RUN: 4DIG001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM052W.rwl.conv LOG FILE PROCESSED: GERM052W.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: 049 1 Seehalde (D), EU-Pr. WIDTH_RING PCAB - 049 2 Germany Norway spruce 1250 4751-802 1756 1995 - 049 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES --- NO GAPS IN DATA FOUND --- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 049011 1791 1995 205 1.415 0.413 0.666 3.945 0.176 0.644 2 049013 1791 1995 205 1.710 0.431 0.578 3.287 0.161 0.640 3 049015 1791 1995 205 1.571 0.504 0.481 2.755 0.159 0.754 4 049017 1790 1995 206 1.264 0.513 1.884 7.584 0.183 0.756 5 049021 1782 1995 214 1.090 0.321 0.870 6.012 0.155 0.769 6 049023 1782 1995 214 1.772 0.638 0.798 3.982 0.165 0.794 7 049025 1782 1995 214 1.247 0.439 1.491 7.679 0.162 0.796 8 049027 1807 1995 189 1.014 0.329 0.693 4.041 0.145 0.859 9 049031 1777 1995 219 1.496 0.574 1.104 4.823 0.179 0.779 10 049033 1777 1995 219 1.669 0.546 0.861 4.710 0.182 0.694 11 049035 1777 1995 219 0.996 0.453 1.331 5.393 0.203 0.743 12 049037 1780 1995 216 0.996 0.609 2.826 12.533 0.191 0.892 13 049041 1756 1995 240 1.481 0.497 0.291 2.598 0.178 0.754 14 049043 1758 1995 238 1.786 0.512 0.304 3.106 0.193 0.663 15 049045 1756 1995 240 1.034 0.403 1.331 4.905 0.169 0.831 16 049047 1757 1995 239 0.964 0.375 0.915 4.320 0.176 0.844 17 049051 1756 1995 240 1.346 0.561 0.597 2.861 0.155 0.897 18 049053 1756 1995 240 1.940 0.629 1.274 5.753 0.141 0.832 19 049055 1763 1995 233 1.114 0.565 0.690 2.280 0.146 0.928 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 049057 1756 1995 240 1.234 0.454 2.174 9.466 0.145 0.849 NUMBER OF SERIES READ IN: 20 FROM 1756 TO 1995 240 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 222 1.357 0.488 1.058 5.102 0.168 0.786 STANDARD DEVIATION 15 0.308 0.094 0.647 2.565 0.018 0.083 MEDIAN (50TH QUANTILE) 219 1.305 0.500 0.866 4.515 0.167 0.787 INTERQUARTILE RANGE 29 0.558 0.142 0.700 2.686 0.025 0.098 MINIMUM VALUE 189 0.964 0.321 0.291 2.280 0.141 0.640 LOWER HINGE (25TH QUANTILE) 210 1.062 0.422 0.631 3.197 0.155 0.748 UPPER HINGE (75TH QUANTILE) 239 1.620 0.563 1.331 5.883 0.180 0.846 MAXIMUM VALUE 240 1.940 0.638 2.826 12.533 0.203 0.928 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.381 0.200 0.014 -0.199 2.718 -0.118 0.870 MINIMUM CORRELATION: -0.118 SERIES 049013 AND 049051 205 YEARS MAXIMUM CORRELATION: 0.870 SERIES 049045 AND 049047 239 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 88.65 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1781. 1810. 1835. 1860. 1885. 1910. 1935. 1960. CORR 10. 105. 190. 190. 190. 190. 190. 190. RBAR 0.510 0.341 0.339 0.413 0.537 0.447 0.511 0.568 SDEV 0.187 0.286 0.355 0.247 0.213 0.246 0.200 0.176 SERR 0.059 0.028 0.026 0.018 0.015 0.018 0.014 0.013 EPS 0.930 0.908 0.911 0.934 0.959 0.942 0.954 0.963 NSS 12.7 19.1 20.0 20.0 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 1756 1995 240 1.364 0.352 0.780 4.253 0.122 0.807 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.417 0.165 0.253 78 162 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.15 0.45 1.00 1.05 1.50 12.38 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.05 0.67 0.86 0.91 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 219. 30. 189. 210. 240. 