RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM056W.rwl.conv LOG FILE PROCESSED: GERM056W.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 20 10 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: 055 1 Sirnitz NE (D), EU-Pr. WIDTH_RING ABAL - 055 2 Germany silver fir, European fir 940 4747-745 1841 1995 - 055 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 3 055025 MISSING VALUES FOUND: 2 IN 1 GAPS / 1979 1980 / -------------------------------------------------------------------- 6 055033 MISSING VALUES FOUND: 2 IN 1 GAPS / 1920 1921 / -------------------------------------------------------------------- 9 055161 MISSING VALUES FOUND: 7 IN 1 GAPS / 1857 1863 / -------------------------------------------------------------------- 12 055167 MISSING VALUES FOUND: 2 IN 1 GAPS / 1936 1937 / -------------------------------------------------------------------- 13 055171 MISSING VALUES FOUND: 2 IN 1 GAPS / 1937 1938 / -------------------------------------------------------------------- 15 055175 MISSING VALUES FOUND: 2 IN 1 GAPS / 1913 1914 / -------------------------------------------------------------------- 19 055215 MISSING VALUES FOUND: 4 IN 1 GAPS / 1941 1944 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 055021 1889 1995 107 2.349 1.075 1.311 4.513 0.185 0.809 2 055023 1865 1995 131 2.483 1.432 1.178 3.660 0.165 0.954 3 055025 1867 1995 129 2.857 1.696 1.194 3.957 0.186 0.928 4 055027 1881 1995 115 2.339 1.519 1.506 4.219 0.171 0.917 5 055031 1869 1995 127 2.677 1.057 -0.342 2.590 0.160 0.906 6 055033 1869 1995 127 2.399 1.221 0.480 2.793 0.178 0.925 7 055035 1869 1995 127 2.584 1.313 -0.062 2.276 0.164 0.924 8 055037 1869 1991 123 3.399 1.077 -0.441 2.691 0.156 0.830 9 055161 1848 1995 148 2.681 0.990 1.124 5.041 0.192 0.755 10 055163 1848 1995 148 1.979 0.878 0.600 3.263 0.178 0.870 11 055165 1855 1995 141 2.292 0.885 0.596 3.197 0.196 0.796 12 055167 1848 1995 148 2.619 0.893 0.668 3.388 0.180 0.776 13 055171 1842 1995 154 2.419 0.991 0.294 2.788 0.202 0.817 14 055173 1848 1995 148 1.837 0.946 1.500 8.835 0.187 0.859 15 055175 1841 1995 155 1.978 0.833 0.238 2.479 0.212 0.797 16 055177 1841 1995 155 1.851 0.868 0.905 3.391 0.187 0.862 17 055211 1875 1995 121 2.779 1.261 0.688 3.838 0.213 0.801 18 055213 1875 1995 121 2.567 1.573 1.858 8.015 0.235 0.851 19 055215 1875 1995 121 2.606 1.032 0.378 2.926 0.198 0.825 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 055217 1875 1995 121 2.455 1.133 1.438 6.200 0.202 0.842 NUMBER OF SERIES READ IN: 20 FROM 1841 TO 1995 155 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 132 2.457 1.134 0.756 4.003 0.187 0.852 STANDARD DEVIATION 14 0.370 0.256 0.637 1.790 0.020 0.058 MEDIAN (50TH QUANTILE) 127 2.469 1.066 0.678 3.389 0.186 0.846 INTERQUARTILE RANGE 26 0.333 0.367 0.917 1.575 0.026 0.106 MINIMUM VALUE 107 1.837 0.833 -0.441 2.276 0.156 0.755 LOWER HINGE (25TH QUANTILE) 121 2.315 0.920 0.336 2.790 0.174 0.805 UPPER HINGE (75TH QUANTILE) 147 2.648 1.287 1.253 4.366 0.200 0.911 MAXIMUM VALUE 155 3.399 1.696 1.858 8.835 0.235 0.954 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.266 0.264 0.019 0.056 2.649 -0.372 0.907 MINIMUM CORRELATION: -0.372 SERIES 055025 AND 055161 129 YEARS MAXIMUM CORRELATION: 0.907 SERIES 055033 AND 055035 127 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 80.46 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1851. 