RUN: SWIT003 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: SWIT167E.rwl.conv LOG FILE PROCESSED: SWIT167E.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: 757 1 Simmental, Iffigenalp WIDTH_EARLY PIMU - 757 2 Switzerland krummholz pine 1900 4624-726 1734 1986 - 757 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 1 757011 MISSING VALUES FOUND: 2 IN 2 GAPS / 1953 1953 / 1961 1961 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 757011 1785 1982 198 0.559 0.363 0.654 3.107 0.307 0.855 2 757012 1811 1982 172 0.624 0.353 1.020 3.528 0.285 0.769 3 757021 1754 1986 233 0.580 0.488 1.077 3.103 0.313 0.905 4 757022 1734 1986 253 0.736 0.676 1.189 3.501 0.288 0.861 5 757031 1829 1986 158 1.094 0.671 0.733 2.524 0.211 0.884 6 757032 1812 1986 175 1.000 0.419 0.424 2.964 0.201 0.805 7 757041 1772 1986 215 0.814 0.393 1.494 5.196 0.195 0.854 8 757042 1764 1986 223 0.836 0.371 0.864 3.246 0.193 0.851 9 757051 1785 1986 202 0.680 0.320 0.694 2.949 0.235 0.789 10 757052 1797 1986 190 0.618 0.321 3.413 28.368 0.272 0.493 11 757061 1751 1986 236 0.712 0.309 1.958 8.028 0.269 0.599 12 757062 1775 1986 212 0.763 0.369 1.908 8.449 0.240 0.745 13 757071 1785 1986 202 0.641 0.338 1.130 3.744 0.235 0.826 14 757072 1772 1986 215 0.711 0.347 1.267 5.337 0.245 0.797 15 757081 1820 1986 167 0.732 0.279 0.699 3.158 0.211 0.755 16 757082 1822 1986 165 0.711 0.284 0.994 3.859 0.258 0.745 17 757091 1808 1986 179 0.777 0.492 1.111 3.159 0.269 0.875 18 757092 1804 1986 183 0.727 0.431 1.299 4.072 0.310 0.805 19 757101 1790 1986 197 0.669 0.289 0.828 3.099 0.207 0.831 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 757102 1783 1986 204 0.780 0.394 0.994 3.444 0.191 0.879 NUMBER OF SERIES READ IN: 20 FROM 1734 TO 1986 253 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 199 0.738 0.395 1.188 5.242 0.247 0.796 STANDARD DEVIATION 25 0.129 0.112 0.653 5.675 0.041 0.099 MEDIAN (50TH QUANTILE) 199 0.720 0.366 1.049 3.472 0.242 0.816 INTERQUARTILE RANGE 38 0.123 0.105 0.503 1.529 0.070 0.096 MINIMUM VALUE 158 0.559 0.279 0.424 2.524 0.191 0.493 LOWER HINGE (25TH QUANTILE) 177 0.655 0.321 0.780 3.105 0.209 0.762 UPPER HINGE (75TH QUANTILE) 215 0.778 0.425 1.283 4.634 0.279 0.858 MAXIMUM VALUE 253 1.094 0.676 3.413 28.368 0.313 0.905 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.515 0.178 0.013 -0.616 3.163 0.009 0.860 MINIMUM CORRELATION: 0.009 SERIES 757031 AND 757062 158 YEARS MAXIMUM CORRELATION: 0.860 SERIES 757031 AND 757032 158 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.59 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1790. 1815. 1840. 1865. 1890. 1915. 1940. CORR 6. 66. 136. 190. 190. 190. 190. RBAR 0.221 0.381 0.247 0.323 0.291 0.226 0.212 SDEV 0.141 0.238 0.275 0.307 0.290 0.222 0.236 SERR 0.058 0.029 0.024 0.022 0.021 0.016 0.017 EPS 0.746 0.909 0.865 0.905 0.891 0.854 0.844 NSS 10.3 16.3 19.5 20.0 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 1734 1986 253 0.821 0.384 1.371 5.487 0.172 0.830 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.236 0.119 0.203 76 177 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.52 0.96 1.00 1.20 2.16 13.14 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.08 0.00 0.86 0.94 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 200. 38. 158. 177. 215. 