RUN: fix002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: NM569E.rwl.conv LOG FILE PROCESSED: NM569E.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: 730 1 Ski Valley, Wheeler Peak WIDTH_EARLY PCEN - 730 2 United States of America Engelmann spruce 3120 3635-10530 1828 1983 730 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 11 730071 MISSING VALUES FOUND: 1 IN 1 GAPS / 1923 1923 / -------------------------------------------------------------------- 14 730082 MISSING VALUES FOUND: 13 IN 2 GAPS / 1906 1916 / 1941 1942 / -------------------------------------------------------------------- 18 730102 MISSING VALUES FOUND: 3 IN 1 GAPS / 1857 1859 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 730011 1836 1983 148 1.583 0.622 0.284 2.333 0.150 0.871 2 730012 1831 1983 153 1.488 0.637 0.568 2.736 0.158 0.882 3 730021 1845 1983 139 1.541 0.560 0.247 2.761 0.199 0.757 4 730022 1848 1983 136 1.706 0.741 0.881 3.838 0.191 0.801 5 730031 1846 1983 138 1.538 0.388 -0.043 2.006 0.149 0.737 6 730032 1858 1983 126 1.866 0.529 -0.283 2.166 0.147 0.795 7 730041 1859 1983 125 0.953 0.328 -0.306 2.227 0.157 0.824 8 730042 1858 1983 126 1.050 0.341 0.004 2.625 0.175 0.730 9 730061 1842 1983 142 0.990 0.299 0.763 4.715 0.190 0.690 10 730062 1863 1983 121 0.990 0.341 -0.358 2.299 0.165 0.839 11 730071 1831 1983 153 0.875 0.477 0.329 2.221 0.185 0.889 12 730072 1830 1919 90 1.216 0.284 0.093 2.757 0.162 0.611 13 730081 1830 1983 154 1.005 0.475 1.748 7.356 0.163 0.825 14 730082 1828 1983 156 1.125 0.512 1.271 6.115 0.164 0.860 15 730091 1845 1965 121 0.955 0.434 0.352 2.042 0.143 0.896 16 730092 1845 1983 139 1.046 0.389 0.020 1.927 0.144 0.889 17 730101 1836 1983 148 1.160 0.628 1.372 5.201 0.149 0.914 18 730102 1837 1983 147 1.044 0.530 1.320 5.384 0.140 0.869 19 730111 1840 1958 119 1.421 0.481 1.227 4.278 0.137 0.817 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 730112 1840 1983 144 1.520 0.569 0.611 3.022 0.152 0.858 21 730121 1833 1983 151 1.112 0.600 0.242 2.230 0.191 0.840 22 730122 1832 1945 114 1.256 0.313 0.727 4.072 0.165 0.626 NUMBER OF SERIES READ IN: 22 FROM 1828 TO 1983 156 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 135 1.247 0.476 0.503 3.378 0.162 0.810 STANDARD DEVIATION 15 0.285 0.129 0.600 1.532 0.018 0.085 MEDIAN (50TH QUANTILE) 139 1.143 0.479 0.341 2.747 0.160 0.832 INTERQUARTILE RANGE 23 0.516 0.228 0.861 2.051 0.026 0.114 MINIMUM VALUE 90 0.875 0.284 -0.358 1.927 0.137 0.611 LOWER HINGE (25TH QUANTILE) 125 1.005 0.341 0.020 2.227 0.149 0.757 UPPER HINGE (75TH QUANTILE) 148 1.520 0.569 0.881 4.278 0.175 0.871 MAXIMUM VALUE 154 1.866 0.741 1.748 7.356 0.199 0.914 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.666 0.179 0.012 -1.517 6.155 -0.119 0.939 MINIMUM CORRELATION: -0.119 SERIES 730062 AND 730072 57 YEARS MAXIMUM CORRELATION: 0.939 SERIES 730101 AND 730102 147 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 79.44 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1880. 1905. 1930. 1955. CORR 153. 210. 190. 153. RBAR 0.495 0.425 0.757 0.544 SDEV 0.227 0.242 0.081 0.301 SERR 0.018 0.017 0.006 0.024 EPS 0.955 0.941 0.985 0.959 NSS 21.6 21.8 21.1 19.6 |======================== 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 1828 1983 156 1.264 0.470 0.941 5.138 0.126 0.868 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.552 0.156 0.202 54 102 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.22 0.36 1.01 1.09 1.45 2.97 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.00 0.88 0.96 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 139. 23. 90. 125. 148. 