1870. 1880. 1890. 1900. 1910. 1920. 1930. 1940. 1950. CORR 1. 28. 91. 153. 190. 190. 190. 190. 190. 190. RBAR 0.928 0.812 0.545 0.534 0.323 0.358 0.466 0.494 0.557 0.408 SDEV 0.000 0.102 0.289 0.301 0.396 0.330 0.360 0.340 0.311 0.316 SERR 0.000 0.019 0.030 0.024 0.029 0.024 0.026 0.025 0.023 0.023 EPS 0.987 0.982 0.954 0.957 0.905 0.918 0.946 0.951 0.962 0.932 NSS 5.8 12.6 17.5 19.5 20.0 20.0 20.0 20.0 20.0 20.0 YEAR 1960. 1970. 1980. CORR 190. 190. 190. RBAR 0.316 0.408 0.418 SDEV 0.338 0.516 0.349 SERR 0.024 0.037 0.025 EPS 0.902 0.932 0.935 NSS 20.0 20.0 20.0 |======================== RAW DATA CHRONOLOGY STATISTICS ======================| |----------------- ROBUST MEAN RAW DATA CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1841 1995 155 2.282 0.633 -0.141 2.961 0.152 0.778 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.461 0.282 0.259 46 109 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.35 0.76 1.00 1.11 1.87 8.07 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.66 0.85 0.93 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 128. 27. 107. 121. 148. 155. |----------- 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 0.773 0.655 0.526 0.429 0.336 0.243 0.161 0.124 0.096 0.084 PACF 0.773 0.142 -0.047 -0.001 -0.028 -0.062 -0.041 0.055 0.024 0.023 95% C.L. 0.161 0.238 0.281 0.305 0.320 0.329 0.334 0.336 0.337 0.338 |------------------ 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 0.639 0.677 0.147 |================== 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 055021 1 2.34135509 0.08215919 0.00000000 2.09319353 2 055023 1 3.76140857 0.03716427 0.00000000 1.73087537 3 055025 1 4.15757179 0.04437727 0.00000000 2.14867997 4 055027 1 6.07358408 0.05058752 0.00000000 1.32409346 5 055031 3 0.00000000 0.00000000 -0.02058352 3.99466825 6 055033 3 0.00000000 0.00000000 -0.02348906 3.89998245 7 055035 3 0.00000000 0.00000000 -0.02691789 4.30707550 8 055037 3 0.00000000 0.00000000 -0.01326766 4.22145653 9 055161 3 0.00000000 0.00000000 0.00433274 2.31347895 10 055163 3 0.00000000 0.00000000 -0.01096866 2.79621887 11 055165 3 0.00000000 0.00000000 -0.00261557 2.47754908 12 055167 3 0.00000000 0.00000000 0.00467048 2.28132606 13 055171 3 0.00000000 0.00000000 0.00935539 1.68787110 14 055173 3 0.00000000 0.00000000 0.00032219 1.81336188 15 055175 3 0.00000000 0.00000000 -0.00442249 2.34219313 16 055177 1 1.86092758 0.00523634 0.00000000 0.57962298 17 055211 3 0.00000000 0.00000000 0.00957153 2.19497943 18 055213 3 0.00000000 0.00000000 0.00875396 2.03311563 19 055215 3 0.00000000 0.00000000 0.00315155 2.40625978 SERIES IDENT OPTION A B C D 20 055217 3 0.00000000 0.00000000 0.00237143 2.31038427 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 055021 1889 1995 107 1.000 0.431 1.997 8.145 0.182 0.782 2 055023 1865 1995 131 1.000 0.408 -0.027 2.119 0.165 0.864 3 055025 1867 1995 129 0.998 0.520 1.778 6.640 0.188 0.879 4 055027 1881 1995 115 1.001 0.297 0.635 3.727 0.169 0.711 5 055031 1869 1995 127 0.997 0.317 -0.534 3.084 0.158 0.786 6 055033 