RUN: fix002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: NM569I.rwl.conv LOG FILE PROCESSED: NM569I.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 DENSITY_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 2.944 0.201 0.534 4.128 0.044 0.606 2 730012 1831 1983 153 2.961 0.199 0.709 3.259 0.045 0.604 3 730021 1845 1983 139 2.996 0.355 1.545 6.818 0.054 0.723 4 730022 1848 1983 136 2.889 0.242 0.471 2.969 0.049 0.696 5 730031 1846 1983 138 2.882 0.237 0.454 3.958 0.049 0.678 6 730032 1858 1983 126 2.751 0.181 0.091 2.978 0.044 0.624 7 730041 1859 1983 125 3.339 0.195 0.749 3.630 0.035 0.710 8 730042 1858 1983 126 3.351 0.268 1.592 7.976 0.041 0.707 9 730061 1842 1983 142 3.277 0.192 0.836 3.977 0.048 0.456 10 730062 1863 1983 121 3.293 0.247 1.517 6.642 0.051 0.600 11 730071 1831 1983 153 3.168 0.234 0.745 6.987 0.048 0.610 12 730072 1830 1919 90 3.263 0.345 1.699 6.354 0.053 0.646 13 730081 1830 1983 154 3.509 0.180 1.554 10.248 0.040 0.338 14 730082 1828 1983 156 3.540 0.179 0.483 3.595 0.042 0.439 15 730091 1845 1965 121 3.497 0.167 -0.073 3.082 0.043 0.289 16 730092 1845 1983 139 3.531 0.168 0.265 3.117 0.043 0.332 17 730101 1836 1983 148 3.593 0.197 0.482 3.020 0.033 0.716 18 730102 1837 1983 147 3.645 0.233 1.584 8.145 0.035 0.738 19 730111 1840 1958 119 3.254 0.190 -0.128 3.400 0.038 0.617 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 730112 1840 1983 144 3.081 0.205 0.569 3.504 0.052 0.512 21 730121 1833 1983 151 3.549 0.341 3.055 15.920 0.054 0.376 22 730122 1832 1945 114 3.418 0.284 3.910 21.813 0.043 0.420 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 3.260 0.229 1.029 6.160 0.045 0.565 STANDARD DEVIATION 15 0.267 0.057 0.983 4.702 0.006 0.144 MEDIAN (50TH QUANTILE) 139 3.285 0.203 0.727 3.967 0.044 0.608 INTERQUARTILE RANGE 23 0.512 0.057 1.083 3.729 0.009 0.257 MINIMUM VALUE 90 2.751 0.167 -0.128 2.969 0.033 0.289 LOWER HINGE (25TH QUANTILE) 125 2.996 0.190 0.471 3.259 0.041 0.439 UPPER HINGE (75TH QUANTILE) 148 3.509 0.247 1.554 6.987 0.049 0.696 MAXIMUM VALUE 154 3.645 0.355 3.910 21.813 0.054 0.738 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.357 0.181 0.012 -0.333 2.992 -0.194 0.753 MINIMUM CORRELATION: -0.194 SERIES 730041 AND 730071 125 YEARS MAXIMUM CORRELATION: 0.753 SERIES 730072 AND 730122 88 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 0.358 0.322 0.377 0.260 SDEV 0.192 0.226 0.221 0.270 SERR 0.016 0.016 0.016 0.022 EPS 0.923 0.912 0.928 0.873 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 3.295 0.197 2.867 16.542 0.035 0.563 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.147 -0.060 0.525 16 140 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.55 0.95 1.05 1.10 2.05 3.65 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.06 0.00 0.85 0.91 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 0.559 0.676 0.451 0.412 0.303 0.280 0.260 0.292 0.205 0.230 PACF 0.559 0.528 -0.047 -0.117 -0.024 0.067 0.113 0.143 -0.125 -0.068 95% C.L. 0.160 0.204 0.255 0.275 0.290 0.298 0.305 0.311 0.318 0.321 |------------------ 