253. |----------- 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 0.826 0.750 0.689 0.651 0.592 0.555 0.570 0.565 0.569 0.598 PACF 0.826 0.212 0.085 0.091 -0.029 0.034 0.188 0.062 0.081 0.162 95% C.L. 0.126 0.193 0.235 0.265 0.289 0.308 0.323 0.339 0.353 0.368 |------------------ 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 0.720 0.636 0.241 |================== 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 757011 3 0.00000000 0.00000000 -0.00513262 1.06577444 2 757012 1 1.13326669 0.01467096 0.00000000 0.21433592 3 757021 -67 156 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 757022 -67 169 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 757031 3 0.00000000 0.00000000 -0.01253327 2.09082556 6 757032 3 0.00000000 0.00000000 -0.00573692 1.50473499 7 757041 1 0.87878257 0.01490952 0.00000000 0.55303246 8 757042 3 0.00000000 0.00000000 -0.00300750 1.17258024 9 757051 3 0.00000000 0.00000000 -0.00378149 1.06416726 10 757052 3 0.00000000 0.00000000 -0.00242489 0.84978777 11 757061 1 0.42629048 0.00623927 0.00000000 0.48996168 12 757062 1 1.20410740 0.03658631 0.00000000 0.61057806 13 757071 1 1.12557590 0.01313903 0.00000000 0.24964345 14 757072 3 0.00000000 0.00000000 -0.00366748 1.10743618 15 757081 1 0.64376229 0.02590656 0.00000000 0.58698279 16 757082 1 0.80210936 0.03253335 0.00000000 0.56477410 17 757091 1 1.61969697 0.01927492 0.00000000 0.32696846 18 757092 1 1.31997049 0.01932886 0.00000000 0.36796999 19 757101 1 0.86080581 0.02900221 0.00000000 0.52119374 SERIES IDENT OPTION A B C D 20 757102 1 1.31309795 0.03114223 0.00000000 0.57657939 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 757011 1785 1982 198 0.997 0.456 2.407 18.499 0.306 0.461 2 757012 1811 1982 172 1.001 0.344 0.630 3.012 0.283 0.381 3 757021 1754 1986 233 0.994 0.469 1.165 5.206 0.311 0.623 4 757022 1734 1986 253 0.991 0.405 0.733 3.987 0.286 0.575 5 757031 1829 1986 158 1.090 0.532 2.755 12.996 0.210 0.802 6 757032 1812 1986 175 0.997 0.309 0.482 3.294 0.200 0.650 7 757041 1772 1986 215 1.000 0.362 0.659 2.843 0.194 0.737 8 757042 1764 1986 223 0.999 0.344 0.280 2.997 0.193 0.749 9 757051 1785 1986 202 1.002 0.339 0.468 2.812 0.234 0.588 10 757052 1797 1986 190 1.000 0.431 1.883 13.059 0.271 0.485 11 757061 1751 1986 236 1.000 0.378 1.240 5.610 0.267 0.557 12 757062 1775 1986 212 1.000 0.319 0.242 2.781 0.239 0.564 13 757071 1785 1986 202 1.000 0.278 0.742 4.202 0.234 0.440 14 757072 1772 1986 215 1.008 0.356 0.695 3.886 0.244 0.612 15 757081 1820 1986 167 1.000 0.313 0.309 2.650 0.210 0.625 16 757082 1822 1986 165 0.999 0.287 -0.015 2.724 0.256 0.489 17 757091 1808 1986 179 1.004 0.363 0.572 2.860 0.268 0.544 18 757092 1804 1986 183 1.002 0.365 0.623 3.205 0.308 0.397 19 757101 1790 1986 197 1.000 0.329 0.574 3.326 0.206 0.687 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 757102 1783 1986 204 1.000 0.341 0.100 3.021 0.190 0.727 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 199 1.004 0.366 0.827 5.149 0.246 0.585 STANDARD DEVIATION 25 0.020 0.064 0.736 4.380 0.041 0.119 MEDIAN (50TH QUANTILE) 200 1.000 0.350 0.626 3.250 0.241 0.581 INTERQUARTILE RANGE 38 0.002 0.067 0.565 1.853 0.069 0.181 MINIMUM VALUE 158 0.991 0.278 -0.015 2.650 0.190 0.381 LOWER HINGE (25TH QUANTILE) 177 0.999 0.324 0.388 2.851 0.208 0.487 UPPER HINGE (75TH QUANTILE) 215 1.001 0.391 0.953 4.704 0.277 0.668 MAXIMUM VALUE 253 1.090 0.532 2.755 18.499 0.311 0.802 |------------------------ 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 757011 -67 132 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 757012 -67 115 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 757021 -67 