RUN: ITAL001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: ITAL005E.rwl.conv LOG FILE PROCESSED: ITAL005E.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: 621 1 Vizzavona, Mt.Renoso WIDTH_EARLY ABAL - 621 2 France silver fir, European fir 1500 4205-912 1678 1980 - 621 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 5 621031 MISSING VALUES FOUND: 1 IN 1 GAPS / 1884 1884 / -------------------------------------------------------------------- 9 621051 MISSING VALUES FOUND: 1 IN 1 GAPS / 1838 1838 / -------------------------------------------------------------------- 13 621071 MISSING VALUES FOUND: 8 IN 1 GAPS / 1883 1890 / -------------------------------------------------------------------- 15 621081 MISSING VALUES FOUND: 3 IN 1 GAPS / 1923 1925 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 621011 1832 1980 149 0.772 0.258 1.567 8.331 0.175 0.714 2 621012 1822 1980 159 0.867 0.343 0.930 3.487 0.172 0.823 3 621021 1811 1980 170 1.199 0.571 0.494 2.103 0.176 0.884 4 621022 1827 1980 154 1.405 0.617 0.902 3.367 0.160 0.873 5 621031 1678 1962 285 0.844 0.351 0.281 2.153 0.193 0.838 6 621032 1778 1980 203 0.815 0.270 0.468 2.677 0.172 0.782 7 621041 1867 1980 114 1.055 0.548 0.867 3.480 0.223 0.867 8 621042 1873 1980 108 1.029 0.379 0.380 2.849 0.201 0.745 9 621051 1776 1974 199 0.948 0.933 1.547 4.898 0.231 0.935 10 621052 1871 1975 105 1.698 0.954 0.716 3.215 0.208 0.851 11 621061 1872 1980 109 1.465 0.380 0.062 2.590 0.175 0.667 12 621062 1870 1980 111 1.390 0.406 -0.023 3.151 0.146 0.790 13 621071 1842 1980 139 1.336 0.626 0.871 3.274 0.176 0.829 14 621072 1789 1980 192 1.223 0.550 0.758 3.212 0.164 0.871 15 621081 1842 1980 139 1.114 0.574 1.884 8.818 0.231 0.653 16 621082 1850 1978 129 1.245 0.476 0.369 3.344 0.176 0.754 17 621091 1760 1980 221 1.040 0.512 0.886 3.299 0.167 0.894 18 621092 1764 1980 217 1.128 0.417 0.923 3.453 0.163 0.800 19 621101 1881 1980 100 0.529 0.426 3.193 15.448 0.256 0.784 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 621102 1891 1980 90 0.691 0.278 1.596 6.058 0.178 0.791 21 621111 1836 1980 145 1.430 0.716 0.327 2.417 0.202 0.859 22 621112 1831 1980 150 1.729 0.557 -0.223 2.475 0.192 0.709 23 621121 1810 1980 171 1.080 0.500 0.319 2.447 0.183 0.841 24 621122 1852 1980 129 1.234 0.465 0.579 2.862 0.210 0.770 25 621131 1797 1980 184 1.257 0.319 -0.341 2.412 0.123 0.824 26 621132 1765 1980 216 0.897 0.195 0.088 3.229 0.158 0.607 NUMBER OF SERIES READ IN: 26 FROM 1678 TO 1980 303 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 157 1.132 0.485 0.747 4.040 0.185 0.798 STANDARD DEVIATION 47 0.295 0.186 0.751 2.873 0.029 0.080 MEDIAN (50TH QUANTILE) 149 1.121 0.471 0.648 3.222 0.176 0.811 INTERQUARTILE RANGE 78 0.440 0.220 0.604 0.890 0.035 0.106 MINIMUM VALUE 90 0.529 0.195 -0.341 2.103 0.123 0.607 LOWER HINGE (25TH QUANTILE) 114 0.897 0.351 0.319 2.590 0.167 0.754 UPPER HINGE (75TH QUANTILE) 192 1.336 0.571 0.923 3.480 0.202 0.859 MAXIMUM VALUE 284 1.729 0.954 3.193 15.448 0.256 0.935 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.397 0.217 0.012 -0.307 2.373 -0.221 0.831 MINIMUM CORRELATION: -0.221 SERIES 621011 AND 621102 90 YEARS MAXIMUM CORRELATION: 0.831 SERIES 621052 AND 621111 105 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 42.51 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1805. 1830. 1855. 1880. 1905. 1930. 1955. CORR 15. 