156. |----------- 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 0.863 0.781 0.736 0.723 0.683 0.681 0.653 0.641 0.599 0.598 PACF 0.863 0.143 0.141 0.169 -0.016 0.163 -0.027 0.068 -0.075 0.106 95% C.L. 0.160 0.253 0.308 0.350 0.387 0.417 0.444 0.468 0.490 0.509 |------------------ 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 0.799 0.513 0.105 0.087 0.239 |================== 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 730011 3 0.00000000 0.00000000 -0.01285444 2.54076385 2 730012 3 0.00000000 0.00000000 -0.01245513 2.44714999 3 730021 3 0.00000000 0.00000000 -0.00842160 2.13073516 4 730022 3 0.00000000 0.00000000 -0.01255620 2.56634974 5 730031 3 0.00000000 0.00000000 -0.00416810 1.82765365 6 730032 3 0.00000000 0.00000000 -0.00948406 2.46803164 7 730041 3 0.00000000 0.00000000 -0.00598716 1.32983100 8 730042 3 0.00000000 0.00000000 -0.00666061 1.47294855 9 730061 1 0.82132822 0.01207063 0.00000000 0.59931386 10 730062 3 0.00000000 0.00000000 -0.00689249 1.41077268 11 730071 3 0.00000000 0.00000000 -0.00995478 1.63852596 12 730072 3 0.00000000 0.00000000 -0.00696572 1.53327334 13 730081 1 1.60927188 0.02567154 0.00000000 0.61080444 14 730082 1 1.77617323 0.01001244 0.00000000 0.23977792 15 730091 3 0.00000000 0.00000000 -0.01105169 1.62952483 16 730092 3 0.00000000 0.00000000 -0.00820752 1.62049735 17 730101 1 2.29701829 0.03719553 0.00000000 0.75259614 18 730102 1 1.85293031 0.02905267 0.00000000 0.63454217 19 730111 1 1.76327634 0.05038673 0.00000000 1.13457954 SERIES IDENT OPTION A B C D 20 730112 1 2.24046063 0.01163601 0.00000000 0.44003928 21 730121 3 0.00000000 0.00000000 -0.01189122 2.01591778 22 730122 3 0.00000000 0.00000000 -0.00627626 1.61667442 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 730011 1836 1983 148 0.999 0.177 -0.098 2.437 0.149 0.464 2 730012 1831 1983 153 1.014 0.261 1.077 5.095 0.158 0.705 3 730021 1845 1983 139 0.995 0.277 0.081 3.229 0.198 0.629 4 730022 1848 1983 136 0.991 0.280 1.008 5.451 0.189 0.607 5 730031 1846 1983 138 0.998 0.223 -0.011 2.328 0.148 0.676 6 730032 1858 1983 126 0.996 0.213 -0.192 2.758 0.146 0.668 7 730041 1859 1983 125 0.994 0.272 0.171 2.971 0.156 0.734 8 730042 1858 1983 126 0.996 0.232 0.123 2.338 0.173 0.557 9 730061 1842 1983 142 1.000 0.227 -0.027 3.140 0.188 0.524 10 730062 1863 1983 121 0.993 0.251 -0.283 3.393 0.163 0.684 11 730071 1831 1983 153 1.019 0.290 1.519 7.841 0.185 0.613 12 730072 1830 1919 90 0.999 0.179 -0.005 2.730 0.160 0.427 13 730081 1830 1983 154 0.999 0.232 0.348 3.104 0.162 0.626 14 730082 1828 1983 156 0.997 0.255 0.563 3.134 0.161 0.667 15 730091 1845 1965 121 1.001 0.187 0.286 2.759 0.141 0.484 16 730092 1845 1983 139 1.002 0.229 0.508 3.234 0.143 0.683 17 730101 1836 1983 148 0.999 0.321 0.239 2.142 0.148 0.865 18 730102 1837 1983 147 0.999 0.289 0.557 2.770 0.141 0.836 19 730111 1840 1958 119 1.000 0.194 0.328 3.493 0.136 0.591 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 730112 1840 1983 144 0.999 0.178 -0.053 2.922 0.150 0.446 21 730121 1833 1983 151 1.031 0.475 2.552 12.260 0.190 0.833 22 730122 1832 1945 114 1.000 0.179 0.204 3.192 0.163 0.377 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 136 1.001 0.246 0.404 3.760 0.161 0.623 STANDARD DEVIATION 16 0.009 0.066 0.650 2.285 0.018 0.133 MEDIAN (50TH QUANTILE) 139 0.999 0.232 0.221 3.119 0.159 0.628 INTERQUARTILE RANGE 23 0.004 0.083 0.568 0.635 0.026 0.160 MINIMUM VALUE 90 0.991 0.177 -0.283 2.142 0.136 0.377 LOWER HINGE (25TH QUANTILE) 125 0.996 0.194 -0.011 2.758 0.148 0.524 UPPER HINGE (75TH QUANTILE) 148 1.000 0.277 0.557 3.393 0.173 0.684 MAXIMUM VALUE 156 1.031 0.475 2.552 12.260 0.198 0.865 |------------------------ 