240. |----------- 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 0.804 0.725 0.650 0.568 0.485 0.428 0.402 0.396 0.404 0.424 PACF 0.804 0.224 0.054 -0.032 -0.054 0.017 0.091 0.109 0.101 0.090 95% C.L. 0.129 0.195 0.236 0.264 0.284 0.297 0.307 0.316 0.324 0.333 |------------------ 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 0.667 0.633 0.215 |================== 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 049011 1 0.80901527 0.03430701 0.00000000 1.30220330 2 049013 3 0.00000000 0.00000000 0.00176776 1.52811623 3 049015 1 0.94556612 0.02970068 0.00000000 1.41857147 4 049017 1 1.42736232 0.03120591 0.00000000 1.04559493 5 049021 1 0.83815354 0.05478607 0.00000000 1.02073359 6 049023 1 0.65638673 0.03898023 0.00000000 1.69533193 7 049025 1 1.54961765 0.08161307 0.00000000 1.16148078 8 049027 3 0.00000000 0.00000000 0.00241837 0.78401160 9 049031 3 0.00000000 0.00000000 -0.00301501 1.82726777 10 049033 3 0.00000000 0.00000000 -0.00055777 1.73035026 11 049035 1 1.25042260 0.01629122 0.00000000 0.65772343 12 049037 1 2.89800000 0.05678589 0.00000000 0.76603055 13 049041 3 0.00000000 0.00000000 -0.00119396 1.62516356 14 049043 1 0.97566783 0.14319550 0.00000000 1.75942314 15 049045 1 1.23935854 0.03431809 0.00000000 0.88617796 16 049047 1 1.32421303 0.04760242 0.00000000 0.84987020 17 049051 3 0.00000000 0.00000000 -0.00637698 2.11430120 18 049053 3 0.00000000 0.00000000 0.00115251 1.80095565 19 049055 1 2.03920674 0.00665004 0.00000000 0.08050277 SERIES IDENT OPTION A B C D 20 049057 1 1.48026395 0.03734609 0.00000000 1.07147551 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 049011 1791 1995 205 1.000 0.258 0.269 3.745 0.175 0.592 2 049013 1791 1995 205 1.000 0.248 0.854 4.659 0.160 0.608 3 049015 1791 1995 205 1.000 0.279 0.029 2.727 0.158 0.733 4 049017 1790 1995 206 1.000 0.278 0.569 4.045 0.181 0.639 5 049021 1782 1995 214 1.000 0.253 -0.147 2.784 0.154 0.717 6 049023 1782 1995 214 1.000 0.357 1.020 4.927 0.165 0.795 7 049025 1782 1995 214 1.000 0.293 0.561 3.719 0.160 0.747 8 049027 1807 1995 189 1.001 0.302 0.562 3.409 0.144 0.821 9 049031 1777 1995 219 0.999 0.354 0.847 3.770 0.178 0.762 10 049033 1777 1995 219 1.000 0.326 0.820 4.443 0.181 0.696 11 049035 1777 1995 219 1.000 0.317 0.604 3.522 0.202 0.669 12 049037 1780 1995 216 1.000 0.288 0.509 3.349 0.188 0.667 13 049041 1756 1995 240 1.000 0.332 0.315 2.624 0.177 0.747 14 049043 1758 1995 238 1.000 0.284 0.400 3.378 0.192 0.650 15 049045 1756 1995 240 0.999 0.287 0.522 4.003 0.169 0.707 16 049047 1757 1995 239 0.999 0.304 0.083 2.985 0.175 0.745 17 049051 1756 1995 240 1.005 0.260 0.344 3.165 0.154 0.674 18 049053 1756 1995 240 1.000 0.320 1.195 5.608 0.141 0.824 19 049055 1763 1995 233 1.006 0.312 0.284 2.605 0.145 0.817 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 049057 1756 1995 240 1.000 0.241 0.437 3.859 0.145 0.693 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 222 1.000 0.295 0.504 3.666 0.167 0.715 STANDARD DEVIATION 15 0.002 0.034 0.333 0.799 0.017 0.068 MEDIAN (50TH QUANTILE) 219 1.000 0.290 0.516 3.620 0.167 0.712 INTERQUARTILE RANGE 29 0.000 0.049 0.413 0.949 0.025 0.087 MINIMUM VALUE 189 0.999 0.241 -0.147 2.605 0.141 0.592 LOWER HINGE (25TH QUANTILE) 210 1.000 0.269 0.299 3.075 0.154 0.668 UPPER HINGE (75TH QUANTILE) 239 1.000 0.319 0.712 4.024 0.179 0.755 MAXIMUM VALUE 240 1.006 0.357 1.195 5.608 0.202 0.824 |------------------------ 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 049011 -67 137 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 049013 -67 137 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 049015 -67 137 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 049017 -67 138 