28. 66. 171. 276. 325. 231. RBAR 0.258 0.105 0.297 0.229 0.304 0.370 0.285 SDEV 0.244 0.355 0.258 0.294 0.256 0.267 0.240 SERR 0.063 0.067 0.032 0.023 0.015 0.015 0.016 EPS 0.747 0.603 0.886 0.873 0.918 0.938 0.910 NSS 8.5 13.0 18.4 23.2 25.8 26.0 25.5 |======================== 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 1678 1980 303 1.122 0.271 -0.021 2.643 0.139 0.743 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.288 0.262 0.043 74 229 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.25 0.74 1.00 1.09 1.83 7.78 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.85 0.93 0.00 0.00 0.93 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 150. 78. 90. 114. 192. 285. |----------- 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 0.741 0.640 0.578 0.523 0.482 0.484 0.456 0.460 0.432 0.440 PACF 0.741 0.203 0.115 0.056 0.049 0.121 0.023 0.091 -0.001 0.086 95% C.L. 0.115 0.166 0.196 0.218 0.234 0.246 0.259 0.269 0.279 0.288 |------------------ 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 3 0.588 0.558 0.150 0.119 |================== 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 621011 1 0.86724210 0.07059640 0.00000000 0.69217783 2 621012 3 0.00000000 0.00000000 -0.00531022 1.29217577 3 621021 3 0.00000000 0.00000000 -0.00865478 1.93857217 4 621022 1 1.97708941 0.01643473 0.00000000 0.69212264 5 621031 3 0.00000000 0.00000000 -0.00256581 1.21081018 6 621032 1 0.85654950 0.00609938 0.00000000 0.32492864 7 621041 3 0.00000000 0.00000000 -0.00943667 1.59804690 8 621042 1 0.58475751 0.01689311 0.00000000 0.76226002 9 621051 -67 133 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 621052 3 0.00000000 0.00000000 -0.02620744 3.08651829 11 621061 3 0.00000000 0.00000000 -0.00705996 1.85343528 12 621062 3 0.00000000 0.00000000 -0.00741523 1.80552340 13 621071 1 2.03782463 0.01865023 0.00000000 0.61328709 14 621072 1 1.51801729 0.01076301 0.00000000 0.58504707 15 621081 3 0.00000000 0.00000000 -0.00544296 1.50158298 16 621082 3 0.00000000 0.00000000 -0.00254355 1.41036940 17 621091 3 0.00000000 0.00000000 -0.00527665 1.62597978 18 621092 3 0.00000000 0.00000000 -0.00432281 1.59906685 19 621101 3 0.00000000 0.00000000 -0.00157324 0.60884845 SERIES IDENT OPTION A B C D 20 621102 3 0.00000000 0.00000000 -0.00459143 0.89946568 21 621111 3 0.00000000 0.00000000 -0.01024000 2.17752004 22 621112 1 0.95962185 0.01794064 0.00000000 1.39924192 23 621121 3 0.00000000 0.00000000 -0.00691295 1.67468941 24 621122 3 0.00000000 0.00000000 -0.00836510 1.77799535 25 621131 3 0.00000000 0.00000000 -0.00220135 1.46052742 26 621132 3 0.00000000 0.00000000 0.00027056 0.86731136 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 621011 1832 1980 149 1.000 0.261 0.703 3.347 0.174 0.598 2 621012 1822 1980 159 1.003 0.267 0.626 3.464 0.170 0.677 3 621021 1811 1980 170 0.997 0.309 0.922 4.294 0.175 0.743 4 621022 1827 1980 154 1.001 0.264 0.245 2.693 0.159 0.704 5 621031 1678 1962 285 0.995 0.352 1.175 5.063 0.193 0.758 6 621032 1778 1980 203 1.000 0.263 0.639 3.444 0.171 0.620 7 621041 1867 1980 114 0.997 0.421 0.459 2.481 0.222 0.784 8 621042 1873 1980 108 1.000 0.370 1.075 4.917 0.199 0.741 9 621051 1776 1974 199 1.060 0.579 1.716 6.918 0.231 0.725 10 621052 1871 1975 105 1.016 0.345 1.676 5.846 0.206 0.605 11 621061 1872 1980 109 1.000 0.215 0.057 2.813 0.173 0.482 12 621062 1870 1980 111 0.996 