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 730011 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 730012 -67 102 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 730021 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 730022 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 730031 -67 92 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 730032 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 730041 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 730042 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 730061 -67 95 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 730062 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 730071 -67 102 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 730072 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 730081 -67 103 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 730082 -67 104 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 730091 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 730092 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 730101 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 730102 -67 98 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 730111 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 730112 -67 96 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 730121 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 730122 -67 76 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 730011 1836 1983 148 0.999 0.173 -0.105 2.524 0.149 0.436 2 730012 1831 1983 153 0.997 0.209 0.099 2.706 0.157 0.571 3 730021 1845 1983 139 0.994 0.228 0.027 2.910 0.198 0.440 4 730022 1848 1983 136 0.994 0.211 0.448 4.225 0.189 0.373 5 730031 1846 1983 138 0.998 0.153 -0.262 2.491 0.148 0.343 6 730032 1858 1983 126 0.998 0.160 -0.610 4.089 0.145 0.425 7 730041 1859 1983 125 0.996 0.219 -0.004 3.583 0.156 0.606 8 730042 1858 1983 126 0.997 0.203 0.256 3.050 0.173 0.404 9 730061 1842 1983 142 0.997 0.211 -0.035 3.584 0.188 0.444 10 730062 1863 1983 121 0.997 0.205 -0.624 4.561 0.162 0.532 11 730071 1831 1983 153 0.999 0.247 0.228 4.393 0.185 0.553 12 730072 1830 1919 90 0.999 0.170 -0.034 2.795 0.160 0.352 13 730081 1830 1983 154 0.998 0.195 0.339 3.415 0.162 0.481 14 730082 1828 1983 156 0.995 0.208 0.655 3.476 0.161 0.516 15 730091 1845 1965 121 0.999 0.177 0.244 2.616 0.141 0.448 16 730092 1845 1983 139 0.995 0.189 0.352 2.984 0.142 0.574 17 730101 1836 1983 148 0.984 0.231 0.155 2.454 0.148 0.740 18 730102 1837 1983 147 0.991 0.209 0.082 2.735 0.141 0.685 19 730111 1840 1958 119 0.997 0.138 0.375 3.431 0.135 0.226 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 730112 1840 1983 144 0.999 0.165 0.015 2.978 0.150 0.353 21 730121 1833 1983 151 0.988 0.300 0.019 4.738 0.190 0.666 22 730122 1832 1945 114 0.999 0.174 0.217 3.161 0.163 0.339 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 136 0.996 0.199 0.084 3.314 0.161 0.478 STANDARD DEVIATION 16 0.004 0.036 0.306 0.702 0.019 0.129 MEDIAN (50TH QUANTILE) 139 0.997 0.204 0.091 3.106 0.159 0.446 INTERQUARTILE RANGE 23 0.004 0.038 0.290 0.849 0.025 0.198 MINIMUM VALUE 90 0.984 0.138 -0.624 2.454 0.135 0.226 LOWER HINGE (25TH QUANTILE) 125 0.995 0.173 -0.034 2.735 0.148 0.373 UPPER HINGE (75TH QUANTILE) 148 0.999 0.211 0.256 3.584 0.173 0.571 MAXIMUM VALUE 156 0.999 0.300 0.655 4.738 0.198 0.740 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.422 0.136 0.009 -0.316 4.122 -0.021 0.835 MINIMUM CORRELATION: -0.021 SERIES 730041 AND 730071 125 YEARS MAXIMUM CORRELATION: 0.835 SERIES 730101 AND 730102 147 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 79.44 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1880. 