141 3 0.00000000 0.00000000 -0.00470014 1.32106078 28 402142 3 0.00000000 0.00000000 -0.00577894 1.36103630 29 402151 1 1.26877987 0.01697888 0.00000000 0.83256304 30 402152 1 1.20707643 0.01193462 0.00000000 0.21555306 31 402161 3 0.00000000 0.00000000 -0.00551487 1.28288746 32 402162 3 0.00000000 0.00000000 -0.00032375 1.08547008 33 402171 1 1.38584244 0.11110154 0.00000000 0.67849016 34 402172 3 0.00000000 0.00000000 0.00098918 0.66476697 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 400011 1743 1976 234 1.026 0.441 0.886 4.488 0.293 0.609 2 400012 1671 1976 306 1.117 0.896 3.792 20.732 0.281 0.754 3 400021 1691 1976 286 0.990 0.630 1.014 3.866 0.280 0.824 4 400022 1690 1976 287 1.000 0.488 1.291 7.101 0.244 0.733 5 400031 1739 1976 238 0.988 0.402 0.127 2.822 0.232 0.751 6 400032 1681 1976 296 1.043 0.932 5.626 47.742 0.270 0.688 7 400041 1808 1976 169 0.999 0.434 0.692 3.235 0.184 0.816 8 400042 1791 1976 186 0.998 0.504 0.722 3.149 0.240 0.801 9 400051 1777 1976 200 0.992 0.491 0.499 2.598 0.239 0.828 10 400052 1747 1976 230 1.000 0.644 0.969 3.100 0.248 0.888 11 401061 1700 1976 277 0.991 0.485 1.066 3.989 0.231 0.835 12 401062 1696 1976 281 0.994 0.529 1.277 4.793 0.241 0.823 13 401071 1825 1976 152 1.000 0.315 -0.116 3.585 0.205 0.673 14 401072 1825 1976 152 1.000 0.259 -0.454 3.831 0.191 0.563 15 401081 1820 1976 157 0.999 0.328 0.737 4.212 0.230 0.616 16 401082 1818 1976 159 1.000 0.312 0.479 3.074 0.208 0.657 17 401091 1667 1976 310 1.000 0.329 0.321 2.831 0.211 0.701 18 401092 1717 1952 236 1.000 0.421 0.747 3.731 0.223 0.778 19 401101 1747 1976 230 1.000 0.559 1.281 4.998 0.263 0.762 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 401102 1744 1976 233 0.997 0.452 0.857 4.252 0.258 0.726 21 401111 1826 1976 151 1.001 0.416 1.337 5.886 0.197 0.738 22 401112 1837 1976 140 1.000 0.301 1.530 9.860 0.200 0.554 23 401121 1834 1976 143 1.000 0.312 0.078 2.750 0.221 0.643 24 402122 1827 1975 149 1.000 0.288 -0.078 2.824 0.164 0.715 25 402131 1692 1937 246 0.975 0.382 1.116 4.062 0.213 0.749 26 402132 1715 1937 223 1.000 0.317 0.270 3.027 0.233 0.612 27 402141 1749 1976 228 0.992 0.311 0.297 3.452 0.183 0.704 28 402142 1776 1976 201 0.999 0.368 0.645 3.581 0.199 0.801 29 402151 1828 1976 149 1.000 0.254 0.918 4.334 0.164 0.592 30 402152 1811 1976 166 1.003 0.280 0.080 3.040 0.179 0.637 31 402161 1818 1976 159 0.992 0.377 0.477 3.085 0.262 0.617 32 402162 1801 1976 176 1.000 0.380 0.287 3.017 0.271 0.624 33 402171 1829 1976 148 1.000 0.385 0.708 3.375 0.164 0.859 34 402172 1823 1976 154 1.001 0.488 0.630 2.777 0.197 0.858 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 207 1.003 0.433 0.886 5.682 0.224 0.721 STANDARD DEVIATION 55 0.023 0.158 1.099 8.097 0.036 0.093 MEDIAN (50TH QUANTILE) 200 1.000 0.394 0.715 3.583 0.226 0.729 INTERQUARTILE RANGE 84 0.003 0.174 0.769 1.293 0.051 0.165 MINIMUM VALUE 140 0.975 0.254 -0.454 2.598 0.164 0.554 LOWER HINGE (25TH QUANTILE) 154 0.997 0.315 0.297 3.040 0.197 0.637 UPPER HINGE (75TH QUANTILE) 238 1.000 0.488 1.066 4.334 0.248 0.801 MAXIMUM VALUE 310 1.117 0.932 5.626 47.742 0.293 0.888 |------------------------ 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 400011 -67 156 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 400012 -67 205 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 400021 -67 191 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 400022 -67 192 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 400031 -67 159 