0.239 0.427 4.288 0.144 0.659 13 621071 1842 1980 139 0.999 0.267 0.649 3.292 0.171 0.640 14 621072 1789 1980 192 0.999 0.354 0.929 3.430 0.163 0.825 15 621081 1842 1980 139 0.998 0.441 1.415 6.297 0.229 0.613 16 621082 1850 1978 129 0.999 0.389 0.639 3.638 0.174 0.761 17 621091 1760 1980 221 0.990 0.339 1.570 6.111 0.166 0.801 18 621092 1764 1980 217 1.000 0.265 0.886 4.325 0.162 0.665 19 621101 1881 1980 100 0.998 0.760 2.941 13.782 0.254 0.771 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 621102 1891 1980 90 0.997 0.339 1.663 7.341 0.177 0.704 21 621111 1836 1980 145 0.981 0.396 0.282 2.799 0.201 0.767 22 621112 1831 1980 150 1.000 0.310 0.084 2.825 0.191 0.669 23 621121 1810 1980 171 0.997 0.359 0.989 7.393 0.182 0.665 24 621122 1852 1980 129 0.999 0.280 0.781 3.744 0.208 0.566 25 621131 1797 1980 184 0.999 0.241 -0.043 2.443 0.122 0.797 26 621132 1765 1980 216 1.000 0.217 0.094 3.194 0.157 0.603 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 157 1.001 0.340 0.869 4.622 0.184 0.690 STANDARD DEVIATION 47 0.013 0.118 0.672 2.413 0.029 0.084 MEDIAN (50TH QUANTILE) 149 0.999 0.324 0.742 3.691 0.175 0.691 INTERQUARTILE RANGE 78 0.003 0.106 0.748 2.652 0.034 0.141 MINIMUM VALUE 90 0.981 0.215 -0.043 2.443 0.122 0.482 LOWER HINGE (25TH QUANTILE) 114 0.997 0.264 0.427 3.194 0.166 0.620 UPPER HINGE (75TH QUANTILE) 192 1.000 0.370 1.175 5.846 0.201 0.761 MAXIMUM VALUE 285 1.060 0.760 2.941 13.782 0.254 0.825 |------------------------ 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 621011 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 621012 -67 106 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 621021 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 621022 -67 103 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 621031 -67 190 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 621032 -67 136 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 621041 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 621042 -67 72 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 621051 -67 133 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 621052 -67 70 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 621061 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 621062 -67 74 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 621071 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 621072 -67 128 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 621081 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 621082 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 621091 -67 148 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 621092 -67 145 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 621101 -67 67 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 621102 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 621111 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 621112 -67 100 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 621121 -67 114 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 621122 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 25 621131 -67 123 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 26 621132 -67 144 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 621011 1832 1980 149 0.998 0.239 0.720 3.389 0.174 0.524 2 621012 1822 1980 159 0.999 0.256 0.617 3.585 0.170 0.650 3 621021 1811 1980 