1905. 1930. 1955. CORR 153. 210. 190. 153. RBAR 0.444 0.398 0.499 0.485 SDEV 0.180 0.170 0.139 0.190 SERR 0.015 0.012 0.010 0.015 EPS 0.945 0.935 0.955 0.949 NSS 21.6 21.8 21.1 19.6 |======================== 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 1828 1983 156 1.001 0.144 -0.070 3.189 0.128 0.428 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.011 0.004 0.143 45 111 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.27 0.40 1.01 1.14 1.54 6.96 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 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 0.425 0.286 0.275 0.230 0.156 0.236 0.102 0.026 -0.066 -0.038 PACF 0.425 0.129 0.142 0.064 -0.005 0.148 -0.097 -0.070 -0.143 -0.004 95% C.L. 0.160 0.187 0.198 0.207 0.214 0.217 0.223 0.224 0.224 0.225 |------------------ 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 0.215 0.357 0.067 0.146 |======================= 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 0.431 0.312 0.311 0.189 0.110 0.249 0.088 0.001 -0.064 -0.036 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 0.431 2 0.365 0.154 3 0.339 0.095 0.164 4 0.343 0.097 0.171 -0.021 5 0.342 0.103 0.175 -0.009 -0.037 6 0.350 0.105 0.139 -0.030 -0.106 0.203 7 0.372 0.093 0.136 -0.014 -0.095 0.242 -0.111 8 0.362 0.114 0.128 -0.015 -0.082 0.250 -0.078 -0.089 9 0.349 0.103 0.164 -0.027 -0.085 0.268 -0.061 -0.037 -0.143 10 0.356 0.105 0.166 -0.039 -0.081 0.269 -0.068 -0.042 -0.158 0.043 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) 1086.68 1056.56 1054.79 1052.54 1054.47 1056.25 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1051.71 1051.78 1052.52 1051.28 1053.00 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 0.339 0.095 0.164 R-SQUARED DUE TO POOLED AUTOREGRESSION: 22.69 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 129.34 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.339 0.210 0.267 0.166 0.116 0.099 0.072 0.053 0.041 0.0307 0.023 0.017 0.013 0.010 0.007 0.006 0.004 0.003 0.002 0.0018 0.001 0.001 0.001 0.001 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 730011 3 0.198 0.477 -0.092 0.006 2 730012 3 0.373 0.550 -0.121 0.263 3 730021 3 0.218 0.360 0.127 0.076 4 730022 3 0.160 0.378 -0.053 0.128 5 730031 3 0.136 0.304 0.064 0.097 6 730032 3 0.234 0.401 -0.054 0.231 7 730041 3 0.419 0.501 0.093 0.112 8 730042 3 0.216 0.432 -0.105 0.208 9 730061 3 0.242 0.331 0.206 0.059 10 730062 3 0.304 0.473 0.103 0.018 11 730071 3 0.344 0.521 0.094 -0.041 12 730072 3 0.139 0.336 0.043 0.040 13 730081 3 0.250 0.455 0.092 -0.027 14 730082 3 0.284 0.465 0.058 0.077 15 730091 3 0.243 0.386 0.177 -0.029 16 730092 3 0.346 0.485 0.103 0.071 17 730101 3 0.569 0.609 0.118 0.075 18 730102 3 0.496 0.613 0.168 -0.061 19 730111 3 0.076 0.198 0.148 -0.024 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 730112 3 0.163 0.308 0.124 0.040 21 730121 3 0.482 0.509 0.118 0.146 22 730122 3 0.136 0.343 0.005 0.020 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.274 0.429 0.064 0.067 STANDARD DEVIATION 0 0.131 0.105 0.095 0.088 MEDIAN 3 0.243 0.444 0.094 0.065 INTERQUARTILE RANGE 0 0.184 0.158 0.119 0.106 MINIMUM VALUE 3 0.076 0.198 -0.121 -0.061 LOWER HINGE 3 0.163 0.343 0.005 0.006 UPPER HINGE 3 0.346 0.501 0.124 0.112 MAXIMUM VALUE 3 0.569 0.613 0.206 0.263 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 730011 1836 1983 148 1.000 0.155 -0.380 3.451 0.179 0.000 2 730012 1831 1983 153 1.000 0.165 0.205 3.116 0.191 -0.002 3 730021 1845 1983 139 1.000 0.201 0.161 3.551 0.229 -0.001 4 730022 1848 1983 136 1.000 0.194 0.373 3.538 0.225 0.008 5 730031 1846 1983 138 1.000 0.142 -0.255 2.623 0.170 -0.001 