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 400032 -67 198 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 400041 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 400042 -67 124 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 400051 -67 134 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 400052 -67 154 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 401061 -67 185 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 401062 -67 188 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 401071 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 401072 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 401081 -67 105 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 401082 -67 106 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 401091 -67 207 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 401092 -67 158 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 401101 -67 154 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 401102 -67 156 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 401111 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 401112 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 401121 -67 95 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 402122 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 25 402131 -67 164 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 26 402132 -67 149 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 27 402141 -67 152 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 28 402142 -67 134 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 29 402151 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 30 402152 -67 111 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 31 402161 -67 106 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 32 402162 -67 117 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 33 402171 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 34 402172 -67 103 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 400011 1743 1976 234 0.992 0.382 0.679 3.781 0.293 0.536 2 400012 1671 1976 306 0.995 0.452 0.750 3.716 0.280 0.645 3 400021 1691 1976 286 0.986 0.503 1.128 5.793 0.279 0.691 4 400022 1690 1976 287 0.988 0.445 1.117 6.219 0.244 0.695 5 400031 1739 1976 238 0.993 0.375 0.278 3.394 0.231 0.690 6 400032 1681 1976 296 0.966 0.553 2.026 12.472 0.269 0.717 7 400041 1808 1976 169 0.977 0.335 0.541 3.532 0.183 0.713 8 400042 1791 1976 186 0.971 0.420 0.671 3.354 0.238 0.720 9 400051 1777 1976 200 0.982 0.349 -0.038 3.311 0.240 0.668 10 400052 1747 1976 230 0.999 0.396 0.540 4.249 0.249 0.706 11 401061 1700 1976 277 0.996 0.325 0.574 4.144 0.231 0.613 12 401062 1696 1976 281 0.995 0.366 1.723 10.766 0.241 0.543 13 401071 1825 1976 152 0.992 0.284 -0.012 3.747 0.205 0.600 14 401072 1825 1976 152 0.997 0.250 -0.363 3.681 0.191 0.526 15 401081 1820 1976 157 0.994 0.287 0.542 3.605 0.230 0.488 16 401082 1818 1976 159 0.997 0.298 0.412 3.187 0.208 0.622 17 401091 1667 1976 310 0.998 0.319 0.285 2.880 0.211 0.683 18 401092 1717 1952 236 0.988 0.354 0.571 3.630 0.223 0.703 19 401101 1747 1976 230 0.988 0.449 0.860 3.962 0.263 0.717 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 401102 1744 1976 233 0.987 0.404 0.641 4.066 0.258 0.669 21 401111 1826 1976 151 0.994 0.262 0.069 2.793 0.196 0.537 22 401112 1837 1976 140 0.997 0.248 0.601 4.846 0.199 0.442 23 401121 1834 1976 143 0.998 0.292 -0.065 2.841 0.221 0.611 24 402122 1827 1975 149 0.993 0.233 -0.099 2.763 0.163 0.600 25 402131 1692 