RUN: fix002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: NM569W.rwl.conv LOG FILE PROCESSED: NM569W.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_RING 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 1.805 0.696 0.251 2.263 0.138 0.882 2 730012 1831 1983 153 1.703 0.702 0.498 2.558 0.147 0.890 3 730021 1845 1983 139 1.724 0.594 0.174 2.713 0.183 0.770 4 730022 1848 1983 136 1.887 0.784 0.809 3.721 0.177 0.815 5 730031 1846 1983 138 1.725 0.417 -0.130 2.008 0.139 0.746 6 730032 1858 1983 126 2.099 0.592 -0.317 2.163 0.135 0.821 7 730041 1859 1983 125 1.119 0.360 -0.286 2.223 0.151 0.818 8 730042 1858 1983 126 1.227 0.382 -0.038 2.607 0.170 0.736 9 730061 1842 1983 142 1.155 0.346 0.803 4.421 0.175 0.730 10 730062 1863 1983 121 1.140 0.383 -0.420 2.225 0.149 0.860 11 730071 1831 1983 153 1.043 0.536 0.336 2.054 0.159 0.912 12 730072 1830 1919 90 1.443 0.351 0.212 3.005 0.162 0.611 13 730081 1830 1983 154 1.164 0.544 1.817 7.896 0.148 0.831 14 730082 1828 1983 156 1.307 0.575 1.190 5.846 0.144 0.873 15 730091 1845 1965 121 1.090 0.494 0.449 2.208 0.140 0.889 16 730092 1845 1983 139 1.196 0.442 0.032 1.884 0.140 0.896 17 730101 1836 1983 148 1.348 0.715 1.310 4.979 0.140 0.919 18 730102 1837 1983 147 1.225 0.635 1.386 5.298 0.132 0.883 19 730111 1840 1958 119 1.628 0.545 1.240 4.336 0.126 0.832 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 730112 1840 1983 144 1.759 0.634 0.450 2.771 0.140 0.875 21 730121 1833 1983 151 1.302 0.666 0.208 2.116 0.154 0.904 22 730122 1832 1945 114 1.458 0.441 2.084 10.038 0.151 0.764 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 1.434 0.538 0.548 3.606 0.150 0.830 STANDARD DEVIATION 15 0.306 0.133 0.699 2.122 0.015 0.077 MEDIAN (50TH QUANTILE) 139 1.328 0.545 0.392 2.660 0.148 0.846 INTERQUARTILE RANGE 23 0.560 0.218 1.158 2.213 0.020 0.119 MINIMUM VALUE 90 1.043 0.346 -0.420 1.884 0.126 0.611 LOWER HINGE (25TH QUANTILE) 125 1.164 0.417 0.032 2.208 0.140 0.770 UPPER HINGE (75TH QUANTILE) 148 1.724 0.635 1.190 4.421 0.159 0.889 MAXIMUM VALUE 154 2.099 0.784 2.084 10.038 0.183 0.919 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.682 0.173 0.011 -1.583 6.375 -0.085 0.961 MINIMUM CORRELATION: -0.085 SERIES 730032 AND 730072 62 YEARS MAXIMUM CORRELATION: 0.961 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 0.507 0.430 0.757 0.544 SDEV 0.225 0.237 0.081 0.304 SERR 0.018 0.016 0.006 0.025 EPS 0.957 0.943 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 1.461 0.542 0.955 4.949 0.118 0.886 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.555 0.155 0.209 54 102 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.17 0.25 1.00 1.05 1.30 3.55 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.00 0.86 0.93 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 0.880 0.800 0.752 0.731 0.693 0.686 0.666 0.653 0.618 0.619 PACF 0.880 0.114 0.124 0.151 -0.018 0.158 0.004 0.053 -0.050 0.124 95% C.L. 0.160 0.256 0.313 0.357 0.393 0.423 0.451 0.475 0.498 0.517 |------------------ 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 0.821 