6 730032 1858 1983 126 1.000 0.140 -0.434 3.334 0.167 0.020 7 730041 1859 1983 125 1.000 0.170 0.013 3.268 0.189 0.025 8 730042 1858 1983 126 1.000 0.179 0.373 3.017 0.203 0.007 9 730061 1842 1983 142 1.000 0.183 -0.404 3.585 0.214 -0.003 10 730062 1863 1983 121 1.000 0.172 -0.261 3.981 0.199 0.001 11 730071 1831 1983 153 1.000 0.204 0.465 4.128 0.231 -0.004 12 730072 1830 1919 90 1.000 0.158 0.046 2.783 0.185 -0.008 13 730081 1830 1983 154 1.000 0.169 0.289 3.423 0.194 -0.013 14 730082 1828 1983 156 1.000 0.176 0.884 5.489 0.198 0.002 15 730091 1845 1965 121 1.000 0.155 0.677 3.378 0.166 -0.003 16 730092 1845 1983 139 1.000 0.153 0.323 3.187 0.178 -0.003 17 730101 1836 1983 148 1.000 0.152 0.246 2.468 0.173 -0.004 18 730102 1837 1983 147 1.000 0.148 0.093 2.368 0.172 -0.008 19 730111 1840 1958 119 1.000 0.133 0.415 3.527 0.147 0.001 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 730112 1840 1983 144 1.000 0.152 0.050 2.715 0.169 0.015 21 730121 1833 1983 151 1.000 0.216 0.343 5.196 0.225 -0.003 22 730122 1832 1945 114 1.000 0.163 0.330 3.343 0.181 -0.006 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 136 1.000 0.167 0.161 3.430 0.190 0.001 STANDARD DEVIATION 16 0.000 0.022 0.346 0.763 0.023 0.009 MEDIAN (50TH QUANTILE) 139 1.000 0.164 0.225 3.361 0.187 -0.002 INTERQUARTILE RANGE 23 0.000 0.027 0.360 0.534 0.031 0.006 MINIMUM VALUE 90 1.000 0.133 -0.434 2.368 0.147 -0.013 LOWER HINGE (25TH QUANTILE) 125 1.000 0.152 0.013 3.017 0.172 -0.004 UPPER HINGE (75TH QUANTILE) 148 1.000 0.179 0.373 3.551 0.203 0.002 MAXIMUM VALUE 156 1.000 0.216 0.884 5.489 0.231 0.025 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.461 0.101 0.007 0.511 3.761 0.163 0.794 MINIMUM CORRELATION: 0.163 SERIES 730071 AND 730082 153 YEARS MAXIMUM CORRELATION: 0.794 SERIES 730111 AND 730112 119 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 79.44 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1880. 1905. 1930. 1955. CORR 153. 210. 190. 153. RBAR 0.548 0.481 0.496 0.463 SDEV 0.116 0.128 0.138 0.129 SERR 0.009 0.009 0.010 0.010 EPS 0.963 0.953 0.954 0.944 NSS 21.6 21.8 21.1 19.6 |======================== 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 1828 1983 156 1.002 0.130 0.165 4.087 0.154 -0.053 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.092 0.030 0.089 53 103 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.28 0.64 1.00 1.12 1.76 4.94 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 0.00 0.87 0.93 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 -0.053 -0.025 0.023 0.048 -0.068 0.183 0.005 -0.012 -0.121 0.006 PACF -0.053 -0.028 0.020 0.050 -0.062 0.180 0.017 0.000 -0.128 -0.028 95% C.L. 0.160 0.161 0.161 0.161 0.161 0.162 0.167 0.167 0.167 0.169 |------------------ 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 -0.001 0.003 -0.005 0.051 -0.054 0.184 0.008 -0.013 -0.125 0.003 PACF -0.001 0.003 -0.005 0.051 -0.054 0.185 0.007 -0.016 -0.122 -0.018 95% C.L. 0.160 0.160 0.160 0.160 0.161 0.161 0.166 0.166 0.166 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 0.003 -0.001 0.003 -0.005 |========================= 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 1828 1983 156 1.004 0.151 0.055 3.498 0.130 0.458 |------------ 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 0.455 0.339 0.349 0.268 0.170 0.251 0.124 0.048 -0.036 -0.001 PACF 0.455 0.165 0.187 0.038 -0.039 0.141 -0.093 -0.065 -0.143 0.028 95% C.L. 0.160 0.190 0.205 0.220 0.228 0.231 0.238 0.240 0.240 0.240 |------------------- 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 0.262 0.351 0.086 0.200 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.19 MINUTES