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 049021 -67 143 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 049023 -67 143 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 049025 -67 143 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 049027 -67 126 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 049031 -67 146 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 049033 -67 146 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 049035 -67 146 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 049037 -67 144 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 049041 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 049043 -67 159 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 049045 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 049047 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 049051 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 049053 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 049055 -67 156 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 049057 -67 160 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 049011 1791 1995 205 0.999 0.240 0.004 3.291 0.175 0.550 2 049013 1791 1995 205 0.998 0.222 0.429 3.871 0.160 0.531 3 049015 1791 1995 205 0.995 0.240 -0.368 3.105 0.158 0.653 4 049017 1790 1995 206 0.998 0.255 0.232 3.729 0.181 0.581 5 049021 1782 1995 214 0.999 0.241 -0.229 2.754 0.154 0.689 6 049023 1782 1995 214 0.990 0.290 0.495 4.039 0.165 0.718 7 049025 1782 1995 214 0.996 0.225 0.169 3.005 0.160 0.587 8 049027 1807 1995 189 0.994 0.247 0.140 3.139 0.144 0.740 9 049031 1777 1995 219 0.993 0.309 0.842 3.688 0.178 0.703 10 049033 1777 1995 219 0.998 0.309 0.759 4.705 0.181 0.660 11 049035 1777 1995 219 0.997 0.301 0.550 3.349 0.202 0.639 12 049037 1780 1995 216 1.000 0.285 0.459 3.240 0.188 0.662 13 049041 1756 1995 240 0.992 0.287 0.243 2.700 0.177 0.676 14 049043 1758 1995 238 0.999 0.277 0.331 3.428 0.192 0.637 15 049045 1756 1995 240 0.994 0.247 0.453 3.840 0.168 0.620 16 049047 1757 1995 239 0.994 0.271 0.032 3.146 0.175 0.681 17 049051 1756 1995 240 0.999 0.251 0.375 3.193 0.154 0.674 18 049053 1756 1995 240 0.995 0.271 0.820 4.757 0.140 0.769 19 049055 1763 1995 233 0.989 0.221 0.158 3.032 0.145 0.678 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 049057 1756 1995 240 0.999 0.229 0.480 4.056 0.145 0.659 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 222 0.996 0.261 0.319 3.503 0.167 0.655 STANDARD DEVIATION 15 0.003 0.029 0.319 0.575 0.017 0.060 MEDIAN (50TH QUANTILE) 219 0.997 0.253 0.353 3.320 0.167 0.661 INTERQUARTILE RANGE 29 0.005 0.046 0.338 0.733 0.025 0.057 MINIMUM VALUE 189 0.989 0.221 -0.368 2.700 0.140 0.531 LOWER HINGE (25TH QUANTILE) 210 0.994 0.240 0.149 3.122 0.154 0.629 UPPER HINGE (75TH QUANTILE) 239 0.999 0.286 0.487 3.856 0.179 0.685 MAXIMUM VALUE 240 1.000 0.309 0.842 4.757 0.202 0.769 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.417 0.141 0.010 0.135 2.932 0.019 0.774 MINIMUM CORRELATION: 0.019 SERIES 049013 AND 049055 205 YEARS MAXIMUM CORRELATION: 0.774 SERIES 049045 AND 049047 239 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 88.65 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1781. 1810. 1835. 1860. 1885. 1910. 1935. 1960. CORR 10. 105. 190. 190. 190. 190. 190. 