1937 246 0.993 0.303 0.377 2.974 0.212 0.610 26 402132 1715 1937 223 0.998 0.310 0.274 3.017 0.233 0.600 27 402141 1749 1976 228 0.998 0.302 0.099 3.117 0.183 0.687 28 402142 1776 1976 201 0.992 0.328 0.263 3.274 0.199 0.756 29 402151 1828 1976 149 0.997 0.220 0.461 3.282 0.164 0.500 30 402152 1811 1976 166 0.996 0.250 -0.159 3.163 0.178 0.555 31 402161 1818 1976 159 0.989 0.335 0.631 3.400 0.261 0.505 32 402162 1801 1976 176 0.995 0.361 0.329 3.269 0.271 0.595 33 402171 1829 1976 148 0.994 0.243 0.367 3.306 0.163 0.659 34 402172 1823 1976 154 0.988 0.315 0.332 3.270 0.195 0.694 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 207 0.991 0.340 0.482 4.083 0.224 0.626 STANDARD DEVIATION 55 0.008 0.079 0.491 2.067 0.036 0.081 MEDIAN (50TH QUANTILE) 200 0.993 0.327 0.437 3.397 0.226 0.633 INTERQUARTILE RANGE 84 0.009 0.095 0.377 0.776 0.053 0.138 MINIMUM VALUE 140 0.966 0.220 -0.363 2.763 0.163 0.442 LOWER HINGE (25TH QUANTILE) 154 0.988 0.287 0.263 3.187 0.196 0.555 UPPER HINGE (75TH QUANTILE) 238 0.997 0.382 0.641 3.962 0.249 0.694 MAXIMUM VALUE 310 0.999 0.553 2.026 12.472 0.293 0.756 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 561 0.412 0.118 0.005 0.251 3.808 0.016 0.920 MINIMUM CORRELATION: 0.016 SERIES 400011 AND 401121 143 YEARS MAXIMUM CORRELATION: 0.920 SERIES 400051 AND 400052 200 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 55.37 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1720. 1745. 1770. 1795. 1820. 1845. 1870. 1895. 1920. 1945. CORR 15. 45. 78. 120. 171. 300. 561. 561. 496. 465. RBAR 0.433 0.454 0.306 0.515 0.614 0.578 0.492 0.472 0.451 0.336 SDEV 0.198 0.223 0.236 0.179 0.168 0.154 0.162 0.188 0.196 0.215 SERR 0.051 0.033 0.027 0.016 0.013 0.009 0.007 0.008 0.009 0.010 EPS 0.876 0.916 0.880 0.953 0.976 0.978 0.971 0.968 0.965 0.942 NSS 9.2 13.0 16.7 19.2 25.9 32.5 34.0 34.0 33.7 32.4 |======================== 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 1667 1976 310 0.967 0.245 0.018 3.412 0.176 0.639 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.338 0.224 0.081 88 222 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.22 0.42 1.00 1.07 1.49 19.37 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.08 0.00 0.87 0.94 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 0.637 0.501 0.369 0.279 0.173 0.135 0.105 0.087 0.056 0.054 PACF 0.637 0.159 -0.001 0.004 -0.062 0.030 0.019 0.013 -0.020 0.016 95% C.L. 0.114 0.153 0.173 0.183 0.188 0.190 0.191 0.192 0.193 0.193 |------------------ STANDARD CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 2 0.423 0.540 0.155 |======================= 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 0.622 0.480 0.385 0.297 0.208 0.171 0.063 0.045 -0.023 -0.021 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 0.622 2 0.527 0.153 3 0.517 0.121 0.061 4 0.517 0.120 0.059 0.004 5 0.517 0.123 0.064 0.023 -0.038 6 0.518 0.122 0.062 0.020 -0.051 0.025 7 0.521 0.116 0.064 0.027 -0.037 0.084 -0.115 8 0.524 0.114 0.065 0.027 -0.038 0.081 -0.129 0.027 9 0.526 0.104 0.072 0.024 -0.036 0.086 -0.120 0.067 -0.077 10 0.529 0.101 0.076 0.020 -0.035 0.085 -0.123 0.063 -0.097 0.037 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) 2850.12 2700.67 2695.34 2696.18 2698.18 2699.73 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 2701.54 2699.43 2701.20 2701.36 2702.93 SELECTED AUTOREGRESSION ORDER: 2 AR ORDER SELECTION CRITERION: IPP=0 FIRST-MINIMUM AIC SELECTION THE AIC TRACE SHOULD BE CHECKED TO SEE IF AR ORDER SELECTION CRITERION