RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit015l.rwl LOG FILE PROCESSED: brit015l.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: 380 1 Inverey WIDTH_LATE PISY - 380 2 Great Britain Scots pine, Scotch pine 500 5700-335 1706 1976 - 380 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 3 380021 MISSING VALUES FOUND: 20 IN 1 GAPS / 1880 1899 / -------------------------------------------------------------------- 4 380022 MISSING VALUES FOUND: 12 IN 1 GAPS / 1915 1926 / -------------------------------------------------------------------- 7 380041 MISSING VALUES FOUND: 19 IN 1 GAPS / 1874 1892 / -------------------------------------------------------------------- 14 381072 MISSING VALUES FOUND: 5 IN 1 GAPS / 1962 1966 / -------------------------------------------------------------------- 17 381091 MISSING VALUES FOUND: 12 IN 1 GAPS / 1881 1892 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 380011 1717 1976 260 0.247 0.147 0.812 3.523 0.343 0.739 2 380012 1731 1976 246 0.301 0.193 1.844 7.008 0.297 0.770 3 380021 1706 1976 271 0.320 0.181 0.735 3.301 0.249 0.823 4 380022 1720 1976 257 0.332 0.248 1.006 3.621 0.285 0.856 5 380031 1754 1976 223 0.319 0.251 3.645 23.384 0.324 0.756 6 380032 1792 1976 185 0.384 0.185 1.652 6.547 0.315 0.641 7 380041 1754 1976 223 0.567 0.502 2.102 7.918 0.276 0.851 8 380042 1738 1848 111 0.545 0.247 0.891 3.552 0.325 0.554 9 380051 1744 1976 233 0.360 0.214 0.959 3.365 0.319 0.754 10 381052 1731 1976 246 0.309 0.282 4.093 24.971 0.346 0.740 11 381061 1809 1976 168 0.299 0.155 0.948 4.067 0.375 0.555 12 381062 1750 1976 227 0.341 0.188 0.875 3.384 0.354 0.655 13 381071 1754 1976 223 0.267 0.201 1.131 4.334 0.635 0.603 14 381072 1775 1976 202 0.305 0.255 1.088 3.764 0.610 0.750 15 381081 1731 1975 245 0.274 0.181 1.560 5.660 0.355 0.653 16 381082 1721 1976 256 0.276 0.184 1.918 9.383 0.385 0.609 17 381091 1724 1976 253 0.293 0.204 1.802 6.571 0.332 0.761 18 381092 1724 1976 253 0.366 0.265 1.579 5.509 0.340 0.771 19 382101 1716 1976 261 0.393 0.281 1.046 3.798 0.393 0.751 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 382102 1763 1976 214 0.385 0.311 2.049 8.101 0.360 0.752 21 382111 1793 1976 184 0.450 0.265 1.105 4.140 0.342 0.652 22 382112 1769 1976 208 0.286 0.190 1.705 7.444 0.471 0.650 23 382121 1784 1976 193 0.280 0.179 0.932 3.680 0.434 0.684 24 382122 1783 1976 194 0.344 0.275 1.633 7.835 0.486 0.635 NUMBER OF SERIES READ IN: 24 FROM 1706 TO 1976 271 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 220 0.343 0.233 1.546 6.869 0.373 0.707 STANDARD DEVIATION 35 0.081 0.073 0.836 5.653 0.095 0.086 MEDIAN (50TH QUANTILE) 225 0.320 0.209 1.346 4.922 0.344 0.739 INTERQUARTILE RANGE 50 0.085 0.081 0.869 3.989 0.067 0.113 MINIMUM VALUE 111 0.247 0.147 0.735 3.301 0.249 0.554 LOWER HINGE (25TH QUANTILE) 195 0.290 0.185 0.954 3.650 0.322 0.646 UPPER HINGE (75TH QUANTILE) 246 0.375 0.265 1.823 7.640 0.389 0.759 MAXIMUM VALUE 261 0.567 0.502 4.093 24.971 0.635 0.856 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.506 0.169 0.010 -0.432 2.469 0.033 0.873 MINIMUM CORRELATION: 0.033 SERIES 380021 AND 382111 184 YEARS MAXIMUM CORRELATION: 0.873 SERIES 381091 AND 381092 253 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 73.91 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1760. 