1869 1995 127 0.993 0.373 0.689 3.743 0.177 0.808 7 055035 1869 1995 127 0.975 0.371 0.195 2.887 0.164 0.810 8 055037 1869 1991 123 0.998 0.305 0.139 3.211 0.155 0.797 9 055161 1848 1995 148 1.000 0.361 1.133 5.425 0.191 0.736 10 055163 1848 1995 148 0.994 0.383 1.184 5.339 0.178 0.809 11 055165 1855 1995 141 1.000 0.393 0.862 3.893 0.195 0.790 12 055167 1848 1995 148 1.000 0.323 0.353 2.729 0.176 0.756 13 055171 1842 1995 154 0.998 0.368 0.137 2.679 0.199 0.787 14 055173 1848 1995 148 1.000 0.512 1.436 8.530 0.186 0.853 15 055175 1841 1995 155 0.999 0.429 0.596 3.167 0.210 0.773 16 055177 1841 1995 155 1.000 0.479 1.860 7.431 0.185 0.834 17 055211 1875 1995 121 1.000 0.402 0.015 3.268 0.211 0.777 18 055213 1875 1995 121 1.002 0.541 1.016 5.422 0.233 0.831 19 055215 1875 1995 121 1.000 0.386 0.323 2.983 0.197 0.812 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 055217 1875 1995 121 1.000 0.450 1.170 5.179 0.201 0.837 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 133 0.998 0.403 0.748 4.480 0.186 0.801 STANDARD DEVIATION 14 0.006 0.071 0.694 1.934 0.020 0.042 MEDIAN (50TH QUANTILE) 128 1.000 0.390 0.662 3.735 0.185 0.802 INTERQUARTILE RANGE 27 0.002 0.076 1.010 2.390 0.026 0.053 MINIMUM VALUE 107 0.975 0.297 -0.534 2.119 0.155 0.711 LOWER HINGE (25TH QUANTILE) 121 0.998 0.365 0.167 3.034 0.172 0.779 UPPER HINGE (75TH QUANTILE) 148 1.000 0.441 1.177 5.423 0.198 0.833 MAXIMUM VALUE 155 1.002 0.541 1.997 8.530 0.233 0.879 |------------------------ 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 055021 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 055023 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 055025 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 055027 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 055031 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 055033 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 055035 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 055037 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 055161 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 055163 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 055165 -67 94 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 055167 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 055171 -67 103 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 055173 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 055175 -67 103 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 055177 -67 103 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 055211 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 055213 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 055215 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 055217 -67 81 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 055021 1889 1995 107 0.991 0.240 -0.106 4.116 0.180 0.523 2 055023 1865 1995 131 0.982 0.313 -0.045 2.343 0.163 0.785 3 055025 1867 1995 129 0.987 0.280 0.661 3.838 0.186 0.632 4 055027 1881 1995 115 0.993 0.231 0.332 3.299 0.167 0.593 5 055031 1869 1995 127 0.996 0.309 -0.262 3.276 0.158 0.780 6 055033 1869 1995 127 0.990 0.331 0.380 3.022 0.176 0.764 7 055035 1869 1995 127 0.991 0.346 1.439 8.877 0.163 0.691 8 055037 1869 