IS ADEQUATE. E.G. IF AR-ORDERS OF THE FIRST-MINIMUM AND THE FULL-MINIMUM AIC ARE CLOSE, AN ARSTAN RUN WITH FULL-MINIMUM AIC ORDER SELECTION MIGHT BE TRIED AUTOREGRESSION COEFFICIENTS: T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 0.527 0.153 R-SQUARED DUE TO POOLED AUTOREGRESSION: 40.08 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 166.90 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.527 0.430 0.307 0.227 0.167 0.123 0.090 0.066 0.049 0.0357 0.026 0.019 0.014 0.010 0.008 0.006 0.004 0.003 0.002 0.0016 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 400011 2 0.318 0.427 0.204 2 400012 2 0.440 0.563 0.140 3 400021 2 0.540 0.642 0.114 4 400022 2 0.550 0.601 0.175 5 400031 2 0.500 0.614 0.117 6 400032 2 0.626 0.620 0.205 7 400041 2 0.573 0.513 0.293 8 400042 2 0.591 0.467 0.359 9 400051 2 0.487 0.528 0.211 10 400052 2 0.538 0.516 0.271 11 401061 2 0.412 0.571 0.104 12 401062 2 0.310 0.468 0.140 13 401071 2 0.382 0.610 0.009 14 401072 2 0.302 0.558 -0.020 15 401081 2 0.249 0.496 -0.005 16 401082 2 0.402 0.574 0.087 17 401091 2 0.472 0.627 0.084 18 401092 2 0.504 0.626 0.110 19 401101 2 0.543 0.582 0.195 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 401102 2 0.495 0.595 0.144 21 401111 2 0.320 0.637 -0.158 22 401112 2 0.208 0.440 0.018 23 401121 2 0.380 0.642 -0.044 24 402122 2 0.379 0.531 0.126 25 402131 2 0.397 0.494 0.192 26 402132 2 0.384 0.496 0.179 27 402141 2 0.499 0.619 0.117 28 402142 2 0.612 0.532 0.298 29 402151 2 0.266 0.435 0.132 30 402152 2 0.361 0.466 0.192 31 402161 2 0.292 0.408 0.202 32 402162 2 0.364 0.549 0.080 33 402171 2 0.450 0.608 0.082 34 402172 2 0.491 0.622 0.106 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.430 0.549 0.131 STANDARD DEVIATION 0 0.110 0.070 0.104 MEDIAN 2 0.426 0.561 0.129 INTERQUARTILE RANGE 0 0.143 0.119 0.111 MINIMUM VALUE 2 0.208 0.408 -0.158 LOWER HINGE 2 0.361 0.496 0.084 UPPER HINGE 2 0.504 0.614 0.195 MAXIMUM VALUE 2 0.626 0.642 0.359 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 400011 1743 1976 234 1.000 0.315 0.866 4.847 0.337 -0.001 2 400012 1671 1976 306 1.000 0.336 1.132 6.862 0.343 -0.011 3 400021 1691 1976 286 1.000 0.336 0.574 4.775 0.349 -0.051 4 400022 1690 1976 287 1.000 0.292 0.685 5.853 0.308 -0.045 5 400031 1739 1976 238 1.000 0.266 0.613 4.701 0.290 0.012 6 400032 1681 1976 296 1.003 0.306 0.805 6.086 0.303 -0.065 7 400041 1808 1976 169 1.000 0.220 0.932 7.845 0.228 -0.032 8 400042 1791 1976 186 1.000 0.269 0.512 3.870 0.271 -0.011 9 400051 1777 1976 200 1.000 0.253 0.834 4.810 0.277 -0.036 10 400052 1747 1976 230 1.000 0.269 0.859 4.827 0.290 0.009 11 401061 1700 1976 277 1.000 0.247 0.229 3.568 0.286 -0.013 12 401062 1696 1976 281 1.001 0.303 2.403 21.451 0.287 0.007 13 401071 1825 1976 152 1.000 0.223 0.283 3.476 0.248 0.013 14 401072 1825 1976 152 1.000 0.209 0.070 3.180 0.233 0.020 15 401081 1820 1976 157 1.000 0.249 0.116 3.574 0.292 0.001 16 401082 1818 1976 159 1.000 0.230 0.421 5.155 0.263 -0.009 17 401091 1667 1976 310 1.000 0.231 0.255 3.204 0.259 0.001 18 401092 1717 1952 236 1.000 0.250 0.546 4.016 0.285 -0.007 19 401101 1747 1976 230 1.000 0.304 0.795 5.342 0.315 -0.011 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 401102 1744 1976 233 1.000 0.283 0.544 3.872 0.298 -0.015 21 401111 1826 1976 151 1.000 0.215 -0.003 3.062 0.245 -0.005 22 401112 1837 1976 140 1.000 0.221 0.655 5.551 0.238 -0.003 23 401121 1834 1976 143 1.000 0.230 -0.248 3.438 0.271 0.006 24 402122 1827 1975 149 1.000 0.184 -0.048 3.755 