1785. 1810. 1835. 1860. 1885. 1910. 1935. CORR 45. 120. 210. 253. 253. 253. 253. 253. RBAR 0.450 0.642 0.462 0.378 0.355 0.441 0.272 0.268 SDEV 0.200 0.157 0.182 0.223 0.230 0.247 0.231 0.217 SERR 0.030 0.014 0.013 0.014 0.014 0.016 0.015 0.014 EPS 0.926 0.973 0.952 0.935 0.928 0.948 0.896 0.894 NSS 15.3 20.2 23.2 23.8 23.3 23.0 23.0 23.0 |======================== 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 1706 1976 271 0.345 0.177 0.834 3.143 0.240 0.806 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.748 0.330 0.034 129 142 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.55 1.65 1.01 1.17 2.81 10.39 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.00 0.86 0.94 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 225. 55. 111. 198. 253. 271. |----------- 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 0.803 0.746 0.725 0.714 0.669 0.673 0.647 0.637 0.641 0.630 PACF 0.803 0.283 0.207 0.161 0.008 0.131 0.015 0.057 0.097 0.026 95% C.L. 0.121 0.184 0.224 0.256 0.284 0.307 0.328 0.346 0.363 0.379 |------------------ 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 4 0.701 0.475 0.139 0.129 0.167 |================== 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 380011 3 0.00000000 0.00000000 -0.00140177 0.43004632 2 380012 1 0.67704147 0.03059674 0.00000000 0.21244447 3 380021 3 0.00000000 0.00000000 -0.00163315 0.52847135 4 380022 1 0.72364998 0.01156078 0.00000000 0.09025584 5 380031 1 0.63720655 0.00975161 0.00000000 0.06057793 6 380032 3 0.00000000 0.00000000 -0.00148433 0.52242070 7 380041 1 1.67128193 0.02022086 0.00000000 0.15986620 8 380042 1 0.70821536 0.01120525 0.00000000 0.14252950 9 380051 1 0.63728708 0.01140794 0.00000000 0.13838872 10 381052 1 1.23242116 0.05444696 0.00000000 0.21961707 11 381061 3 0.00000000 0.00000000 -0.00152397 0.42800185 12 381062 3 0.00000000 0.00000000 -0.00140659 0.50127673 13 381071 1 0.37542662 0.06808957 0.00000000 0.24260962 14 381072 3 0.00000000 0.00000000 -0.00269458 0.57564771 15 381081 3 0.00000000 0.00000000 -0.00139168 0.44517663 16 381082 3 0.00000000 0.00000000 -0.00116603 0.42592829 17 381091 1 0.71873468 0.02701540 0.00000000 0.18076301 18 381092 1 0.93445677 0.02355957 0.00000000 0.21111813 19 382101 3 0.00000000 0.00000000 -0.00258329 0.73097819 SERIES IDENT OPTION A B C D 20 382102 1 0.77165323 0.01834583 0.00000000 0.19395849 21 382111 3 0.00000000 0.00000000 -0.00073509 0.51772451 22 382112 1 0.14008728 0.10154943 0.00000000 0.27994883 23 382121 3 0.00000000 0.00000000 -0.00067110 0.34468263 24 382122 3 0.00000000 0.00000000 -0.00288969 0.62607443 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 380011 1717 1976 260 0.997 0.422 0.777 3.698 0.342 0.463 2 380012 1731 1976 246 1.001 0.426 1.171 5.183 0.296 0.546 3 380021 1706 1976 271 1.028 0.532 1.887 8.143 0.243 0.783 4 380022 1720 1976 257 1.004 0.654 1.751 7.357 0.282 0.798 5 380031 1754 1976 223 1.002 0.468 2.337 12.743 0.323 0.553 6 380032 1792 1976 185 1.001 0.408 1.145 4.622 0.313 0.524 7 380041 1754 1976 223 1.006 0.562 0.777 4.069 0.286 0.766 8 380042 1738 1848 111 1.000 0.386 1.292 5.653 0.323 0.440 9 380051 1744 1976 233 0.998 0.431 1.189 5.267 0.318 0.494 10 381052 1731 1976 