156 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 757022 -67 169 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 757031 -67 105 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 757032 -67 117 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 757041 -67 144 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 757042 -67 149 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 757051 -67 135 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 757052 -67 127 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 757061 -67 158 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 757062 -67 142 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 757071 -67 135 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 757072 -67 144 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 757081 -67 111 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 757082 -67 110 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 757091 -67 119 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 757092 -67 122 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 757101 -67 131 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 757102 -67 136 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 757011 1785 1982 198 0.991 0.429 2.697 21.760 0.306 0.397 2 757012 1811 1982 172 0.998 0.339 0.623 2.897 0.283 0.372 3 757021 1754 1986 233 0.999 0.466 1.132 5.119 0.311 0.605 4 757022 1734 1986 253 0.998 0.394 0.588 3.388 0.286 0.566 5 757031 1829 1986 158 0.995 0.305 0.608 3.162 0.210 0.630 6 757032 1812 1986 175 0.995 0.292 0.677 3.832 0.200 0.609 7 757041 1772 1986 215 0.995 0.340 0.710 2.989 0.194 0.712 8 757042 1764 1986 223 0.992 0.308 0.226 2.874 0.193 0.699 9 757051 1785 1986 202 0.994 0.317 0.526 2.840 0.234 0.547 10 757052 1797 1986 190 0.994 0.409 1.737 12.157 0.271 0.469 11 757061 1751 1986 236 0.995 0.352 1.013 4.808 0.268 0.511 12 757062 1775 1986 212 0.998 0.309 0.180 2.696 0.239 0.536 13 757071 1785 1986 202 0.999 0.274 0.702 4.032 0.234 0.430 14 757072 1772 1986 215 0.998 0.332 0.412 2.930 0.244 0.581 15 757081 1820 1986 167 0.998 0.298 0.307 2.808 0.210 0.579 16 757082 1822 1986 165 0.997 0.269 0.082 2.961 0.256 0.416 17 757091 1808 1986 179 0.996 0.341 0.537 2.710 0.267 0.489 18 757092 1804 1986 183 0.996 0.346 0.621 3.436 0.308 0.350 19 757101 1790 1986 197 0.999 0.325 0.630 3.557 0.206 0.678 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 757102 1783 1986 204 0.997 0.331 0.047 2.806 0.190 0.719 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 199 0.996 0.339 0.703 4.688 0.246 0.545 STANDARD DEVIATION 25 0.002 0.051 0.606 4.526 0.041 0.114 MEDIAN (50TH QUANTILE) 200 0.997 0.332 0.615 3.076 0.241 0.556 INTERQUARTILE RANGE 38 0.003 0.042 0.347 1.075 0.069 0.170 MINIMUM VALUE 158 0.991 0.269 0.047 2.696 0.190 0.350 LOWER HINGE (25TH QUANTILE) 177 0.995 0.307 0.359 2.857 0.208 0.450 UPPER HINGE (75TH QUANTILE) 215 0.998 0.349 0.706 3.932 0.277 0.620 MAXIMUM VALUE 253 0.999 0.466 2.697 21.760 0.311 0.719 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.237 0.148 0.011 0.451 3.643 -0.206 0.725 MINIMUM CORRELATION: -0.206 SERIES 757042 AND 757102 204 YEARS MAXIMUM CORRELATION: 0.725 SERIES 757101 AND 757102 197 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.59 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1790. 1815. 1840. 1865. 1890. 1915. 1940. CORR 6. 66. 136. 190. 190. 190. 