RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit020w.rwl LOG FILE PROCESSED: brit020w.rwl_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: 569 1 Glen Derry WIDTH_RING PISY - 569 2 Great Britain Scots pine, Scotch pine 457 5701-334 1773 1978 - 569 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 2 569012 MISSING VALUES FOUND: 1 IN 1 GAPS / 1970 1970 / -------------------------------------------------------------------- 3 569021 MISSING VALUES FOUND: 1 IN 1 GAPS / 1821 1821 / -------------------------------------------------------------------- 7 569041 MISSING VALUES FOUND: 1 IN 1 GAPS / 1879 1879 / -------------------------------------------------------------------- 20 568102 MISSING VALUES FOUND: 1 IN 1 GAPS / 1953 1953 / -------------------------------------------------------------------- 21 568111 MISSING VALUES FOUND: 1 IN 1 GAPS / 1928 1928 / -------------------------------------------------------------------- 22 568112 MISSING VALUES FOUND: 13 IN 1 GAPS / 1907 1919 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 569011 1814 1978 165 1.896 0.919 2.178 13.003 0.202 0.763 2 569012 1773 1978 206 0.824 0.466 1.200 3.923 0.210 0.881 3 569021 1779 1978 200 1.089 0.653 1.499 4.272 0.206 0.898 4 569022 1809 1978 170 0.917 0.417 1.004 4.075 0.217 0.815 5 569031 1779 1978 200 0.871 0.528 0.720 2.550 0.221 0.910 6 569032 1806 1978 173 0.782 0.514 0.715 2.507 0.211 0.911 7 569041 1823 1978 156 1.451 0.771 1.003 3.420 0.218 0.856 8 569042 1820 1978 159 1.302 0.676 1.358 4.597 0.192 0.871 9 569051 1811 1978 168 1.230 1.057 1.620 4.701 0.216 0.919 10 569052 1784 1978 195 1.147 0.466 1.014 4.192 0.176 0.818 11 569061 1838 1978 141 1.600 0.600 0.943 4.200 0.198 0.781 12 569062 1796 1978 183 0.883 0.352 0.845 3.844 0.234 0.717 13 569071 1817 1978 162 1.013 0.517 1.833 7.143 0.252 0.691 14 569072 1790 1978 189 0.756 0.479 1.942 7.376 0.293 0.777 15 569081 1864 1978 115 1.496 0.374 0.630 3.096 0.161 0.690 16 569082 1810 1978 169 1.289 0.512 0.702 3.010 0.164 0.881 17 569091 1833 1978 146 1.647 0.574 0.267 2.782 0.177 0.792 18 569092 1833 1978 146 1.615 0.423 0.423 2.367 0.140 0.795 19 568101 1846 1978 133 1.429 0.568 1.760 8.099 0.186 0.769 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 568102 1808 1978 171 1.114 0.710 1.431 4.605 0.184 0.907 21 568111 1786 1978 193 1.249 0.869 1.504 4.813 0.213 0.928 22 568112 1773 2088 316 1.601 0.920 0.535 2.353 0.170 0.909 23 568122 1801 1978 178 1.203 0.539 0.267 2.875 0.208 0.821 24 572131 1878 1978 101 0.738 0.279 0.991 4.286 0.253 0.699 25 572132 1856 1978 123 1.862 0.673 0.883 3.395 0.220 0.713 NUMBER OF SERIES READ IN: 25 FROM 1773 TO 2088 316 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 170 1.240 0.594 1.091 4.459 0.205 0.821 STANDARD DEVIATION 38 0.346 0.194 0.526 2.336 0.033 0.080 MEDIAN (50TH QUANTILE) 169 1.230 0.539 1.003 4.075 0.208 0.818 INTERQUARTILE RANGE 43 0.578 0.210 0.784 1.595 0.033 0.130 MINIMUM VALUE 101 0.738 0.279 0.267 2.353 0.140 0.690 LOWER HINGE (25TH QUANTILE) 146 0.917 0.466 0.715 3.010 0.184 0.769 UPPER HINGE (75TH QUANTILE) 189 1.496 0.676 1.499 4.605 0.218 0.898 MAXIMUM VALUE 303 1.896 1.057 2.178 13.003 0.293 0.928 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 300 0.430 0.306 0.018 -1.334 4.949 -0.644 0.870 MINIMUM CORRELATION: -0.644 SERIES 569091 AND 568112 146 YEARS MAXIMUM CORRELATION: 0.870 SERIES 569042 AND 569051 159 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 47.33 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1798. 