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 0.521 0.262 0.540 |================== 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 0.00199010 2.79579139 2 730012 3 0.00000000 0.00000000 0.00061387 2.91364717 3 730021 3 0.00000000 0.00000000 0.00059069 2.95505476 4 730022 3 0.00000000 0.00000000 0.00366419 2.63753271 5 730031 1 0.62584406 0.07814168 0.00000000 2.82659435 6 730032 3 0.00000000 0.00000000 0.00188529 2.63083935 7 730041 3 0.00000000 0.00000000 0.00196289 3.21561813 8 730042 3 0.00000000 0.00000000 0.00276331 3.17595816 9 730061 3 0.00000000 0.00000000 0.00063926 3.23098302 10 730062 1 1.27247012 0.19515985 0.00000000 3.24376392 11 730071 3 0.00000000 0.00000000 -0.00152910 3.28941846 12 730072 1 1.23259652 0.05661063 0.00000000 3.02919221 13 730081 3 0.00000000 0.00000000 0.00032298 3.48386550 14 730082 3 0.00000000 0.00000000 0.00087709 3.45650792 15 730091 1 0.22717555 0.07455597 0.00000000 3.47302127 16 730092 3 0.00000000 0.00000000 0.00097145 3.46264625 17 730101 1 0.44533283 0.04609101 0.00000000 3.52925134 18 730102 1 0.55817091 0.05129783 0.00000000 3.57143879 19 730111 1 0.19785525 0.05985104 0.00000000 3.22718310 SERIES IDENT OPTION A B C D 20 730112 1 0.50488919 0.10745617 0.00000000 3.04999614 21 730121 3 0.00000000 0.00000000 -0.00204301 3.70454049 22 730122 1 1.57711983 0.19768658 0.00000000 3.35425234 |-------------------- 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 0.062 0.324 3.368 0.044 0.517 2 730012 1831 1983 153 1.000 0.067 0.766 3.685 0.045 0.587 3 730021 1845 1983 139 1.000 0.119 1.765 7.745 0.054 0.713 4 730022 1848 1983 136 1.000 0.069 1.313 6.443 0.048 0.510 5 730031 1846 1983 138 1.000 0.072 0.194 2.339 0.049 0.606 6 730032 1858 1983 126 1.000 0.062 0.950 4.731 0.043 0.554 7 730041 1859 1983 125 1.000 0.054 0.648 3.295 0.035 0.663 8 730042 1858 1983 126 1.000 0.073 1.327 7.422 0.040 0.667 9 730061 1842 1983 142 1.000 0.058 0.745 4.015 0.048 0.437 10 730062 1863 1983 121 1.000 0.057 0.173 2.519 0.051 0.379 11 730071 1831 1983 153 1.000 0.071 0.762 5.180 0.049 0.577 12 730072 1830 1919 90 1.000 0.053 0.936 4.913 0.051 -0.003 13 730081 1830 1983 154 1.000 0.051 1.673 11.393 0.039 0.327 14 730082 1828 1983 156 1.000 0.051 0.349 3.216 0.041 0.455 15 730091 1845 1965 121 1.000 0.046 -0.008 3.300 0.043 0.235 16 730092 1845 1983 139 1.000 0.046 0.197 3.046 0.042 0.291 17 730101 1836 1983 148 1.000 0.047 0.350 3.016 0.033 0.617 18 730102 1837 1983 147 1.000 0.053 0.317 4.518 0.035 0.605 19 730111 1840 1958 119 1.000 0.057 0.038 3.424 0.038 0.601 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 730112 1840 1983 144 1.000 0.061 0.610 3.468 0.052 0.433 21 730121 1833 1983 151 1.000 0.091 2.500 12.699 0.053 0.355 22 730122 1832 1945 114 1.000 0.056 3.064 19.627 0.042 0.195 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 136 1.000 0.063 0.863 5.607 0.044 0.469 STANDARD DEVIATION 16 0.000 0.017 0.802 4.152 0.006 0.180 MEDIAN (50TH QUANTILE) 139 1.000 0.057 0.696 3.850 0.044 0.514 INTERQUARTILE RANGE 23 0.000 0.017 0.996 3.149 0.009 0.250 MINIMUM VALUE 90 1.000 0.046 -0.008 