246 1.002 0.481 1.495 7.303 0.344 0.441 11 381061 1809 1976 168 0.997 0.453 0.858 3.761 0.373 0.391 12 381062 1750 1976 227 0.997 0.476 0.849 3.883 0.352 0.581 13 381071 1754 1976 223 1.000 0.748 1.203 4.523 0.632 0.619 14 381072 1775 1976 202 1.116 0.985 2.004 7.883 0.606 0.548 15 381081 1731 1975 245 1.005 0.511 0.960 3.532 0.353 0.588 16 381082 1721 1976 256 0.991 0.574 2.254 12.062 0.384 0.529 17 381091 1724 1976 253 1.000 0.462 1.341 5.928 0.327 0.528 18 381092 1724 1976 253 1.000 0.467 1.238 6.121 0.339 0.530 19 382101 1716 1976 261 1.052 0.615 1.411 6.033 0.392 0.650 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 382102 1763 1976 214 0.996 0.569 1.249 4.471 0.358 0.633 21 382111 1793 1976 184 0.999 0.583 1.153 4.283 0.341 0.651 22 382112 1769 1976 208 1.000 0.669 1.801 7.932 0.468 0.653 23 382121 1784 1976 193 0.997 0.628 0.867 3.419 0.432 0.665 24 382122 1783 1976 194 0.993 0.666 1.625 6.371 0.484 0.600 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 222 1.008 0.549 1.360 6.010 0.371 0.582 STANDARD DEVIATION 37 0.026 0.134 0.452 2.465 0.094 0.106 MEDIAN (50TH QUANTILE) 225 1.000 0.522 1.244 5.460 0.343 0.567 INTERQUARTILE RANGE 55 0.006 0.164 0.636 3.154 0.068 0.124 MINIMUM VALUE 111 0.991 0.386 0.777 3.419 0.243 0.391 LOWER HINGE (25TH QUANTILE) 198 0.997 0.457 1.052 4.176 0.320 0.526 UPPER HINGE (75TH QUANTILE) 253 1.003 0.621 1.688 7.330 0.388 0.650 MAXIMUM VALUE 271 1.116 0.985 2.337 12.743 0.632 0.798 |------------------------ 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 380011 -67 174 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 380012 -67 164 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 380021 -67 181 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 380022 -67 172 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 380031 -67 149 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 380032 -67 123 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 380041 -67 149 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 380042 -67 74 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 380051 -67 156 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 381052 -67 164 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 381061 -67 112 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 381062 -67 152 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 381071 -67 149 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 381072 -67 135 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 381081 -67 164 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 381082 -67 171 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 381091 -67 169 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 381092 -67 169 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 382101 -67 174 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 382102 -67 143 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 382111 -67 123 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 382112 -67 139 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 382121 -67 129 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 382122 -67 129 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 380011 1717 1976 260 0.995 0.402 0.762 4.054 0.342 0.407 2 380012 