190. RBAR 0.354 0.267 0.316 0.469 0.581 0.479 0.510 0.590 SDEV 0.234 0.287 0.316 0.206 0.204 0.202 0.195 0.152 SERR 0.074 0.028 0.023 0.015 0.015 0.015 0.014 0.011 EPS 0.875 0.874 0.902 0.946 0.965 0.948 0.954 0.966 NSS 12.7 19.1 20.0 20.0 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 1756 1995 240 0.987 0.176 -0.407 3.474 0.123 0.604 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.415 0.155 0.040 80 160 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.27 0.46 1.00 1.07 1.53 5.03 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.05 0.33 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 0.601 0.479 0.337 0.202 0.069 -0.001 -0.061 -0.052 -0.034 -0.022 PACF 0.601 0.183 -0.013 -0.078 -0.106 -0.025 -0.030 0.052 0.042 0.000 95% C.L. 0.129 0.169 0.191 0.200 0.204 0.204 0.204 0.204 0.205 0.205 |------------------ 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 0.398 0.501 0.183 |======================= 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 0.625 0.511 0.379 0.253 0.101 0.035 -0.039 -0.039 -0.023 -0.040 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 0.625 2 0.502 0.197 3 0.502 0.198 -0.001 4 0.502 0.210 0.032 -0.064 5 0.493 0.215 0.061 0.006 -0.140 6 0.491 0.215 0.062 0.009 -0.134 -0.014 7 0.490 0.210 0.062 0.011 -0.126 0.004 -0.036 8 0.492 0.210 0.069 0.011 -0.129 -0.008 -0.063 0.057 9 0.489 0.214 0.070 0.018 -0.130 -0.012 -0.076 0.027 0.060 10 0.491 0.215 0.067 0.018 -0.136 -0.012 -0.073 0.036 0.080 -0.043 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) 1889.40 1772.59 1765.06 1767.06 1768.06 1765.28 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1767.23 1768.93 1770.16 1771.31 1772.87 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 0.502 0.197 R-SQUARED DUE TO POOLED AUTOREGRESSION: 41.42 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 170.70 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.502 0.449 0.324 0.251 0.190 0.145 0.110 0.084 0.064 0.0485 0.037 0.028 0.021 0.016 0.012 0.009 0.007 0.005 0.004 0.0032 0.002 0.002 0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.0002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 049011 2 0.363 0.414 0.262 2 049013 2 0.310 0.442 0.176 3 049015 2 0.453 0.535 0.187 4 049017 2 0.356 0.508 0.130 5 049021 2 0.483 0.652 0.058 6 049023 2 0.537 0.683 0.060 7 049025 2 0.363 0.523 0.119 8 049027 2 0.564 0.637 0.140 9 049031 2 0.501 0.647 0.083 10 049033 2 0.446 0.594 0.103 11 049035 2 0.443 0.502 0.216 12 049037 2 0.449 0.579 0.126 13 049041 2 0.470 0.591 0.129 14 049043 2 0.409 0.606 0.050 15 049045 2 0.407 0.546 0.132 16 049047 2 0.488 0.574 0.160 17 049051 2 0.484 0.601 0.128 18 049053 2 0.601 0.736 0.050 19 049055 2 0.475 0.590 0.134 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 049057 2 0.454 0.609 0.090 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.453 0.579 0.127 STANDARD DEVIATION 0 0.072 0.078 0.055 MEDIAN 2 0.453 0.591 0.129 INTERQUARTILE RANGE 0 0.078 0.094 0.063 MINIMUM VALUE 2 0.310 0.414 0.050 LOWER HINGE 2 0.408 0.529 0.087 UPPER HINGE 2 0.486 0.623 0.150 MAXIMUM VALUE 2 0.601 0.736 0.262 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 049011 1791 1995 205 1.000 0.191 0.206 3.516 0.206 0.015 2 049013 1791 1995 205 1.000 0.184 0.401 4.027 0.194 -0.002 3 049015 1791 1995 205 1.000 0.177 0.114 3.937 0.191 -0.012 4 049017 1790 1995 206 1.000 0.205 0.278 4.307 0.220 0.009 5 049021 1782 1995 214 1.000 0.174 -0.006 3.325 0.198 0.003 6 049023 1782 1995 214 1.000 0.198 0.740 4.246 0.217 -0.011 7 049025 1782 1995 214 1.000 0.179 0.258 3.357 0.203 -0.009 8 049027 1807 1995 189 1.000 0.164 -0.272 4.240 0.188 0.014 9 049031 1777 1995 219 1.000 0.218 0.534 4.569 0.241 -0.005 10 049033 1777 