2.339 0.033 -0.003 LOWER HINGE (25TH QUANTILE) 125 1.000 0.053 0.317 3.295 0.040 0.355 UPPER HINGE (75TH QUANTILE) 148 1.000 0.069 1.313 6.443 0.049 0.605 MAXIMUM VALUE 156 1.000 0.119 3.064 19.627 0.054 0.713 |------------------------ 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 0.051 0.612 4.174 0.044 0.286 2 730012 1831 1983 153 1.000 0.055 0.455 3.403 0.044 0.404 3 730021 1845 1983 139 0.999 0.070 0.994 6.049 0.054 0.359 4 730022 1848 1983 136 1.000 0.057 0.876 4.486 0.048 0.290 5 730031 1846 1983 138 1.000 0.058 0.453 2.901 0.049 0.378 6 730032 1858 1983 126 1.000 0.048 0.295 3.086 0.044 0.280 7 730041 1859 1983 125 1.000 0.044 0.962 4.899 0.035 0.484 8 730042 1858 1983 126 1.000 0.062 1.874 10.674 0.040 0.538 9 730061 1842 1983 142 1.000 0.053 0.571 3.827 0.048 0.325 10 730062 1863 1983 121 1.000 0.049 0.214 3.211 0.051 0.172 11 730071 1831 1983 153 1.000 0.064 0.683 4.859 0.048 0.480 12 730072 1830 1919 90 1.000 0.051 1.013 4.907 0.051 -0.060 13 730081 1830 1983 154 1.000 0.043 1.432 8.948 0.039 0.159 14 730082 1828 1983 156 1.000 0.049 0.442 3.251 0.041 0.416 15 730091 1845 1965 121 1.000 0.043 0.136 3.820 0.043 0.111 16 730092 1845 1983 139 1.000 0.044 0.285 2.932 0.042 0.229 17 730101 1836 1983 148 1.000 0.039 0.448 3.295 0.033 0.435 18 730102 1837 1983 147 1.000 0.050 0.271 4.862 0.035 0.551 19 730111 1840 1958 119 1.000 0.045 0.308 3.205 0.038 0.375 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 730112 1840 1983 144 1.000 0.058 0.567 3.486 0.052 0.368 21 730121 1833 1983 151 1.000 0.084 2.785 14.670 0.053 0.276 22 730122 1832 1945 114 1.000 0.054 3.123 20.182 0.042 0.137 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 136 1.000 0.053 0.854 5.688 0.044 0.318 STANDARD DEVIATION 16 0.000 0.010 0.799 4.342 0.006 0.151 MEDIAN (50TH QUANTILE) 139 1.000 0.051 0.569 4.001 0.044 0.342 INTERQUARTILE RANGE 23 0.000 0.013 0.685 1.656 0.009 0.188 MINIMUM VALUE 90 0.999 0.039 0.136 2.901 0.033 -0.060 LOWER HINGE (25TH QUANTILE) 125 1.000 0.045 0.308 3.251 0.040 0.229 UPPER HINGE (75TH QUANTILE) 148 1.000 0.058 0.994 4.907 0.049 0.416 MAXIMUM VALUE 156 1.000 0.084 3.123 20.182 0.054 0.551 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.339 0.123 0.008 -0.268 2.878 0.029 0.643 MINIMUM CORRELATION: 0.029 SERIES 730032 AND 730111 101 YEARS MAXIMUM CORRELATION: 0.643 SERIES 730012 AND 730031 138 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 0.396 0.377 0.302 0.253 SDEV 0.160 0.159 0.188 0.203 SERR 0.013 0.011 0.014 0.016 EPS 0.934 0.929 0.901 0.869 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 0.034 0.943 4.726 0.033 0.265 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.364 0.178 -0.137 72 84 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.25 0.55 1.00 1.08 1.63 13.39 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.05 0.00 0.87 0.92 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 0.264 0.315 0.053 0.020 -0.102 -0.084 -0.116 0.018 -0.198 -0.111 PACF 0.264 0.264 -0.090 -0.066 -0.095 -0.032 -0.035 0.097 -0.214 -0.096 95% C.L. 0.160 0.171 0.185 0.186 0.186 0.187 