0.558 0.106 0.071 0.213 |================== 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 -0.01456202 2.88987041 2 730012 3 0.00000000 0.00000000 -0.01385536 2.76973867 3 730021 3 0.00000000 0.00000000 -0.00953894 2.39211440 4 730022 3 0.00000000 0.00000000 -0.01361991 2.82031703 5 730031 3 0.00000000 0.00000000 -0.00510844 2.07996392 6 730032 3 0.00000000 0.00000000 -0.01124493 2.81278348 7 730041 3 0.00000000 0.00000000 -0.00687846 1.55198324 8 730042 3 0.00000000 0.00000000 -0.00769692 1.71573842 9 730061 1 0.94696641 0.01643337 0.00000000 0.79120392 10 730062 3 0.00000000 0.00000000 -0.00822788 1.64214873 11 730071 3 0.00000000 0.00000000 -0.01122938 1.90424907 12 730072 3 0.00000000 0.00000000 -0.00883228 1.84509110 13 730081 1 1.88472426 0.02606372 0.00000000 0.70933688 14 730082 1 2.14543390 0.00874275 0.00000000 0.14986435 15 730091 3 0.00000000 0.00000000 -0.01238856 1.84578514 16 730092 3 0.00000000 0.00000000 -0.00933205 1.84971845 17 730101 1 2.60944939 0.03478776 0.00000000 0.85313982 18 730102 1 2.28250289 0.03108192 0.00000000 0.75086743 19 730111 1 2.01424575 0.04901938 0.00000000 1.29223108 SERIES IDENT OPTION A B C D 20 730112 1 2.90427256 0.00809985 0.00000000 0.05161327 21 730121 3 0.00000000 0.00000000 -0.01364733 2.33872056 22 730122 1 1.28787315 0.01507952 0.00000000 0.84756237 |-------------------- 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 0.165 -0.099 2.530 0.137 0.461 2 730012 1831 1983 153 1.011 0.239 0.940 4.816 0.146 0.697 3 730021 1845 1983 139 0.996 0.258 0.157 3.033 0.182 0.625 4 730022 1848 1983 136 0.992 0.266 1.014 5.244 0.175 0.622 5 730031 1846 1983 138 0.998 0.207 -0.017 2.317 0.138 0.670 6 730032 1858 1983 126 0.996 0.203 -0.152 2.848 0.134 0.690 7 730041 1859 1983 125 0.995 0.243 0.113 3.069 0.150 0.701 8 730042 1858 1983 126 0.997 0.217 0.126 2.579 0.168 0.534 9 730061 1842 1983 142 1.000 0.214 -0.094 3.069 0.173 0.546 10 730062 1863 1983 121 0.994 0.232 -0.413 3.609 0.147 0.695 11 730071 1831 1983 153 1.022 0.259 1.476 6.492 0.159 0.663 12 730072 1830 1919 90 0.999 0.184 0.276 2.885 0.161 0.416 13 730081 1830 1983 154 0.999 0.215 0.377 3.159 0.147 0.630 14 730082 1828 1983 156 0.997 0.237 0.672 3.270 0.143 0.671 15 730091 1845 1965 121 1.002 0.191 0.404 2.910 0.138 0.519 16 730092 1845 1983 139 1.002 0.226 0.545 3.162 0.139 0.700 17 730101 1836 1983 148 0.999 0.307 0.296 2.277 0.139 0.863 18 730102 1837 1983 147 0.999 0.277 0.569 2.743 0.134 0.839 19 730111 1840 1958 119 1.000 0.185 0.312 3.534 0.125 0.627 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 730112 1840 1983 144 0.999 0.172 0.035 2.948 0.139 0.501 21 730121 1833 1983 151 1.033 0.440 2.793 12.825 0.153 0.864 22 730122 1832 1945 114 1.000 0.199 1.070 6.221 0.149 0.549 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 136 1.001 0.233 0.473 3.888 0.149 0.640 STANDARD DEVIATION 16 0.009 0.058 0.691 2.313 0.015 0.120 MEDIAN (50TH QUANTILE) 139 0.999 0.221 0.304 3.069 0.147 0.646 INTERQUARTILE RANGE 23 0.004 0.060 0.637 0.760 0.022 0.151 MINIMUM VALUE 90 0.992 0.165 -0.413 2.277 