1731 1976 246 0.997 0.411 1.120 5.067 0.296 0.519 3 380021 1706 1976 271 0.991 0.410 0.799 3.497 0.243 0.688 4 380022 1720 1976 257 0.963 0.553 1.765 7.510 0.282 0.759 5 380031 1754 1976 223 0.997 0.456 2.400 13.318 0.323 0.539 6 380032 1792 1976 185 0.992 0.373 0.980 4.077 0.313 0.441 7 380041 1754 1976 223 0.980 0.499 0.588 3.814 0.286 0.719 8 380042 1738 1848 111 0.997 0.368 1.099 4.977 0.322 0.394 9 380051 1744 1976 233 0.995 0.404 1.058 4.961 0.318 0.443 10 381052 1731 1976 246 0.997 0.475 1.580 7.681 0.344 0.438 11 381061 1809 1976 168 0.994 0.433 0.983 4.338 0.372 0.325 12 381062 1750 1976 227 0.990 0.440 0.690 3.525 0.352 0.509 13 381071 1754 1976 223 0.979 0.662 0.804 3.378 0.632 0.566 14 381072 1775 1976 202 0.961 0.621 1.097 6.006 0.606 0.392 15 381081 1731 1975 245 0.996 0.499 1.002 3.664 0.353 0.581 16 381082 1721 1976 256 0.993 0.526 1.756 8.516 0.384 0.468 17 381091 1724 1976 253 0.997 0.441 1.172 5.275 0.327 0.496 18 381092 1724 1976 253 0.996 0.439 0.987 5.066 0.339 0.481 19 382101 1716 1976 261 0.983 0.494 0.929 3.888 0.391 0.546 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 382102 1763 1976 214 0.992 0.540 1.226 4.607 0.358 0.593 21 382111 1793 1976 184 0.996 0.537 1.040 3.796 0.341 0.612 22 382112 1769 1976 208 0.995 0.647 1.698 7.496 0.468 0.638 23 382121 1784 1976 193 0.995 0.618 0.956 3.556 0.433 0.657 24 382122 1783 1976 194 0.992 0.648 1.532 5.912 0.485 0.581 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 222 0.990 0.496 1.168 5.333 0.371 0.533 STANDARD DEVIATION 37 0.010 0.091 0.421 2.264 0.094 0.111 MEDIAN (50TH QUANTILE) 225 0.995 0.485 1.049 4.784 0.343 0.529 INTERQUARTILE RANGE 55 0.006 0.125 0.436 2.154 0.068 0.161 MINIMUM VALUE 111 0.961 0.368 0.588 3.378 0.243 0.325 LOWER HINGE (25TH QUANTILE) 198 0.990 0.422 0.943 3.805 0.320 0.442 UPPER HINGE (75TH QUANTILE) 253 0.996 0.547 1.379 5.959 0.388 0.603 MAXIMUM VALUE 271 0.997 0.662 2.400 13.318 0.632 0.759 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.369 0.132 0.008 -0.014 3.217 0.012 0.766 MINIMUM CORRELATION: 0.012 SERIES 382101 AND 382121 193 YEARS MAXIMUM CORRELATION: 0.766 SERIES 380042 AND 382112 80 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 73.91 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1760. 1785. 1810. 1835. 1860. 1885. 1910. 1935. CORR 45. 120. 210. 253. 253. 253. 253. 253. RBAR 0.547 0.591 0.522 0.372 0.340 0.400 0.326 0.263 SDEV 0.123 0.154 0.195 0.223 0.219 0.229 0.230 0.201 SERR 0.018 0.014 0.013 0.014 0.014 0.014 0.014 0.013 EPS 0.949 0.967 0.962 0.934 0.923 0.939 0.918 0.892 NSS 15.3 20.2 23.2 23.8 23.3 23.0 23.0 23.0 |======================== 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 1706 1976 271 0.960 0.293 0.945 5.252 0.242 0.447 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.565 0.281 0.067 116 155 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.30 0.85 1.00 1.08 1.93 5.99 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.07 0.00 0.86 0.93 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 0.445 0.305 0.204 0.210 0.137 0.176 0.120 0.071 0.069 0.087 PACF 0.445 0.133 0.034 0.102 -0.010 0.095 -0.009 -0.036 0.027 0.031 95% C.L. 0.121 0.144 0.153 0.157 0.161 0.163 0.165 0.167 0.167 0.168 |------------------ 