1830. 1855. 1880. 1905. 1930. CORR 1. 36. 153. 231. 300. 300. RBAR 0.336 0.478 0.378 0.205 0.289 0.183 SDEV 0.000 0.293 0.218 0.238 0.287 0.230 SERR 0.000 0.049 0.018 0.016 0.017 0.013 EPS 0.815 0.943 0.931 0.863 0.911 0.848 NSS 8.7 17.9 22.2 24.3 25.0 25.0 |======================== 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 1773 2088 316 1.393 0.601 0.938 3.821 0.150 0.861 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.053 0.029 0.349 97 219 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.41 0.82 1.00 1.18 2.00 5.38 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.00 0.89 0.00 0.00 0.89 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 169. 43. 101. 146. 189. 316. |----------- 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 0.858 0.742 0.649 0.578 0.530 0.483 0.442 0.419 0.381 0.373 PACF 0.858 0.023 0.026 0.042 0.063 0.002 0.011 0.067 -0.049 0.103 95% C.L. 0.113 0.177 0.213 0.236 0.254 0.267 0.278 0.287 0.295 0.301 |------------------ 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 1 0.746 0.863 |================== 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 569011 3 0.00000000 0.00000000 -0.00399308 2.22730446 2 569012 1 1.47639322 0.02447983 0.00000000 0.53455538 3 569021 1 2.40901089 0.02567461 0.00000000 0.62927550 4 569022 1 1.43222070 0.01415124 0.00000000 0.37944576 5 569031 3 0.00000000 0.00000000 -0.00746242 1.62112355 6 569032 3 0.00000000 0.00000000 -0.00783925 1.46444285 7 569041 1 2.53121090 0.01763925 0.00000000 0.59801960 8 569042 1 2.33962512 0.02533900 0.00000000 0.73920840 9 569051 1 4.15852261 0.03097745 0.00000000 0.44720867 10 569052 1 1.25425780 0.01356895 0.00000000 0.70968020 11 569061 3 0.00000000 0.00000000 -0.00480770 1.94134653 12 569062 1 1.04662657 0.03570198 0.00000000 0.72637820 13 569071 1 1.61872137 0.03296643 0.00000000 0.71670192 14 569072 1 1.87526572 0.04296215 0.00000000 0.52971095 15 569081 3 0.00000000 0.00000000 -0.00692188 1.89712131 16 569082 1 2.06287861 0.00814987 0.00000000 0.17345491 17 569091 3 0.00000000 0.00000000 -0.00934729 2.33449125 18 569092 1 1.62161970 0.00867214 0.00000000 0.69927329 19 568101 3 0.00000000 0.00000000 -0.00390437 1.69038963 SERIES IDENT OPTION A B C D 20 568102 1 2.45163035 0.03170783 0.00000000 0.66585118 21 568111 1 3.32073665 0.02918362 0.00000000 0.66546673 22 568112 1 2.50115871 0.07499279 0.00000000 1.51712668 23 568122 3 0.00000000 0.00000000 -0.00700882 1.83060372 24 572131 1 0.88519442 0.06882081 0.00000000 0.61531973 25 572132 1 2.02996516 0.02189638 0.00000000 1.16651070 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 569011 1814 1978 165 1.000 0.487 2.344 13.057 0.201 0.762 2 569012 1773 1978 206 1.000 0.418 2.027 9.284 0.209 0.729 3 569021 1779 1978 200 1.002 0.274 0.237 2.717 0.203 0.589 4 569022 1809 1978 170 0.999 0.243 0.394 3.628 0.215 0.401 5 569031 1779 1978 200 1.056 0.461 1.615 7.670 0.220 0.732 6 569032 1806 1978 173 1.067 0.692 3.575 20.445 0.214 0.774 7 569041 1823 1978 156 0.999 0.310 0.873 4.037 0.217 0.621 8 569042 1820 1978 159 