0.125 0.416 LOWER HINGE (25TH QUANTILE) 125 0.997 0.199 0.035 2.848 0.138 0.546 UPPER HINGE (75TH QUANTILE) 148 1.000 0.258 0.672 3.609 0.159 0.697 MAXIMUM VALUE 156 1.033 0.440 2.793 12.825 0.182 0.864 |------------------------ 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 1.000 0.162 -0.110 2.626 0.137 0.434 2 730012 1831 1983 153 0.997 0.196 0.091 2.799 0.146 0.577 3 730021 1845 1983 139 0.995 0.214 0.151 2.770 0.181 0.467 4 730022 1848 1983 136 0.995 0.202 0.527 4.011 0.174 0.404 5 730031 1846 1983 138 0.998 0.147 -0.274 2.399 0.137 0.369 6 730032 1858 1983 126 0.998 0.155 -0.536 4.358 0.134 0.469 7 730041 1859 1983 125 0.997 0.202 -0.141 3.490 0.149 0.579 8 730042 1858 1983 126 0.998 0.192 0.157 2.962 0.168 0.396 9 730061 1842 1983 142 0.997 0.199 -0.115 3.464 0.173 0.468 10 730062 1863 1983 121 0.997 0.197 -0.682 4.608 0.146 0.572 11 730071 1831 1983 153 0.999 0.207 0.135 3.176 0.160 0.557 12 730072 1830 1919 90 0.999 0.174 0.285 2.888 0.160 0.341 13 730081 1830 1983 154 0.998 0.180 0.390 3.676 0.147 0.485 14 730082 1828 1983 156 0.996 0.194 0.782 3.660 0.144 0.527 15 730091 1845 1965 121 0.998 0.178 0.372 2.784 0.138 0.476 16 730092 1845 1983 139 0.995 0.185 0.434 2.970 0.139 0.591 17 730101 1836 1983 148 0.986 0.221 0.149 2.572 0.139 0.736 18 730102 1837 1983 147 0.992 0.199 0.086 2.684 0.134 0.685 19 730111 1840 1958 119 0.997 0.130 0.445 3.453 0.124 0.266 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 730112 1840 1983 144 0.999 0.158 0.018 2.901 0.139 0.406 21 730121 1833 1983 151 0.990 0.261 0.161 4.795 0.153 0.718 22 730122 1832 1945 114 0.999 0.191 1.151 6.498 0.149 0.511 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 136 0.996 0.188 0.158 3.434 0.149 0.502 STANDARD DEVIATION 16 0.003 0.028 0.404 0.959 0.015 0.120 MEDIAN (50TH QUANTILE) 139 0.997 0.193 0.150 3.073 0.146 0.480 INTERQUARTILE RANGE 23 0.003 0.028 0.500 0.892 0.022 0.171 MINIMUM VALUE 90 0.986 0.130 -0.682 2.399 0.124 0.266 LOWER HINGE (25TH QUANTILE) 125 0.995 0.174 -0.110 2.784 0.138 0.406 UPPER HINGE (75TH QUANTILE) 148 0.998 0.202 0.390 3.676 0.160 0.577 MAXIMUM VALUE 156 1.000 0.261 1.151 6.498 0.181 0.736 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.425 0.124 0.008 0.071 3.755 0.081 0.863 MINIMUM CORRELATION: 0.081 SERIES 730062 AND 730091 103 YEARS MAXIMUM CORRELATION: 0.863 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 0.436 0.396 0.506 0.507 SDEV 0.178 0.172 0.138 0.163 SERR 0.014 0.012 0.010 0.013 EPS 0.944 0.935 0.956 0.953 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 0.999 0.137 0.008 3.193 0.119 0.453 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.022 0.007 0.132 42 114 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.25 0.49 1.00 1.12 1.61 3.77 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 0.450 0.296 0.279 0.212 0.145 0.226 0.101 0.025 -0.060 -0.042 PACF 0.450 0.118 0.137 0.034 -0.005 0.149 -0.094 -0.061 -0.133 0.004 95% C.L. 0.160 0.190 0.201 0.211 0.216 0.219 0.225 0.226 0.226 0.226 |------------------ 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 