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 0.214 0.387 0.133 |======================= 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 0.468 0.314 0.233 0.231 0.148 0.208 0.162 0.079 0.057 0.074 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 0.468 2 0.411 0.122 3 0.403 0.097 0.061 4 0.397 0.087 0.020 0.102 5 0.400 0.087 0.022 0.111 -0.024 6 0.403 0.073 0.019 0.100 -0.077 0.132 7 0.403 0.073 0.019 0.100 -0.077 0.131 0.003 8 0.403 0.082 0.013 0.107 -0.075 0.136 0.030 -0.069 9 0.403 0.082 0.013 0.107 -0.076 0.136 0.030 -0.070 0.003 10 0.403 0.083 0.012 0.104 -0.074 0.134 0.030 -0.071 -0.004 0.018 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) 2531.64 2466.73 2464.69 2465.69 2464.86 2466.71 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 2463.94 2465.93 2466.65 2468.65 2470.56 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 0.411 0.122 R-SQUARED DUE TO POOLED AUTOREGRESSION: 23.03 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 129.93 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.411 0.290 0.169 0.105 0.064 0.039 0.024 0.014 0.009 0.0054 0.003 0.002 0.001 0.001 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 380011 2 0.169 0.399 0.029 2 380012 2 0.280 0.466 0.106 3 380021 2 0.491 0.580 0.158 4 380022 2 0.608 0.565 0.257 5 380031 2 0.295 0.501 0.071 6 380032 2 0.234 0.393 0.112 7 380041 2 0.527 0.619 0.140 8 380042 2 0.165 0.382 0.040 9 380051 2 0.207 0.404 0.091 10 381052 2 0.226 0.427 0.030 11 381061 2 0.112 0.303 0.070 12 381062 2 0.264 0.482 0.058 13 381071 2 0.330 0.543 0.045 14 381072 2 0.207 0.301 0.238 15 381081 2 0.342 0.567 0.026 16 381082 2 0.231 0.455 0.031 17 381091 2 0.267 0.422 0.150 18 381092 2 0.267 0.390 0.191 19 382101 2 0.351 0.397 0.274 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 382102 2 0.373 0.494 0.171 21 382111 2 0.391 0.586 0.050 22 382112 2 0.457 0.479 0.249 23 382121 2 0.459 0.640 0.041 24 382122 2 0.351 0.599 -0.025 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.317 0.475 0.108 STANDARD DEVIATION 0 0.124 0.096 0.085 MEDIAN 2 0.287 0.473 0.081 INTERQUARTILE RANGE 0 0.153 0.168 0.124 MINIMUM VALUE 2 0.112 0.301 -0.025 LOWER HINGE 2 0.229 0.398 0.040 UPPER HINGE 2 0.382 0.566 0.165 MAXIMUM VALUE 2 0.608 0.640 0.274 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 380011 1717 1976 260 1.000 0.366 0.635 4.038 0.397 0.000 2 380012 1731 1976 246 1.000 0.348 1.078 5.209 0.350 -0.002 3 380021 1706 1976 271 1.000 0.293 0.695 4.458 0.307 -0.014 4 380022 1720 1976 257 1.001 0.344 1.006 6.070 0.344 -0.010 5 380031 1754 1976 223 1.001 0.379 1.928 13.705 0.415 0.001 6 380032 1792 1976 185 1.000 0.333 0.707 3.297 0.368 -0.022 7 380041 1754 1976 223 1.002 0.337 0.673 5.082 0.353 0.009 8 380042 1738 1848 111 1.000 0.337 1.024 4.769 0.363 -0.001 9 380051 1744 1976 233 1.000 0.361 1.301 6.040 0.378 -0.003 10 381052 1731 1976 246 1.000 0.426 1.606 8.139 0.415 -0.006 11 381061 1809 1976 168 1.000 0.408 1.216 5.196 0.416 0.001 12 381062 1750 1976 227 1.000 0.376 0.738 4.264 0.413 0.002 13 381071 1754 1976 223 1.001 0.540 0.785 4.007 0.654 -0.005 14 381072 1775 1976 202 1.001 0.552 1.115 6.234 0.617 -0.016 15 381081 1731 1975 245 1.002 0.399 0.813 3.802 0.429 0.020 16 381082 1721 1976 256 1.000 0.464 1.619 8.050 0.473 -0.002 17 