170 0.996 0.283 0.572 3.399 0.174 0.695 4 621022 1827 1980 154 0.996 0.229 0.431 2.927 0.158 0.606 5 621031 1678 1962 285 0.994 0.299 0.728 3.633 0.193 0.672 6 621032 1778 1980 203 0.996 0.239 0.674 3.400 0.171 0.554 7 621041 1867 1980 114 0.985 0.368 0.307 2.441 0.221 0.733 8 621042 1873 1980 108 0.997 0.355 0.910 4.415 0.199 0.723 9 621051 1776 1974 199 0.986 0.412 1.023 4.087 0.231 0.715 10 621052 1871 1975 105 0.992 0.270 1.161 4.194 0.206 0.475 11 621061 1872 1980 109 0.999 0.207 0.065 2.962 0.174 0.435 12 621062 1870 1980 111 0.998 0.181 0.681 4.485 0.144 0.445 13 621071 1842 1980 139 0.995 0.230 0.662 3.168 0.171 0.537 14 621072 1789 1980 192 0.990 0.269 0.386 3.047 0.163 0.728 15 621081 1842 1980 139 0.983 0.349 0.933 4.622 0.228 0.517 16 621082 1850 1978 129 0.982 0.236 0.992 4.759 0.173 0.483 17 621091 1760 1980 221 0.994 0.260 0.668 4.380 0.167 0.677 18 621092 1764 1980 217 0.998 0.254 0.835 4.245 0.162 0.636 19 621101 1881 1980 100 0.968 0.563 2.988 14.486 0.251 0.718 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 621102 1891 1980 90 0.992 0.250 1.586 7.010 0.176 0.539 21 621111 1836 1980 145 0.991 0.331 0.612 4.086 0.200 0.634 22 621112 1831 1980 150 0.998 0.304 0.125 2.752 0.191 0.660 23 621121 1810 1980 171 0.991 0.336 1.945 15.132 0.182 0.576 24 621122 1852 1980 129 0.997 0.260 0.632 3.185 0.208 0.484 25 621131 1797 1980 184 0.997 0.185 -0.159 2.612 0.122 0.677 26 621132 1765 1980 216 1.000 0.215 0.130 3.342 0.157 0.599 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 157 0.993 0.284 0.778 4.606 0.183 0.604 STANDARD DEVIATION 47 0.007 0.081 0.636 3.145 0.029 0.095 MEDIAN (50TH QUANTILE) 149 0.995 0.260 0.671 3.609 0.174 0.620 INTERQUARTILE RANGE 78 0.007 0.095 0.502 1.247 0.034 0.153 MINIMUM VALUE 90 0.968 0.181 -0.159 2.441 0.122 0.435 LOWER HINGE (25TH QUANTILE) 114 0.991 0.236 0.431 3.168 0.167 0.524 UPPER HINGE (75TH QUANTILE) 192 0.998 0.331 0.933 4.415 0.200 0.677 MAXIMUM VALUE 285 1.000 0.563 2.988 15.132 0.251 0.733 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.274 0.147 0.008 -0.087 2.943 -0.207 0.624 MINIMUM CORRELATION: -0.207 SERIES 621041 AND 621131 114 YEARS MAXIMUM CORRELATION: 0.624 SERIES 621031 AND 621032 185 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 42.51 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1805. 1830. 1855. 1880. 1905. 1930. 1955. CORR 15. 28. 66. 171. 276. 325. 231. RBAR 0.245 0.148 0.282 0.286 0.295 0.380 0.294 SDEV 0.266 0.323 0.232 0.224 0.230 0.204 0.236 SERR 0.069 0.061 0.029 0.017 0.014 0.011 0.015 EPS 0.733 0.693 0.879 0.903 0.915 0.941 0.914 NSS 8.5 13.0 18.4 23.2 25.8 26.0 25.5 |======================== 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 1678 1980 303 0.997 0.170 0.075 2.869 0.137 0.505 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.050 -0.033 0.194 92 211 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.28 0.86 1.00 1.08 1.94 23.28 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.86 0.92 0.00 0.00 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 0.504 0.285 0.203 0.091 -0.023 -0.004 -0.004 0.062 0.040 0.013 PACF 0.504 0.042 0.059 -0.053 -0.090 0.048 0.001 0.103 -0.036 -0.028 95% C.L. 0.115 0.141 0.148 0.152 0.153 0.153 0.153 0.153 0.153 0.153 |------------------ 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 0.258 0.507 |======================= 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 