1995 219 1.000 0.230 1.895 11.622 0.213 -0.004 11 049035 1777 1995 219 1.000 0.226 0.346 3.723 0.244 -0.023 12 049037 1780 1995 216 1.000 0.211 0.571 4.130 0.235 0.001 13 049041 1756 1995 240 1.000 0.209 -0.245 3.894 0.233 -0.007 14 049043 1758 1995 238 1.000 0.213 0.420 3.809 0.247 -0.001 15 049045 1756 1995 240 1.000 0.190 0.313 4.345 0.220 -0.015 16 049047 1757 1995 239 1.000 0.195 -0.031 3.638 0.227 -0.019 17 049051 1756 1995 240 1.000 0.179 0.429 3.954 0.195 -0.003 18 049053 1756 1995 240 1.000 0.170 0.375 7.332 0.185 -0.004 19 049055 1763 1995 233 1.000 0.160 -0.002 3.248 0.187 -0.002 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 049057 1756 1995 240 1.000 0.168 0.382 4.590 0.186 -0.015 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 222 1.000 0.192 0.335 4.490 0.211 -0.004 STANDARD DEVIATION 15 0.000 0.021 0.451 1.882 0.021 0.010 MEDIAN (50TH QUANTILE) 219 1.000 0.190 0.330 3.991 0.209 -0.004 INTERQUARTILE RANGE 29 0.000 0.035 0.369 0.646 0.037 0.012 MINIMUM VALUE 189 1.000 0.160 -0.272 3.248 0.185 -0.023 LOWER HINGE (25TH QUANTILE) 210 1.000 0.175 0.056 3.680 0.193 -0.012 UPPER HINGE (75TH QUANTILE) 239 1.000 0.210 0.425 4.326 0.230 0.000 MAXIMUM VALUE 240 1.000 0.230 1.895 11.622 0.247 0.015 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.462 0.095 0.007 0.760 3.131 0.308 0.733 MINIMUM CORRELATION: 0.308 SERIES 049017 AND 049057 206 YEARS MAXIMUM CORRELATION: 0.733 SERIES 049021 AND 049027 189 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 88.65 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1781. 1810. 1835. 1860. 1885. 1910. 1935. 1960. CORR 10. 105. 190. 190. 190. 190. 190. 190. RBAR 0.473 0.408 0.380 0.512 0.588 0.490 0.521 0.575 SDEV 0.153 0.158 0.170 0.129 0.100 0.137 0.121 0.094 SERR 0.049 0.015 0.012 0.009 0.007 0.010 0.009 0.007 EPS 0.919 0.929 0.925 0.955 0.966 0.951 0.956 0.964 NSS 12.7 19.1 20.0 20.0 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 1756 1995 240 0.996 0.133 -0.293 4.269 0.160 -0.092 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.381 0.139 -0.002 71 169 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.19 0.47 1.00 1.07 1.54 3.44 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.05 0.66 0.87 0.92 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 -0.092 0.023 0.068 0.006 -0.075 -0.045 -0.086 -0.046 0.010 0.039 PACF -0.092 0.014 0.072 0.018 -0.077 -0.065 -0.096 -0.052 0.015 0.055 95% C.L. 0.129 0.130 0.130 0.131 0.131 0.132 0.132 0.133 0.133 0.133 |------------------ 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 0.009 -0.093 |---------- 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 0.000 0.006 0.075 0.006 -0.080 -0.059 -0.095 -0.054 0.012 0.038 PACF 0.000 0.006 0.075 0.006 -0.081 -0.066 -0.096 -0.044 0.023 0.050 95% C.L. 0.129 0.129 0.129 0.130 0.130 0.131 0.131 0.132 0.133 0.133 |----------------- 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 0.006 0.000 0.006 |========================= 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 1756 1995 240 0.994 0.171 -0.337 3.206 0.119 0.615 |------------ 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 0.612 0.488 0.355 0.207 0.068 -0.005 -0.063 -0.066 -0.050 -0.045 PACF 0.612 0.181 -0.001 -0.098 -0.117 -0.027 -0.018 0.038 0.038 -0.011 95% C.L. 0.129 0.171 0.193 0.203 0.207 0.207 0.207 0.207 0.208 0.208 |------------------- 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 0.403 0.507 0.181 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.19 MINUTES