190. RBAR 0.256 0.176 0.206 0.226 0.261 0.222 0.231 SDEV 0.155 0.246 0.259 0.257 0.246 0.212 0.217 SERR 0.063 0.030 0.022 0.019 0.018 0.015 0.016 EPS 0.780 0.777 0.835 0.854 0.876 0.851 0.857 NSS 10.3 16.3 19.5 20.0 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 1734 1986 253 0.969 0.196 0.345 2.916 0.178 0.422 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.333 0.188 0.090 59 194 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.18 0.53 1.01 1.07 1.60 8.45 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.00 0.87 0.95 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 0.420 0.258 0.173 0.190 0.027 0.036 0.010 0.026 -0.055 -0.015 PACF 0.420 0.099 0.041 0.106 -0.126 0.029 -0.013 0.014 -0.064 0.019 95% C.L. 0.126 0.146 0.153 0.156 0.160 0.160 0.160 0.160 0.160 0.161 |------------------ 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 0.186 0.380 0.098 |======================= 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 0.370 0.220 0.135 0.141 -0.033 -0.021 -0.021 -0.038 -0.125 -0.105 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 0.370 2 0.334 0.097 3 0.331 0.087 0.030 4 0.329 0.080 0.004 0.078 5 0.340 0.081 0.015 0.124 -0.140 6 0.340 0.080 0.015 0.124 -0.141 0.002 7 0.340 0.080 0.015 0.124 -0.141 0.002 0.000 8 0.340 0.080 0.010 0.128 -0.140 0.004 0.012 -0.033 9 0.337 0.081 0.011 0.115 -0.129 0.005 0.019 -0.002 -0.092 10 0.333 0.081 0.012 0.115 -0.133 0.009 0.019 0.001 -0.079 -0.037 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) 1960.61 1925.46 1925.09 1926.87 1927.34 1924.30 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1926.30 1928.30 1930.02 1929.87 1931.52 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 0.334 0.097 R-SQUARED DUE TO POOLED AUTOREGRESSION: 14.46 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 116.91 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.334 0.208 0.102 0.054 0.028 0.015 0.008 0.004 0.002 0.0011 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 757011 2 0.240 0.439 0.068 2 757012 2 0.156 0.340 0.107 3 757021 2 0.374 0.668 -0.101 4 757022 2 0.327 0.525 0.075 5 757031 2 0.436 0.524 0.169 6 757032 2 0.434 0.425 0.304 7 757041 2 0.522 0.667 0.072 8 757042 2 0.516 0.550 0.215 9 757051 2 0.350 0.421 0.238 10 757052 2 0.301 0.460 0.140 11 757061 2 0.265 0.503 0.019 12 757062 2 0.298 0.493 0.085 13 757071 2 0.189 0.451 -0.045 14 757072 2 0.377 0.482 0.176 15 757081 2 0.383 0.480 0.181 16 757082 2 0.203 0.354 0.156 17 757091 2 0.276 0.393 0.199 18 757092 2 0.140 0.301 0.141 19 757101 2 0.490 0.571 0.162 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 757102 2 0.547 0.570 0.209 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.341 0.481 0.129 STANDARD DEVIATION 0 0.124 0.097 0.097 MEDIAN 2 0.339 0.481 0.148 INTERQUARTILE RANGE 0 0.183 0.114 0.116 MINIMUM VALUE 2 0.140 0.301 -0.101 LOWER HINGE 2 0.252 0.423 0.074 UPPER HINGE 2 0.435 0.537 0.190 MAXIMUM VALUE 2 0.547 0.668 0.304 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 757011 1785 1982 198 1.000 0.377 3.241 26.207 0.334 0.060 2 757012 1811 1982 172 1.000 0.311 0.543 3.272 0.332 0.007 3 757021 1754 1986 233 1.000 0.368 1.027 5.794 0.381 0.003 4 757022 1734 1986 253 1.000 0.323 0.419 3.638 0.345 0.008 5 757031 1829 1986 158 1.000 0.233 0.360 3.227 0.261 -0.033 6 757032 1812 1986 175 1.000 0.220 0.470 4.055 0.237 -0.032 7 757041 1772 1986 215 1.000 0.235 0.410 3.562 0.257 0.000 8 757042 1764 1986 223 1.000 0.215 0.435 3.370 0.233 0.011 9 757051 1785 1986 202 1.000 0.256 0.486 4.054 0.275 0.017 10 757052 1797 1986 190 1.001 