0.440 0.096 0.041 -0.087 -0.259 -0.238 -0.176 -0.034 -0.028 -0.023 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 0.440 2 0.494 -0.122 3 0.501 -0.151 0.060 4 0.510 -0.174 0.136 -0.151 5 0.480 -0.147 0.101 -0.050 -0.199 6 0.470 -0.149 0.106 -0.057 -0.175 -0.051 7 0.466 -0.162 0.102 -0.049 -0.185 -0.017 -0.071 8 0.473 -0.160 0.120 -0.045 -0.195 -0.002 -0.116 0.098 9 0.483 -0.172 0.120 -0.064 -0.200 0.010 -0.132 0.144 -0.098 10 0.480 -0.167 0.115 -0.063 -0.207 0.008 -0.128 0.138 -0.081 -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) 2314.25 2250.94 2248.43 2249.34 2244.34 2234.07 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 2235.29 2235.77 2234.85 2233.91 2235.54 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 0.494 -0.122 R-SQUARED DUE TO POOLED AUTOREGRESSION: 20.58 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 125.92 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.494 0.122 0.000 -0.015 -0.007 -0.002 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 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 621011 2 0.283 0.552 -0.039 2 621012 2 0.445 0.757 -0.160 3 621021 2 0.499 0.586 0.157 4 621022 2 0.371 0.616 -0.012 5 621031 2 0.478 0.554 0.178 6 621032 2 0.349 0.542 0.023 7 621041 2 0.543 0.677 0.078 8 621042 2 0.562 0.686 0.072 9 621051 2 0.546 0.550 0.234 10 621052 2 0.242 0.532 -0.101 11 621061 2 0.223 0.406 0.082 12 621062 2 0.205 0.447 -0.001 13 621071 2 0.293 0.549 -0.016 14 621072 2 0.551 0.708 0.033 15 621081 2 0.336 0.373 0.289 16 621082 2 0.265 0.471 0.048 17 621091 2 0.470 0.599 0.119 18 621092 2 0.411 0.636 0.008 19 621101 2 0.546 0.764 -0.063 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 621102 2 0.310 0.619 -0.141 21 621111 2 0.427 0.606 0.067 22 621112 2 0.451 0.668 0.002 23 621121 2 0.372 0.471 0.188 24 621122 2 0.252 0.538 -0.103 25 621131 2 0.483 0.597 0.128 26 621132 2 0.365 0.560 0.068 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.395 0.579 0.044 STANDARD DEVIATION 0 0.114 0.098 0.112 MEDIAN 2 0.392 0.573 0.041 INTERQUARTILE RANGE 0 0.190 0.098 0.135 MINIMUM VALUE 2 0.205 0.373 -0.160 LOWER HINGE 2 0.293 0.538 -0.016 UPPER HINGE 2 0.483 0.636 0.119 MAXIMUM VALUE 2 0.562 0.764 0.289 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 621011 1832 1980 149 1.000 0.202 0.706 4.485 0.218 0.004 2 621012 1822 1980 159 1.000 0.191 0.434 3.752 0.219 -0.016 3 621021 1811 1980 170 1.000 0.201 0.108 4.265 0.223 -0.012 4 621022 1827 1980 154 1.000 0.182 0.717 3.439 0.196 0.001 5 621031 1678 1962 285 1.000 0.217 0.506 3.642 0.238 -0.020 6 621032 1778 1980 203 1.000 0.198 0.622 4.041 0.209 -0.005 7 621041 1867 1980 114 1.000 0.248 0.184 3.374 0.280 0.002 8 621042 1873 1980 108 1.000 0.239 0.671 4.160 0.264 0.026 9 621051 1776 1974 199 1.000 0.278 0.295 4.949 0.297 -0.031 10 621052 1871 1975 105 1.000 0.235 1.069 5.068 0.247 0.006 11 621061 1872 1980 109 1.000 0.185 0.107 3.225 0.206 -0.007 12 621062 1870 1980 111 1.000 0.162 0.992 4.873 0.173 0.002 13 621071 1842 1980 139 1.000 0.193 0.158 3.129 0.212 0.002 14 621072 1789 1980 192 1.000 0.183 0.166 3.481 0.209 -0.008 15 621081 1842 1980 139 1.000 0.282 0.877 5.636 0.264 -0.004 16 621082 1850 1978 129 1.000 0.204 1.090 5.846 0.208 -0.018 17 621091 1760 1980 221 1.000 0.189 0.457 3.245 0.214 0.000 18 621092 1764 1980 217 1.000 0.195 0.712 4.704 0.209 0.000 19 621101 