0.188 0.190 0.190 0.195 |------------------ 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 0.143 0.195 0.264 |======================= 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 0.187 0.235 0.017 -0.013 -0.084 -0.040 -0.065 0.125 -0.117 -0.002 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 0.187 2 0.148 0.208 3 0.161 0.217 -0.062 4 0.157 0.230 -0.052 -0.060 5 0.153 0.226 -0.036 -0.049 -0.068 6 0.153 0.226 -0.036 -0.049 -0.068 0.000 7 0.153 0.225 -0.038 -0.050 -0.063 0.004 -0.026 8 0.157 0.224 -0.028 -0.042 -0.057 -0.031 -0.050 0.160 9 0.183 0.216 -0.033 -0.051 -0.063 -0.036 -0.014 0.185 -0.163 10 0.177 0.222 -0.033 -0.053 -0.066 -0.038 -0.015 0.193 -0.156 -0.035 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) 638.04 634.51 629.62 631.03 632.47 633.74 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 635.74 637.64 635.62 633.42 635.23 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 0.148 0.208 R-SQUARED DUE TO POOLED AUTOREGRESSION: 7.65 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 108.29 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.148 0.230 0.065 0.057 0.022 0.015 0.007 0.004 0.002 0.0012 0.001 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 0.0000 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 2 0.107 0.245 0.148 2 730012 2 0.207 0.322 0.215 3 730021 2 0.199 0.264 0.275 4 730022 2 0.181 0.226 0.230 5 730031 2 0.264 0.265 0.313 6 730032 2 0.134 0.215 0.236 7 730041 2 0.257 0.404 0.167 8 730042 2 0.303 0.535 0.029 9 730061 2 0.174 0.237 0.274 10 730062 2 0.056 0.145 0.160 11 730071 2 0.268 0.379 0.214 12 730072 2 0.071 -0.055 0.112 13 730081 2 0.063 0.148 0.177 14 730082 2 0.226 0.361 0.147 15 730091 2 0.081 0.088 0.212 16 730092 2 0.114 0.175 0.238 17 730101 2 0.275 0.298 0.319 18 730102 2 0.330 0.481 0.141 19 730111 2 0.186 0.302 0.196 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 730112 2 0.149 0.367 0.006 21 730121 2 0.106 0.269 0.118 22 730122 2 0.030 0.137 0.021 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.172 0.264 0.179 STANDARD DEVIATION 0 0.087 0.132 0.087 MEDIAN 2 0.178 0.265 0.186 INTERQUARTILE RANGE 0 0.151 0.186 0.095 MINIMUM VALUE 2 0.030 -0.055 0.006 LOWER HINGE 2 0.106 0.175 0.141 UPPER HINGE 2 0.257 0.361 0.236 MAXIMUM VALUE 2 0.330 0.535 0.319 |------------------- 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 0.048 0.603 4.873 0.050 -0.009 2 730012 1831 1983 153 1.000 0.049 0.563 3.787 0.051 0.004 3 730021 1845 1983 139 1.000 0.062 0.750 4.883 0.062 -0.006 4 730022 1848 1983 136 1.000 0.052 1.170 5.530 0.055 -0.053 5 730031 1846 1983 138 1.000 0.051 0.527 3.736 0.057 -0.053 6 730032 1858 1983 126 1.000 0.044 0.357 3.007 0.048 -0.017 7 730041 1859 1983 125 1.000 0.038 0.708 4.362 0.042 0.005 8 730042 1858 1983 126 1.000 0.051 0.397 6.991 0.053 -0.009 9 730061 1842 1983 142 1.000 0.048 0.404 4.035 0.053 -0.001 10 730062 1863 1983 121 1.000 0.048 0.090 3.675 0.055 0.005 11 730071 1831 1983 153 1.000 0.054 0.526 4.766 0.058 -0.005 12 730072 1830 1919 90 1.000 0.051 1.021 4.904 0.048 0.027 13 730081 1830 1983 