1 0.214 0.452 |======================= 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 0.456 0.321 0.325 0.187 0.121 0.233 0.092 0.002 -0.060 -0.050 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 0.456 2 0.392 0.142 3 0.367 0.074 0.174 4 0.375 0.077 0.191 -0.047 5 0.374 0.081 0.193 -0.039 -0.020 6 0.378 0.088 0.159 -0.054 -0.085 0.176 7 0.395 0.080 0.154 -0.038 -0.077 0.213 -0.098 8 0.386 0.098 0.147 -0.041 -0.063 0.220 -0.064 -0.087 9 0.374 0.089 0.177 -0.050 -0.069 0.240 -0.050 -0.034 -0.138 10 0.378 0.090 0.179 -0.057 -0.067 0.242 -0.056 -0.037 -0.150 0.031 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) 1071.19 1036.76 1035.58 1032.79 1034.45 1036.38 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1033.49 1033.98 1034.78 1033.77 1035.62 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 0.367 0.074 0.174 R-SQUARED DUE TO POOLED AUTOREGRESSION: 24.77 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 132.93 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.367 0.208 0.278 0.181 0.123 0.107 0.080 0.059 0.046 0.0351 0.026 0.020 0.016 0.012 0.009 0.007 0.005 0.004 0.003 0.0023 0.002 0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.0002 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 0.199 0.482 -0.112 0.020 2 730012 3 0.377 0.563 -0.126 0.253 3 730021 3 0.247 0.420 -0.002 0.175 4 730022 3 0.183 0.423 -0.082 0.119 5 730031 3 0.156 0.327 0.062 0.101 6 730032 3 0.264 0.446 -0.054 0.204 7 730041 3 0.390 0.461 0.114 0.123 8 730042 3 0.219 0.435 -0.132 0.227 9 730061 3 0.265 0.351 0.199 0.068 10 730062 3 0.340 0.532 0.064 0.012 11 730071 3 0.339 0.534 0.082 -0.058 12 730072 3 0.137 0.308 0.083 0.046 13 730081 3 0.262 0.451 0.108 -0.014 14 730082 3 0.294 0.470 0.074 0.060 15 730091 3 0.247 0.436 0.099 -0.001 16 730092 3 0.360 0.514 0.099 0.044 17 730101 3 0.564 0.610 0.094 0.100 18 730102 3 0.489 0.618 0.139 -0.038 19 730111 3 0.097 0.231 0.157 -0.026 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 730112 3 0.201 0.373 0.095 0.019 21 730121 3 0.538 0.637 -0.018 0.171 22 730122 3 0.307 0.598 -0.144 -0.003 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.294 0.465 0.036 0.073 STANDARD DEVIATION 0 0.124 0.107 0.102 0.090 MEDIAN 3 0.264 0.456 0.078 0.053 INTERQUARTILE RANGE 0 0.160 0.113 0.154 0.124 MINIMUM VALUE 3 0.097 0.231 -0.144 -0.058 LOWER HINGE 3 0.201 0.420 -0.054 -0.001 UPPER HINGE 3 0.360 0.534 0.099 0.123 MAXIMUM VALUE 3 0.564 0.637 0.199 0.253 |------------------- 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 0.145 -0.544 3.861 0.164 -0.001 2 730012 1831 1983 153 1.000 0.155 0.216 3.414 0.178 -0.007 3 730021 1845 1983 139 1.000 0.185 0.078 3.331 0.216 -0.002 4 730022 1848 1983 136 1.000 0.183 0.469 3.655 0.211 0.009 5 730031 1846 1983 138 1.000 0.135 -0.250 2.636 0.160 -0.001 6 730032 1858 1983 126 1.000 0.133 -0.355 3.530 0.156 0.020 7 730041 1859 1983 125 1.000 0.160 0.005 3.244 0.173 0.024 8 730042 1858 1983 126 1.000 0.170 0.337 2.983 0.193 0.017 9 730061 1842 1983 142 1.000 0.170 -0.514 3.554 0.198 -0.003 10 730062 1863 1983 121 