1991 123 0.996 0.265 0.015 3.177 0.154 0.750 9 055161 1848 1995 148 0.993 0.316 0.941 4.658 0.190 0.668 10 055163 1848 1995 148 0.996 0.344 0.805 3.994 0.178 0.755 11 055165 1855 1995 141 0.997 0.380 0.879 4.030 0.195 0.771 12 055167 1848 1995 148 0.996 0.306 0.560 3.408 0.176 0.732 13 055171 1842 1995 154 0.996 0.347 0.142 2.760 0.199 0.753 14 055173 1848 1995 148 0.979 0.434 1.394 8.707 0.186 0.807 15 055175 1841 1995 155 0.979 0.328 0.390 3.439 0.210 0.656 16 055177 1841 1995 155 0.986 0.341 0.538 3.314 0.185 0.742 17 055211 1875 1995 121 0.992 0.384 -0.060 3.348 0.210 0.768 18 055213 1875 1995 121 0.983 0.457 0.247 3.681 0.232 0.794 19 055215 1875 1995 121 0.992 0.339 0.148 3.554 0.197 0.763 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 055217 1875 1995 121 0.991 0.380 0.239 2.965 0.200 0.820 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 133 0.990 0.334 0.432 3.990 0.185 0.728 STANDARD DEVIATION 14 0.006 0.057 0.475 1.721 0.020 0.077 MEDIAN (50TH QUANTILE) 128 0.992 0.335 0.356 3.424 0.185 0.754 INTERQUARTILE RANGE 27 0.009 0.055 0.655 0.785 0.026 0.096 MINIMUM VALUE 107 0.979 0.231 -0.262 2.343 0.154 0.523 LOWER HINGE (25TH QUANTILE) 121 0.986 0.308 0.078 3.227 0.172 0.680 UPPER HINGE (75TH QUANTILE) 148 0.996 0.363 0.733 4.012 0.198 0.776 MAXIMUM VALUE 155 0.997 0.457 1.439 8.877 0.232 0.820 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.359 0.188 0.014 -0.160 2.811 -0.175 0.797 MINIMUM CORRELATION: -0.175 SERIES 055161 AND 055213 121 YEARS MAXIMUM CORRELATION: 0.797 SERIES 055031 AND 055037 123 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 80.46 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1851. 1870. 1880. 1890. 1900. 1910. 1920. 1930. 1940. 1950. CORR 1. 28. 91. 153. 190. 190. 190. 190. 190. 190. RBAR 0.913 0.811 0.512 0.591 0.382 0.347 0.486 0.517 0.548 0.442 SDEV 0.000 0.088 0.327 0.258 0.314 0.321 0.322 0.345 0.271 0.286 SERR 0.000 0.017 0.034 0.021 0.023 0.023 0.023 0.025 0.020 0.021 EPS 0.984 0.982 0.948 0.966 0.925 0.914 0.950 0.955 0.960 0.941 NSS 5.8 12.6 17.5 19.5 20.0 20.0 20.0 20.0 20.0 20.0 YEAR 1960. 1970. 1980. CORR 190. 190. 190. RBAR 0.331 0.480 0.454 SDEV 0.327 0.440 0.322 SERR 0.024 0.032 0.023 EPS 0.908 0.949 0.943 NSS 20.0 20.0 20.0 |======================== STANDARD CHRONOLOGY STATISTICS ======================| *** VARIANCE STABILIZED WITH BRIFFA RBAR-WEIGHTED METHOD *** |----------------- ROBUST MEAN STANDARD CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1841 1995 155 0.975 0.231 -0.294 2.886 0.152 0.687 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.272 0.109 0.132 49 106 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.26 0.55 1.00 1.13 1.68 8.82 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.71 0.86 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 0.683 0.545 0.389 0.264 0.133 -0.003 -0.132 -0.164 -0.194 -0.224 PACF 0.683 0.148 -0.057 -0.049 -0.091 -0.129 -0.132 0.039 -0.005 -0.063 95% C.L. 0.161 0.223 0.255 0.270 0.277 0.278 0.278 0.280 0.283 0.286 |------------------ 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 0.497 0.591 0.150 |======================= 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 0.672 0.512 0.352 0.244 0.102 -0.039 -0.168 -0.192 -0.222 -0.273 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 0.672 2 0.598 0.110 3 0.604 0.141 -0.052 4 0.603 0.143 -0.046 -0.011 5 0.602 0.137 -0.029 0.061 -0.120 6 0.585 0.146 -0.033 0.081 -0.035 -0.141 7 0.567 0.141 -0.022 0.076 -0.016 -0.064 -0.131 8 0.572 0.144 -0.021 0.073 -0.015 -0.069 -0.152 0.037 9 0.573 0.139 -0.023 0.073 -0.013 -0.070 -0.148 0.054 -0.030 10 0.569 0.145 -0.040 0.065 -0.014 -0.062 -0.150 0.070 0.034 -0.112 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) 1196.20 1105.06 1105.18 1106.76 1108.74 1108.51 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1107.40 1106.72 1108.51 1110.37 1110.42 SELECTED AUTOREGRESSION ORDER: 1 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 0.672 R-SQUARED DUE TO POOLED AUTOREGRESSION: 45.17 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 182.38 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.672 0.452 0.304 0.204 0.137 0.092 0.062 0.042 0.028 0.0188 0.013 0.008 0.006 0.004 0.003 0.002 0.001 0.001 0.001 0.0004 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 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 055021 1 0.301 0.547 2 055023 1 0.645 0.799 3 055025 1 0.421 0.648 4 055027 1 0.364 0.599 5 055031 1 0.627 0.790 6 055033 1 0.605 0.778 7 055035 1 0.611 0.780 8 055037 1 0.582 0.758 9 055161 1 0.451 0.669 10 055163 1 0.585 0.762 11 055165 1 0.607 0.779 12 055167 1 0.540 0.734 13 055171 1 0.569 0.753 14 055173 1 0.668 0.815 15 055175 1 0.449 0.668 16 055177 1 0.576 0.757 17 055211 1 0.598 0.772 18 055213 1 0.638 0.797 19 055215 1 0.585 0.764 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 055217 1 0.690 0.831 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.556 0.740 STANDARD DEVIATION 0 0.104 0.075 MEDIAN 1 0.585 0.763 INTERQUARTILE RANGE 0 0.124 0.083 MINIMUM VALUE 1 0.301 0.547 LOWER HINGE 1 0.495 0.702 UPPER HINGE 1 0.619 0.785 MAXIMUM VALUE 1 0.690 0.831 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 055021 1889 1995 107 1.000 0.199 0.393 3.852 0.218 0.000 2 055023 1865 1995 131 1.000 0.186 0.093 3.559 0.220 -0.119 3 055025 1867 1995 129 1.000 0.211 0.623 4.127 0.235 -0.030 4 055027 1881 1995 115 1.000 0.185 0.248 3.528 0.216 -0.049 5 055031 1869 1995 127 1.000 0.189 0.295 3.960 0.208 -0.065 6 055033 1869 1995 127 1.000 0.208 0.290 3.507 0.235 0.024 7 055035 1869 1995 127 1.000 0.216 1.276 6.355 0.204 0.141 8 055037 1869 1991 123 1.000 0.172 0.301 3.667 0.191 0.091 9 055161 1848 1995 148 1.000 0.234 0.513 5.026 0.244 -0.046 10 055163 1848 1995 148 1.000 0.223 0.327 4.258 0.238 0.078 11 055165 1855 1995 141 1.000 0.238 0.654 4.670 0.256 -0.006 12 055167 1848 1995 148 1.000 0.208 -0.219 4.109 0.235 0.028 13 055171 1842 1995 154 1.000 0.228 0.527 3.353 0.258 -0.054 14 055173 1848 1995 148 1.000 0.248 0.492 7.095 0.256 0.072 15 055175 1841 1995 155 1.000 0.243 0.457 4.756 0.275 -0.047 16 055177 1841 1995 155 1.000 0.221 0.553 4.504 0.248 -0.072 17 055211 1875 1995 121 1.000 0.244 -0.169 3.379 0.281 -0.040 18 055213 1875 1995 121 1.000 0.276 0.076 3.552 0.279 0.077 19 055215 1875 1995 121 1.000 0.219 0.010 4.419 0.245 -0.043 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 055217 1875 1995 121 1.000 0.211 0.134 3.265 0.251 -0.010 