1881 1980 100 1.006 0.372 2.296 12.461 0.320 0.062 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 621102 1891 1980 90 1.000 0.208 1.667 7.711 0.215 0.009 21 621111 1836 1980 145 1.000 0.249 0.282 5.269 0.258 0.002 22 621112 1831 1980 150 1.000 0.226 0.450 4.426 0.245 0.008 23 621121 1810 1980 171 1.000 0.268 3.245 29.238 0.229 -0.029 24 621122 1852 1980 129 1.000 0.226 0.441 2.776 0.247 0.013 25 621131 1797 1980 184 1.000 0.133 0.068 2.421 0.150 -0.019 26 621132 1765 1980 216 1.000 0.171 0.027 2.813 0.191 0.000 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 157 1.000 0.217 0.706 5.478 0.229 -0.001 STANDARD DEVIATION 47 0.001 0.048 0.732 5.236 0.037 0.018 MEDIAN (50TH QUANTILE) 149 1.000 0.203 0.481 4.212 0.218 0.000 INTERQUARTILE RANGE 78 0.000 0.050 0.693 1.694 0.039 0.017 MINIMUM VALUE 90 1.000 0.133 0.027 2.421 0.150 -0.031 LOWER HINGE (25TH QUANTILE) 114 1.000 0.189 0.184 3.374 0.209 -0.012 UPPER HINGE (75TH QUANTILE) 192 1.000 0.239 0.877 5.068 0.247 0.004 MAXIMUM VALUE 285 1.006 0.372 3.245 29.238 0.320 0.062 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.389 0.097 0.005 0.066 3.008 0.156 0.689 MINIMUM CORRELATION: 0.156 SERIES 621021 AND 621101 100 YEARS MAXIMUM CORRELATION: 0.689 SERIES 621031 AND 621032 185 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 42.51 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1805. 1830. 1855. 1880. 1905. 1930. 1955. CORR 15. 28. 66. 171. 276. 325. 231. RBAR 0.374 0.278 0.448 0.457 0.384 0.463 0.415 SDEV 0.117 0.165 0.128 0.126 0.142 0.125 0.148 SERR 0.030 0.031 0.016 0.010 0.009 0.007 0.010 EPS 0.835 0.833 0.937 0.951 0.941 0.957 0.948 NSS 8.5 13.0 18.4 23.2 25.8 26.0 25.5 |======================== 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 1678 1980 303 0.999 0.143 0.184 3.132 0.166 -0.094 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.070 0.037 0.068 91 212 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.40 1.02 1.00 1.14 2.16 32.61 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.86 0.93 0.00 0.00 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 -0.094 -0.110 0.022 -0.008 -0.123 0.014 -0.044 0.052 -0.011 -0.044 PACF -0.094 -0.120 -0.001 -0.019 -0.126 -0.016 -0.075 0.041 -0.021 -0.054 95% C.L. 0.115 0.116 0.117 0.117 0.117 0.119 0.119 0.119 0.120 0.120 |------------------ 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 2 0.024 -0.106 -0.122 |---------- 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 -0.019 -0.033 -0.130 0.002 -0.055 0.046 -0.017 -0.035 PACF -0.001 -0.003 -0.019 -0.033 -0.131 0.000 -0.058 0.040 -0.027 -0.055 95% C.L. 0.115 0.115 0.115 0.115 0.115 0.117 0.117 0.117 0.118 0.118 |----------------- REWHITENED CHRONOLOGY AUTOREGRESSIVE MODEL -----------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 2 0.000 -0.001 -0.003 |========================= 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 1678 1980 303 1.000 0.159 0.154 3.179 0.136 0.434 |------------ 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 0.432 0.076 -0.054 -0.114 -0.153 -0.076 -0.047 0.014 -0.020 -0.030 PACF 0.432 -0.136 -0.041 -0.077 -0.090 0.030 -0.049 0.040 -0.077 -0.012 95% C.L. 0.115 0.135 0.135 0.136 0.137 0.139 0.140 0.140 0.140 0.140 |------------------- 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 0.206 0.495 -0.136 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 1.37 MINUTES