0.999 0.263 0.674 3.576 0.192 0.565 9 569051 1811 1978 168 0.996 0.367 1.563 7.245 0.215 0.689 10 569052 1784 1978 195 1.000 0.296 0.378 2.659 0.176 0.733 11 569061 1838 1978 141 0.998 0.356 1.143 4.462 0.196 0.754 12 569062 1796 1978 183 1.000 0.318 0.608 3.473 0.233 0.541 13 569071 1817 1978 162 1.000 0.319 0.593 3.845 0.249 0.419 14 569072 1790 1978 189 1.000 0.379 0.908 4.225 0.290 0.499 15 569081 1864 1978 115 1.000 0.192 0.518 3.432 0.160 0.500 16 569082 1810 1978 169 1.000 0.204 0.141 2.583 0.163 0.549 17 569091 1833 1978 146 0.997 0.254 0.402 3.863 0.176 0.616 18 569092 1833 1978 146 1.000 0.162 -0.256 2.899 0.139 0.456 19 568101 1846 1978 133 0.999 0.379 1.639 7.386 0.185 0.741 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 568102 1808 1978 171 1.001 0.388 0.405 2.754 0.186 0.810 21 568111 1786 1978 193 1.000 0.383 1.057 4.781 0.211 0.753 22 568112 1773 2088 316 0.999 0.561 0.685 2.789 0.172 0.905 23 568122 1801 1978 178 0.987 0.346 0.514 2.866 0.207 0.688 24 572131 1878 1978 101 1.000 0.286 0.614 3.723 0.250 0.429 25 572132 1856 1978 123 1.000 0.228 -0.003 2.780 0.219 0.330 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 170 1.004 0.343 0.906 5.207 0.204 0.623 STANDARD DEVIATION 40 0.018 0.119 0.840 4.051 0.032 0.150 MEDIAN (50TH QUANTILE) 169 1.000 0.319 0.614 3.723 0.207 0.621 INTERQUARTILE RANGE 43 0.001 0.120 0.741 1.915 0.032 0.240 MINIMUM VALUE 101 0.987 0.162 -0.256 2.583 0.139 0.330 LOWER HINGE (25TH QUANTILE) 146 0.999 0.263 0.402 2.866 0.185 0.500 UPPER HINGE (75TH QUANTILE) 189 1.000 0.383 1.143 4.781 0.217 0.741 MAXIMUM VALUE 316 1.067 0.692 3.575 20.445 0.290 0.905 |------------------------ 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 569011 -67 110 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 569012 -67 138 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 569021 -67 134 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 569022 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 569031 -67 134 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 569032 -67 115 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 569041 -67 104 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 569042 -67 106 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 569051 -67 112 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 569052 -67 130 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 569061 -67 94 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 569062 -67 122 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 569071 -67 108 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 569072 -67 126 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 569081 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 569082 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 569091 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 569092 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 568101 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 568102 -67 114 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 568111 -67 129 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 568112 -67 211 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 568122 -67 119 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 572131 -67 67 