1.000 0.161 -0.378 4.077 0.186 0.002 11 730071 1831 1983 153 1.000 0.171 0.250 3.123 0.200 -0.009 12 730072 1830 1919 90 1.000 0.162 0.423 3.020 0.183 -0.008 13 730081 1830 1983 154 1.000 0.154 0.337 3.542 0.179 -0.017 14 730082 1828 1983 156 1.000 0.163 1.116 6.500 0.177 0.001 15 730091 1845 1965 121 1.000 0.155 0.854 3.793 0.164 0.002 16 730092 1845 1983 139 1.000 0.148 0.368 3.030 0.175 -0.001 17 730101 1836 1983 148 1.000 0.146 0.209 2.626 0.166 0.000 18 730102 1837 1983 147 1.000 0.142 0.037 2.351 0.163 -0.006 19 730111 1840 1958 119 1.000 0.124 0.408 3.494 0.137 0.001 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 730112 1840 1983 144 1.000 0.142 0.065 2.641 0.161 0.013 21 730121 1833 1983 151 1.000 0.177 0.273 3.918 0.191 0.004 22 730122 1832 1945 114 1.000 0.160 0.756 4.874 0.178 -0.010 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 136 1.000 0.156 0.189 3.509 0.178 0.001 STANDARD DEVIATION 16 0.000 0.016 0.426 0.877 0.019 0.010 MEDIAN (50TH QUANTILE) 139 1.000 0.157 0.233 3.454 0.177 -0.001 INTERQUARTILE RANGE 23 0.000 0.025 0.403 0.772 0.027 0.010 MINIMUM VALUE 90 1.000 0.124 -0.544 2.351 0.137 -0.017 LOWER HINGE (25TH QUANTILE) 125 1.000 0.145 0.005 3.020 0.164 -0.006 UPPER HINGE (75TH QUANTILE) 148 1.000 0.170 0.408 3.793 0.191 0.004 MAXIMUM VALUE 156 1.000 0.185 1.116 6.500 0.216 0.024 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.466 0.095 0.006 0.591 3.871 0.245 0.784 MINIMUM CORRELATION: 0.245 SERIES 730071 AND 730082 153 YEARS MAXIMUM CORRELATION: 0.784 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 0.537 0.490 0.500 0.481 SDEV 0.121 0.129 0.138 0.125 SERR 0.010 0.009 0.010 0.010 EPS 0.962 0.954 0.955 0.948 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 1.000 0.122 0.223 4.131 0.144 -0.062 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.101 0.031 0.080 55 101 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.20 0.43 1.00 1.05 1.48 3.12 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.00 0.86 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 -0.062 -0.022 0.027 0.025 -0.093 0.166 0.003 -0.008 -0.114 -0.004 PACF -0.062 -0.026 0.024 0.028 -0.089 0.157 0.016 0.004 -0.122 -0.033 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 0.002 -0.006 0.026 -0.079 0.165 0.008 -0.011 -0.119 -0.007 PACF -0.001 0.002 -0.006 0.026 -0.079 0.166 0.006 -0.013 -0.117 -0.020 95% C.L. 0.160 0.160 0.160 0.160 0.160 0.161 0.166 0.166 0.166 0.168 |----------------- 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 0.001 -0.001 0.003 -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 1828 1983 156 1.002 0.142 0.176 3.667 0.122 0.468 |------------ 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 0.465 0.327 0.338 0.239 0.137 0.219 0.108 0.031 -0.048 -0.021 PACF 0.465 0.142 0.185 0.006 -0.051 0.138 -0.081 -0.054 -0.138 0.026 95% C.L. 0.160 0.192 0.205 0.219 0.226 0.228 0.233 0.235 0.235 0.235 |------------------- 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 0.263 0.374 0.059 0.198 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.26 MINUTES