381091 1724 1976 253 1.000 0.379 0.976 4.596 0.400 0.010 18 381092 1724 1976 253 1.000 0.377 1.162 6.042 0.393 0.015 19 382101 1716 1976 261 1.000 0.397 0.723 3.639 0.432 0.001 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 382102 1763 1976 214 1.000 0.428 1.393 6.843 0.434 0.001 21 382111 1793 1976 184 1.001 0.420 0.846 4.449 0.439 -0.008 22 382112 1769 1976 208 1.001 0.480 1.061 4.676 0.501 0.034 23 382121 1784 1976 193 1.000 0.459 0.723 3.630 0.526 0.004 24 382122 1783 1976 194 1.000 0.525 1.038 4.647 0.586 0.001 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 222 1.000 0.405 1.036 5.453 0.433 0.000 STANDARD DEVIATION 37 0.001 0.068 0.341 2.186 0.087 0.012 MEDIAN (50TH QUANTILE) 225 1.000 0.388 1.015 4.722 0.415 0.000 INTERQUARTILE RANGE 55 0.001 0.089 0.459 1.905 0.083 0.009 MINIMUM VALUE 111 1.000 0.293 0.635 3.297 0.307 -0.022 LOWER HINGE (25TH QUANTILE) 198 1.000 0.355 0.730 4.151 0.373 -0.006 UPPER HINGE (75TH QUANTILE) 253 1.001 0.443 1.189 6.056 0.456 0.003 MAXIMUM VALUE 271 1.002 0.552 1.928 13.705 0.654 0.034 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.422 0.091 0.005 0.320 3.390 0.170 0.718 MINIMUM CORRELATION: 0.170 SERIES 380021 AND 381061 168 YEARS MAXIMUM CORRELATION: 0.718 SERIES 380042 AND 382112 80 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 73.91 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1760. 1785. 1810. 1835. 1860. 1885. 1910. 1935. CORR 45. 120. 210. 253. 253. 253. 253. 253. RBAR 0.569 0.588 0.510 0.452 0.467 0.478 0.333 0.317 SDEV 0.132 0.125 0.142 0.134 0.129 0.152 0.148 0.147 SERR 0.020 0.011 0.010 0.008 0.008 0.010 0.009 0.009 EPS 0.953 0.966 0.960 0.952 0.953 0.955 0.920 0.914 NSS 15.3 20.2 23.2 23.8 23.3 23.0 23.0 23.0 |======================== 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 1706 1976 271 0.983 0.255 0.986 5.450 0.284 -0.083 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.451 0.192 0.080 104 167 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.26 0.61 1.00 1.09 1.69 10.20 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.00 0.85 0.94 1.00 |----------- RESIDUAL CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF -0.083 -0.076 -0.026 0.083 -0.056 0.086 0.057 -0.037 -0.027 -0.002 PACF -0.083 -0.084 -0.041 0.072 -0.048 0.090 0.071 -0.022 -0.009 -0.023 95% C.L. 0.121 0.122 0.123 0.123 0.124 0.124 0.125 0.126 0.126 0.126 |------------------ 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 0.003 -0.038 0.078 -0.039 0.092 0.056 -0.028 -0.025 0.008 PACF -0.004 0.003 -0.038 0.078 -0.038 0.091 0.063 -0.037 -0.012 -0.004 95% C.L. 0.121 0.121 0.121 0.122 0.122 0.123 0.124 0.124 0.124 0.124 |----------------- 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 0.001 -0.004 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 1706 1976 271 0.982 0.290 0.944 5.301 0.230 0.471 |------------ 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 0.469 0.325 0.192 0.191 0.111 0.152 0.115 0.054 0.045 0.069 PACF 0.469 0.134 -0.003 0.092 -0.027 0.092 0.008 -0.059 0.021 0.040 95% C.L. 0.121 0.146 0.156 0.160 0.163 0.164 0.166 0.167 0.168 0.168 |------------------- 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 0.235 0.406 0.135 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.38 MINUTES