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 25 572132 -67 82 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 569011 1814 1978 165 0.990 0.454 2.436 14.414 0.200 0.741 2 569012 1773 1978 206 0.996 0.391 1.977 9.186 0.209 0.712 3 569021 1779 1978 200 0.995 0.240 0.208 2.738 0.203 0.481 4 569022 1809 1978 170 0.998 0.228 0.405 3.873 0.215 0.309 5 569031 1779 1978 200 0.997 0.356 0.707 4.014 0.220 0.689 6 569032 1806 1978 173 0.978 0.409 0.817 3.508 0.212 0.760 7 569041 1823 1978 156 0.999 0.306 0.885 4.171 0.217 0.613 8 569042 1820 1978 159 0.998 0.232 0.414 3.104 0.191 0.470 9 569051 1811 1978 168 0.996 0.292 1.273 6.328 0.215 0.536 10 569052 1784 1978 195 0.993 0.257 0.242 2.778 0.175 0.660 11 569061 1838 1978 141 0.998 0.291 0.725 3.478 0.195 0.625 12 569062 1796 1978 183 0.999 0.313 0.603 3.389 0.233 0.525 13 569071 1817 1978 162 0.999 0.312 0.583 3.649 0.249 0.403 14 569072 1790 1978 189 0.999 0.368 0.825 4.141 0.290 0.480 15 569081 1864 1978 115 0.998 0.180 0.399 3.232 0.160 0.434 16 569082 1810 1978 169 0.999 0.200 0.096 2.557 0.163 0.531 17 569091 1833 1978 146 0.998 0.235 0.346 3.761 0.175 0.566 18 569092 1833 1978 146 0.999 0.155 -0.051 3.058 0.139 0.415 19 568101 1846 1978 133 0.997 0.346 1.166 5.243 0.184 0.709 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 568102 1808 1978 171 0.998 0.378 0.470 3.204 0.186 0.805 21 568111 1786 1978 193 0.997 0.373 1.116 4.902 0.211 0.742 22 568112 1773 2088 316 0.961 0.377 0.492 3.284 0.172 0.834 23 568122 1801 1978 178 0.997 0.309 0.637 3.270 0.206 0.586 24 572131 1878 1978 101 0.998 0.273 0.560 3.805 0.249 0.384 25 572132 1856 1978 123 0.999 0.225 -0.048 2.751 0.219 0.314 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 170 0.995 0.300 0.691 4.314 0.204 0.573 STANDARD DEVIATION 40 0.008 0.077 0.573 2.521 0.032 0.152 MEDIAN (50TH QUANTILE) 169 0.998 0.306 0.583 3.508 0.206 0.566 INTERQUARTILE RANGE 43 0.003 0.133 0.426 0.937 0.033 0.238 MINIMUM VALUE 101 0.961 0.155 -0.051 2.557 0.139 0.309 LOWER HINGE (25TH QUANTILE) 146 0.996 0.235 0.399 3.204 0.184 0.470 UPPER HINGE (75TH QUANTILE) 189 0.999 0.368 0.825 4.141 0.217 0.709 MAXIMUM VALUE 316 0.999 0.454 2.436 14.414 0.290 0.834 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 300 0.186 0.156 0.009 -0.312 3.335 -0.289 0.676 MINIMUM CORRELATION: -0.289 SERIES 569012 AND 569051 168 YEARS MAXIMUM CORRELATION: 0.676 SERIES 569081 AND 569082 115 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 47.33 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1798. 1830. 1855. 1880. 1905. 1930. CORR 1. 36. 153. 231. 300. 300. RBAR -0.425 0.215 0.244 0.214 0.232 0.168 SDEV 0.000 0.215 0.207 0.226 0.228 0.216 SERR 0.000 0.036 0.017 0.015 0.013 0.012 EPS 1.627 0.831 0.878 0.869 0.883 0.835 NSS 8.7 17.9 22.2 24.3 25.0 25.0 |======================== 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 1773 2088 316 0.972 0.218 0.395 3.348 0.172 0.528 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.146 0.090 0.077 85 231 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.22 0.46 1.01 1.06 1.52 4.17 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.80 0.91 0.00 0.00 0.91 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 0.526 0.299 0.119 0.074 0.033 0.075 0.052 -0.005 -0.071 -0.051 PACF 0.526 0.031 -0.069 0.041 -0.010 0.078 -0.019 -0.066 -0.061 0.031 95% C.L. 0.113 0.140 0.148 0.149 0.150 0.150 0.150 0.151 0.151 0.151 |------------------ 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 0.279 0.528 |======================= 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 0.314 0.101 -0.058 -0.045 -0.074 0.017 0.015 -0.059 -0.097 -0.013 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 0.314 2 0.314 0.002 3 0.314 0.034 -0.100 4 0.314 0.034 -0.101 0.002 5 0.314 0.028 -0.099 0.019 -0.055 6 0.317 0.027 -0.093 0.017 -0.073 0.057 7 0.317 0.027 -0.093 0.017 -0.073 0.058 -0.002 8 0.317 0.032 -0.100 0.019 -0.081 0.060 0.026 -0.090 9 0.312 0.034 -0.096 0.014 -0.080 0.055 0.028 -0.072 -0.058 10 0.315 0.037 -0.098 0.011 -0.076 0.054 0.033 -0.073 -0.074 0.051 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) 2368.35 2337.49 2339.49 2338.31 2340.31 2341.35 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 2342.31 2344.31 2343.75 2344.70 2345.89 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 0.314 R-SQUARED DUE TO POOLED AUTOREGRESSION: 9.88 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 110.96 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.314 0.099 0.031 0.010 0.003 0.001 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 569011 1 0.556 0.742 2 569012 1 0.526 0.714 3 569021 1 0.251 0.481 4 569022 1 0.105 0.309 5 569031 1 0.509 0.700 6 569032 1 0.636 0.796 7 569041 1 0.377 0.613 8 569042 1 0.234 0.471 9 569051 1 0.302 0.550 10 569052 1 0.441 0.664 11 569061 1 0.412 0.642 12 569062 1 0.287 0.525 13 569071 1 0.163 0.404 14 569072 1 0.231 0.480 15 569081 1 0.193 0.437 16 569082 1 0.284 0.532 17 569091 1 0.326 0.571 18 569092 1 0.173 0.416 19 568101 1 0.508 0.712 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 568102 1 0.653 0.806 21 568111 1 0.555 0.743 22 568112 1 0.698 0.835 23 568122 1 0.348 0.587 24 572131 1 0.151 0.388 25 572132 1 0.100 0.316 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.361 0.577 STANDARD DEVIATION 0 0.179 0.155 MEDIAN 1 0.326 0.571 INTERQUARTILE RANGE 0 0.279 0.241 MINIMUM VALUE 1 0.100 0.309 LOWER HINGE 1 0.231 0.471 UPPER HINGE 1 0.509 0.712 MAXIMUM VALUE 1 0.698 0.835 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 569011 1814 1978 165 1.000 0.304 3.452 26.904 0.257 0.084 2 569012 1773 1978 206 1.000 0.274 1.968 11.987 0.274 -0.126 3 569021 1779 1978 200 1.000 0.210 0.359 3.112 0.241 -0.075 4 569022 1809 1978 170 1.000 0.217 0.500 3.579 0.246 -0.032 5 569031 1779 1978 200 1.000 0.254 0.959 6.783 0.248 0.143 6 569032 1806 1978 173 1.000 0.247 0.099 3.665 0.278 -0.023 7 569041 1823 1978 156 1.000 0.241 0.758 3.898 0.272 -0.026 8 569042 1820 1978 159 1.000 0.204 0.226 2.746 0.228 0.060 9 569051 1811 1978 168 1.000 0.244 1.030 5.750 0.260 0.021 10 569052 1784 1978 195 1.000 0.192 0.323 3.694 0.225 -0.022 11 569061 1838 1978 141 1.000 0.223 0.666 3.066 0.237 0.032 12 569062 1796 1978 183 1.000 0.266 0.628 3.230 0.297 -0.066 13 569071 1817 1978 162 1.000 0.285 0.840 4.861 0.286 -0.001 14 569072 1790 1978 189 1.000 0.323 0.691 3.684 0.346 0.006 15 569081 1864 1978 115 1.000 0.162 0.172 3.247 0.192 -0.024 16 569082 1810 1978 169 1.000 0.169 0.104 2.595 0.205 -0.022 17 569091 1833 1978 146 1.000 0.193 0.160 3.372 0.214 0.010 18 569092 1833 1978 146 1.000 0.141 