154 1.000 0.042 1.400 8.575 0.042 -0.012 14 730082 1828 1983 156 1.000 0.044 0.269 3.092 0.050 -0.022 15 730091 1845 1965 121 1.000 0.042 0.209 3.755 0.044 0.034 16 730092 1845 1983 139 1.000 0.042 0.406 3.274 0.047 -0.024 17 730101 1836 1983 148 1.000 0.033 0.203 3.530 0.036 0.012 18 730102 1837 1983 147 1.000 0.040 0.150 3.823 0.043 -0.002 19 730111 1840 1958 119 1.000 0.041 0.565 4.582 0.044 -0.022 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 730112 1840 1983 144 1.000 0.054 0.571 3.629 0.060 0.000 21 730121 1833 1983 151 1.000 0.079 2.980 17.265 0.060 -0.031 22 730122 1832 1945 114 1.000 0.053 3.176 20.802 0.046 0.000 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 136 1.000 0.048 0.775 5.767 0.050 -0.008 STANDARD DEVIATION 16 0.000 0.010 0.813 4.516 0.007 0.021 MEDIAN (50TH QUANTILE) 139 1.000 0.048 0.545 4.198 0.050 -0.006 INTERQUARTILE RANGE 23 0.000 0.011 0.394 1.230 0.011 0.026 MINIMUM VALUE 90 1.000 0.033 0.090 3.007 0.036 -0.053 LOWER HINGE (25TH QUANTILE) 125 1.000 0.042 0.357 3.675 0.044 -0.022 UPPER HINGE (75TH QUANTILE) 148 1.000 0.052 0.750 4.904 0.055 0.004 MAXIMUM VALUE 156 1.000 0.079 3.176 20.802 0.062 0.034 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.380 0.105 0.007 0.050 3.043 0.074 0.735 MINIMUM CORRELATION: 0.074 SERIES 730121 AND 730122 113 YEARS MAXIMUM CORRELATION: 0.735 SERIES 730031 AND 730032 126 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 0.435 0.438 0.344 0.287 SDEV 0.132 0.113 0.156 0.153 SERR 0.011 0.008 0.011 0.012 EPS 0.943 0.944 0.917 0.888 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 0.999 0.032 0.791 4.492 0.036 -0.075 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.368 0.177 -0.141 75 81 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.29 0.48 1.01 1.08 1.56 28.99 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.06 0.00 0.88 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 -0.075 0.106 -0.059 -0.014 -0.096 -0.050 -0.079 0.150 -0.174 -0.029 PACF -0.075 0.101 -0.045 -0.032 -0.090 -0.062 -0.073 0.145 -0.158 -0.102 95% C.L. 0.160 0.161 0.163 0.163 0.163 0.165 0.165 0.166 0.170 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 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 0.005 -0.001 -0.038 -0.031 -0.089 -0.078 -0.046 0.147 -0.165 -0.049 PACF 0.005 -0.001 -0.038 -0.030 -0.089 -0.080 -0.050 0.141 -0.182 -0.065 95% C.L. 0.160 0.160 0.160 0.160 0.161 0.162 0.163 0.163 0.166 0.171 |----------------- 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 0.002 0.005 -0.001 |========================= 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 0.999 0.033 0.995 4.916 0.032 0.172 |------------ 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 0.171 0.210 0.001 -0.013 -0.108 -0.081 -0.099 0.069 -0.175 -0.074 PACF 0.171 0.186 -0.064 -0.046 -0.093 -0.043 -0.044 0.118 -0.198 -0.082 95% C.L. 0.160 0.165 0.171 0.171 0.171 0.173 0.174 0.176 0.176 0.181 |------------------- 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 0.068 0.139 0.187 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.24 MINUTES