0.210 0.009 25 402131 1692 1937 246 1.000 0.235 0.450 3.496 0.255 0.005 26 402132 1715 1937 223 1.000 0.243 0.332 2.903 0.270 0.000 27 402141 1749 1976 228 1.000 0.213 0.382 3.562 0.232 0.008 28 402142 1776 1976 201 1.000 0.203 -0.017 3.441 0.233 -0.013 29 402151 1828 1976 149 1.000 0.189 0.223 4.604 0.207 -0.007 30 402152 1811 1976 166 1.000 0.197 0.247 3.720 0.220 -0.035 31 402161 1818 1976 159 1.000 0.282 0.575 4.333 0.314 0.007 32 402162 1801 1976 176 1.000 0.288 0.457 3.471 0.321 -0.005 33 402171 1829 1976 148 1.000 0.181 0.367 3.699 0.208 -0.012 34 402172 1823 1976 154 1.000 0.225 0.680 3.983 0.244 -0.004 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 207 1.000 0.250 0.515 4.833 0.271 -0.009 STANDARD DEVIATION 55 0.001 0.043 0.460 3.145 0.039 0.019 MEDIAN (50TH QUANTILE) 200 1.000 0.245 0.484 3.927 0.271 -0.005 INTERQUARTILE RANGE 84 0.000 0.063 0.438 1.351 0.060 0.019 MINIMUM VALUE 140 1.000 0.181 -0.248 2.903 0.207 -0.065 LOWER HINGE (25TH QUANTILE) 154 1.000 0.220 0.247 3.496 0.238 -0.013 UPPER HINGE (75TH QUANTILE) 238 1.000 0.283 0.685 4.847 0.298 0.006 MAXIMUM VALUE 310 1.003 0.336 2.403 21.451 0.349 0.020 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 561 0.442 0.087 0.004 0.246 5.159 0.130 0.889 MINIMUM CORRELATION: 0.130 SERIES 401082 AND 402131 120 YEARS MAXIMUM CORRELATION: 0.889 SERIES 400051 AND 400052 200 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 55.37 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1720. 1745. 1770. 1795. 1820. 1845. 1870. 1895. 1920. 1945. CORR 15. 45. 78. 120. 171. 300. 561. 561. 496. 465. RBAR 0.302 0.468 0.440 0.519 0.546 0.519 0.505 0.500 0.456 0.392 SDEV 0.216 0.128 0.144 0.147 0.136 0.127 0.125 0.119 0.122 0.133 SERR 0.056 0.019 0.016 0.013 0.010 0.007 0.005 0.005 0.005 0.006 EPS 0.800 0.920 0.929 0.954 0.969 0.972 0.972 0.971 0.966 0.954 NSS 9.2 13.0 16.7 19.2 25.9 32.5 34.0 34.0 33.7 32.4 |======================== 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 1667 1976 310 0.986 0.180 0.126 3.207 0.210 -0.034 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.205 0.122 0.074 125 185 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.20 0.44 1.01 1.09 1.53 7.99 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.09 0.00 0.88 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 -0.034 -0.039 0.004 0.054 -0.105 -0.003 0.001 0.062 -0.056 0.006 PACF -0.034 -0.040 0.001 0.053 -0.101 -0.005 -0.007 0.060 -0.042 -0.002 95% C.L. 0.114 0.114 0.114 0.114 0.114 0.115 0.115 0.115 0.116 0.116 |------------------ 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 0.000 0.002 -0.001 0.049 -0.103 -0.002 -0.003 0.060 -0.054 0.006 PACF 0.000 0.002 -0.001 0.049 -0.104 -0.001 -0.002 0.058 -0.046 -0.004 95% C.L. 0.114 0.114 0.114 0.114 0.114 0.115 0.115 0.115 0.115 0.116 |----------------- REWHITENED CHRONOLOGY AUTOREGRESSIVE MODEL -----------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 2 0.000 0.000 0.002 |========================= 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 1667 1976 310 0.989 0.230 0.128 3.263 0.167 0.614 |------------ 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 0.612 0.468 0.326 0.238 0.114 0.099 0.068 0.065 0.003 0.004 PACF 0.612 0.150 -0.015 0.005 -0.092 0.057 0.012 0.021 -0.076 0.009 95% C.L. 0.114 0.150 0.168 0.176 0.180 0.181 0.182 0.182 0.182 0.182 |------------------- 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 2 0.391 0.524 0.147 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 1.17 MINUTES