0.328 1.284 10.277 0.330 -0.045 11 757061 1751 1986 236 1.000 0.302 0.803 4.570 0.325 0.001 12 757062 1775 1986 212 1.000 0.259 0.089 3.329 0.288 -0.005 13 757071 1785 1986 202 1.000 0.247 0.466 3.897 0.281 0.001 14 757072 1772 1986 215 1.000 0.264 0.337 3.218 0.300 -0.032 15 757081 1820 1986 167 1.000 0.237 0.422 3.370 0.249 0.029 16 757082 1822 1986 165 1.000 0.241 0.028 2.839 0.285 0.011 17 757091 1808 1986 179 1.000 0.291 0.237 3.113 0.323 -0.015 18 757092 1804 1986 183 1.000 0.320 0.627 4.093 0.357 0.000 19 757101 1790 1986 197 1.000 0.235 0.405 4.173 0.268 -0.027 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 757102 1783 1986 204 1.000 0.224 0.169 3.116 0.255 -0.024 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 199 1.000 0.274 0.613 5.159 0.296 -0.003 STANDARD DEVIATION 25 0.000 0.050 0.685 5.209 0.043 0.025 MEDIAN (50TH QUANTILE) 200 1.000 0.258 0.428 3.600 0.286 0.001 INTERQUARTILE RANGE 38 0.000 0.081 0.237 0.884 0.072 0.035 MINIMUM VALUE 158 1.000 0.215 0.028 2.839 0.233 -0.045 LOWER HINGE (25TH QUANTILE) 177 1.000 0.235 0.348 3.249 0.259 -0.025 UPPER HINGE (75TH QUANTILE) 215 1.000 0.316 0.585 4.133 0.331 0.009 MAXIMUM VALUE 253 1.001 0.377 3.241 26.207 0.381 0.060 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.332 0.109 0.008 0.272 4.387 0.003 0.704 MINIMUM CORRELATION: 0.003 SERIES 757021 AND 757081 167 YEARS MAXIMUM CORRELATION: 0.704 SERIES 757091 AND 757092 179 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.59 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1790. 1815. 1840. 1865. 1890. 1915. 1940. CORR 6. 66. 136. 190. 190. 190. 190. RBAR 0.210 0.270 0.302 0.295 0.325 0.301 0.371 SDEV 0.149 0.166 0.155 0.152 0.173 0.158 0.145 SERR 0.061 0.020 0.013 0.011 0.013 0.011 0.011 EPS 0.733 0.858 0.894 0.893 0.906 0.896 0.922 NSS 10.3 16.3 19.5 20.0 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 1734 1986 253 0.987 0.175 0.344 3.416 0.214 -0.081 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.314 0.158 0.048 71 182 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.27 0.74 1.00 1.08 1.83 9.15 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.09 0.00 0.86 0.95 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 -0.081 -0.080 -0.025 0.106 -0.098 -0.016 0.012 0.049 -0.089 -0.005 PACF -0.081 -0.087 -0.040 0.094 -0.087 -0.017 0.000 0.033 -0.067 -0.017 95% C.L. 0.126 0.127 0.127 0.127 0.129 0.130 0.130 0.130 0.130 0.131 |------------------ 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 -0.004 0.005 -0.039 0.089 -0.091 -0.010 -0.001 0.042 -0.086 -0.008 PACF -0.004 0.005 -0.039 0.089 -0.091 -0.012 0.006 0.027 -0.072 -0.013 95% C.L. 0.126 0.126 0.126 0.126 0.127 0.128 0.128 0.128 0.128 0.129 |----------------- 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 -0.004 0.005 |========================= ARSTAN CHRONOLOGY STATISTICS =======================| |----------------- ROBUST MEAN ARSTAN CHRONOLOGY STATISTICS -------------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1734 1986 253 0.987 0.188 0.263 3.084 0.174 0.363 |------------ 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 0.362 0.218 0.083 0.100 -0.036 -0.011 -0.012 0.005 -0.076 -0.032 PACF 0.362 0.100 -0.028 0.069 -0.107 0.012 0.013 0.001 -0.077 0.012 95% C.L. 0.126 0.141 0.146 0.147 0.148 0.148 0.148 0.148 0.148 0.149 |------------------- 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 0.141 0.327 0.099 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 2.02 MINUTES