0.094 2.637 0.162 0.000 19 568101 1846 1978 133 1.000 0.243 -0.006 5.013 0.262 -0.040 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 568102 1808 1978 171 1.000 0.224 0.131 3.193 0.239 0.082 21 568111 1786 1978 193 1.000 0.249 0.705 4.919 0.269 0.065 22 568112 1773 2088 316 1.000 0.207 0.645 4.684 0.224 -0.045 23 568122 1801 1978 178 1.000 0.250 0.596 3.732 0.255 0.043 24 572131 1878 1978 101 1.000 0.252 0.244 3.084 0.284 0.011 25 572132 1856 1978 123 1.000 0.213 0.017 2.596 0.248 -0.005 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 170 1.000 0.232 0.615 5.041 0.250 0.002 STANDARD DEVIATION 40 0.000 0.043 0.733 4.949 0.037 0.057 MEDIAN (50TH QUANTILE) 169 1.000 0.241 0.500 3.665 0.248 -0.001 INTERQUARTILE RANGE 43 0.000 0.044 0.545 1.749 0.044 0.057 MINIMUM VALUE 101 1.000 0.141 -0.006 2.595 0.162 -0.126 LOWER HINGE (25TH QUANTILE) 146 1.000 0.207 0.160 3.112 0.228 -0.026 UPPER HINGE (75TH QUANTILE) 189 1.000 0.252 0.705 4.861 0.272 0.032 MAXIMUM VALUE 316 1.000 0.323 3.452 26.904 0.346 0.143 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 300 0.305 0.108 0.006 -0.157 3.290 -0.024 0.646 MINIMUM CORRELATION: -0.024 SERIES 569012 AND 569051 168 YEARS MAXIMUM CORRELATION: 0.646 SERIES 569091 AND 569092 146 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 47.33 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1798. 1830. 1855. 1880. 1905. 1930. CORR 1. 36. 153. 231. 300. 300. RBAR -0.012 0.263 0.329 0.377 0.364 0.278 SDEV 0.000 0.143 0.147 0.139 0.140 0.143 SERR 0.000 0.024 0.012 0.009 0.008 0.008 EPS -0.112 0.865 0.916 0.936 0.935 0.906 NSS 8.7 17.9 22.2 24.3 25.0 25.0 |======================== 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 1773 2088 316 0.992 0.162 0.282 3.709 0.195 -0.127 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.099 0.058 0.058 80 236 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.18 0.60 1.00 1.07 1.67 11.51 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.79 0.91 0.00 0.00 0.91 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 -0.127 -0.061 -0.081 -0.031 -0.075 0.040 0.040 -0.003 -0.095 -0.059 PACF -0.127 -0.078 -0.101 -0.063 -0.106 -0.003 0.022 -0.010 -0.101 -0.094 95% C.L. 0.113 0.114 0.115 0.115 0.116 0.116 0.116 0.116 0.116 0.117 |------------------ 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 0.022 -0.127 |---------- 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 -0.010 -0.089 -0.095 -0.052 -0.076 0.037 0.046 -0.010 -0.106 -0.066 PACF -0.010 -0.089 -0.098 -0.064 -0.098 0.012 0.019 -0.024 -0.109 -0.078 95% C.L. 0.113 0.113 0.113 0.114 0.115 0.115 0.116 0.116 0.116 0.117 |----------------- 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 0.008 -0.010 |========================= 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 1773 2088 316 0.992 0.167 0.415 4.203 0.165 0.269 |------------ 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 0.268 -0.033 -0.120 -0.104 -0.090 0.015 0.034 -0.033 -0.122 -0.078 PACF 0.268 -0.113 -0.087 -0.054 -0.065 0.041 -0.005 -0.064 -0.109 -0.023 95% C.L. 0.113 0.120 0.120 0.122 0.123 0.124 0.124 0.124 0.124 0.126 |------------------- 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 3 0.094 0.289 -0.088 -0.087 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.23 MINUTES