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 133 1.000 0.218 0.343 4.247 0.240 -0.003 STANDARD DEVIATION 14 0.000 0.025 0.330 0.996 0.025 0.067 MEDIAN (50TH QUANTILE) 128 1.000 0.217 0.314 4.034 0.241 -0.020 INTERQUARTILE RANGE 27 0.000 0.033 0.407 1.046 0.037 0.098 MINIMUM VALUE 107 1.000 0.172 -0.219 3.265 0.191 -0.119 LOWER HINGE (25TH QUANTILE) 121 1.000 0.203 0.113 3.540 0.219 -0.048 UPPER HINGE (75TH QUANTILE) 148 1.000 0.236 0.520 4.587 0.256 0.050 MAXIMUM VALUE 155 1.000 0.276 1.276 7.095 0.281 0.141 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.466 0.111 0.008 0.501 3.115 0.204 0.748 MINIMUM CORRELATION: 0.204 SERIES 055161 AND 055213 121 YEARS MAXIMUM CORRELATION: 0.748 SERIES 055035 AND 055037 123 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 80.46 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1851. 1870. 1880. 1890. 1900. 1910. 1920. 1930. 1940. 1950. CORR 1. 28. 91. 153. 190. 190. 190. 190. 190. 190. RBAR 0.744 0.711 0.424 0.484 0.398 0.397 0.553 0.534 0.561 0.637 SDEV 0.000 0.120 0.249 0.231 0.234 0.269 0.210 0.228 0.183 0.185 SERR 0.000 0.023 0.026 0.019 0.017 0.020 0.015 0.017 0.013 0.013 EPS 0.944 0.969 0.928 0.948 0.930 0.929 0.961 0.958 0.962 0.972 NSS 5.8 12.6 17.5 19.5 20.0 20.0 20.0 20.0 20.0 20.0 YEAR 1960. 1970. 1980. CORR 190. 190. 190. RBAR 0.622 0.528 0.477 SDEV 0.169 0.150 0.197 SERR 0.012 0.011 0.014 EPS 0.971 0.957 0.948 NSS 20.0 20.0 20.0 |======================== RESIDUAL CHRONOLOGY STATISTICS ======================| *** VARIANCE STABILIZED WITH BRIFFA RBAR-WEIGHTED METHOD *** |----------------- ROBUST MEAN RESIDUAL CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1841 1995 155 0.996 0.159 -0.108 3.598 0.191 -0.134 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.261 0.090 0.049 64 91 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.22 0.66 1.01 1.05 1.71 13.51 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.08 0.66 0.86 0.94 1.00 |----------- RESIDUAL CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF -0.133 0.090 0.016 0.055 0.066 -0.025 -0.143 0.005 -0.051 -0.049 PACF -0.133 0.073 0.037 0.056 0.078 -0.017 -0.169 -0.043 -0.039 -0.053 95% C.L. 0.161 0.163 0.165 0.165 0.165 0.166 0.166 0.169 0.169 0.170 |------------------ RESIDUAL CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.024 -0.135 |---------- 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 0.011 0.077 0.036 0.069 0.073 -0.036 -0.151 -0.021 -0.060 -0.069 PACF 0.011 0.077 0.035 0.063 0.067 -0.049 -0.168 -0.025 -0.044 -0.056 95% C.L. 0.161 0.161 0.162 0.162 0.163 0.163 0.164 0.167 0.167 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 1 0.006 0.011 |========================= 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 1841 1995 155 0.992 0.225 -0.071 2.971 0.139 0.715 |------------ 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 0.710 0.526 0.373 0.254 0.131 -0.017 -0.138 -0.167 -0.201 -0.230 PACF 0.710 0.044 -0.032 -0.024 -0.085 -0.156 -0.104 0.048 -0.050 -0.055 95% C.L. 0.161 0.228 0.257 0.271 0.277 0.278 0.278 0.280 0.283 0.286 |------------------- 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 1 0.516 0.718 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.32 MINUTES