RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit021l.rwl LOG FILE PROCESSED: brit021l.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: 377 1 Dimmie Schottland WIDTH_LATE PISY - 377 2 Great Britain Scots pine, Scotch pine 200 5607-320 1828 1976 - 377 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 1 377011 MISSING VALUES FOUND: 8 IN 1 GAPS / 1958 1965 / -------------------------------------------------------------------- 2 377012 MISSING VALUES FOUND: 7 IN 1 GAPS / 1958 1964 / -------------------------------------------------------------------- 3 377022 MISSING VALUES FOUND: 1 IN 1 GAPS / 1896 1896 / -------------------------------------------------------------------- 4 377031 MISSING VALUES FOUND: 1 IN 1 GAPS / 1894 1894 / -------------------------------------------------------------------- 11 378081 MISSING VALUES FOUND: 3 IN 1 GAPS / 1906 1908 / -------------------------------------------------------------------- 12 378082 MISSING VALUES FOUND: 3 IN 1 GAPS / 1896 1898 / -------------------------------------------------------------------- 13 378091 MISSING VALUES FOUND: 8 IN 2 GAPS / 1883 1883 / 1896 1902 / -------------------------------------------------------------------- 14 378092 MISSING VALUES FOUND: 2 IN 1 GAPS / 1884 1885 / -------------------------------------------------------------------- 17 379111 MISSING VALUES FOUND: 3 IN 1 GAPS / 1895 1897 / -------------------------------------------------------------------- 18 379112 MISSING VALUES FOUND: 3 IN 1 GAPS / 1895 1897 / -------------------------------------------------------------------- 20 379122 MISSING VALUES FOUND: 1 IN 1 GAPS / 1895 1895 / -------------------------------------------------------------------- 22 379132 MISSING VALUES FOUND: 1 IN 1 GAPS / 1895 1895 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 377011 1845 1976 132 0.548 0.412 1.815 7.693 0.453 0.658 2 377012 1865 1976 112 0.878 0.547 0.556 3.705 0.467 0.479 3 377022 1837 1974 138 0.430 0.350 0.974 3.777 0.491 0.693 4 377031 1843 1976 134 0.680 0.444 0.803 2.974 0.377 0.692 5 377032 1828 1976 149 0.425 0.278 2.066 11.722 0.384 0.562 6 377051 1838 1976 139 0.611 0.377 0.785 3.038 0.359 0.689 7 377052 1837 1967 131 0.612 0.346 0.817 3.769 0.309 0.680 8 378061 1900 1976 77 0.542 0.434 1.377 4.245 0.516 0.679 9 378071 1831 1976 146 0.404 0.195 0.794 3.954 0.319 0.674 10 378072 1859 1976 118 0.553 0.307 1.108 6.463 0.391 0.574 11 378081 1851 1976 126 0.585 0.429 0.950 3.253 0.444 0.648 12 378082 1838 1976 139 0.369 0.189 0.984 4.181 0.434 0.353 13 378091 1856 1976 121 0.746 0.377 0.578 2.728 0.389 0.491 14 378092 1832 1976 145 0.355 0.248 0.908 3.201 0.431 0.609 15 378101 1853 1976 124 0.329 0.205 0.866 3.311 0.431 0.572 16 378102 1857 1976 120 0.296 0.157 0.912 3.977 0.436 0.480 17 379111 1854 1976 123 0.525 0.357 0.982 3.870 0.425 0.681 18 379112 1863 1976 114 0.542 0.316 1.377 5.457 0.396 0.557 19 379121 1853 1976 124 0.620 0.251 0.269 2.646 0.375 0.415 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 379122 1843 1976 134 0.524 0.214 0.422 2.889 0.369 0.351 21 379131 1864 1976 113 0.510 0.327 0.579 2.685 0.462 0.631 22 379132 1843 1976 134 0.296 0.148 0.428 3.354 0.419 0.567 NUMBER OF SERIES READ IN: 22 FROM 1828 TO 1976 149 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 125 0.517 0.314 0.925 4.222 0.413 0.579 STANDARD DEVIATION 15 0.147 0.106 0.432 2.083 0.052 0.109 MEDIAN (50TH QUANTILE) 124 0.533 0.321 0.887 3.737 0.422 0.591 INTERQUARTILE RANGE 18 0.207 0.163 0.405 1.144 0.067 0.188 MINIMUM VALUE 77 0.296 0.148 0.269 2.646 0.309 0.351 LOWER HINGE (25TH QUANTILE) 118 0.404 0.214 0.579 3.038 0.377 0.491 UPPER HINGE (75TH QUANTILE) 136 0.611 0.377 0.984 4.181 0.444 0.679 MAXIMUM VALUE 149 0.878 0.547 2.066 11.722 0.516 0.693 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.336 0.200 0.013 -1.048 5.002 -0.433 0.831 MINIMUM CORRELATION: -0.433 SERIES 377022 AND 378092 138 YEARS MAXIMUM CORRELATION: 0.831 SERIES 377031 AND 377051 134 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 79.19 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1880. 1905. 1930. CORR 105. 210. 231. RBAR 0.286 0.319 0.293 SDEV 0.193 0.214 0.191 SERR 0.019 0.015 0.013 EPS 0.891 0.910 0.901 NSS 20.4 21.6 22.0 |======================== 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 1828 1976 149 0.504 0.229 2.504 19.506 0.279 0.453 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.440 0.225 0.164 68 81 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.34 0.60 1.01 1.13 1.73 8.19 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.00 0.85 0.93 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 128. 18. 77. 120. 138. 149. |----------- 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 0.450 0.359 0.281 0.184 0.221 0.198 0.266 0.169 0.148 0.192 PACF 0.450 0.197 0.082 -0.013 0.111 0.055 0.146 -0.053 0.000 0.089 95% C.L. 0.164 0.194 0.211 0.221 0.225 0.231 0.235 0.243 0.246 0.249 |------------------ 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 0.327 0.428 0.212 |================== 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 377011 3 0.00000000 0.00000000 -0.00103326 0.59083498 2 377012 3 0.00000000 0.00000000 -0.00658040 1.21216714 3 377022 5 0.00000000 0.00000000 0.00000000 0.42650837 4 377031 3 0.00000000 0.00000000 -0.00654606 1.12035179 5 377032 1 1.02679300 0.07783192 0.00000000 0.33949381 6 377051 3 0.00000000 0.00000000 -0.00598767 1.02985609 7 377052 3 0.00000000 0.00000000 -0.00585993 0.99828184 8 378061 3 0.00000000 0.00000000 -0.00637810 0.79108340 9 378071 3 0.00000000 0.00000000 -0.00041969 0.43454605 10 378072 3 0.00000000 0.00000000 -0.00541135 0.87460232 11 378081 1 0.68745798 0.05421308 0.00000000 0.47973546 12 378082 1 0.19059733 0.02438863 0.00000000 0.30959338 13 378091 3 0.00000000 0.00000000 0.00026618 0.70470202 14 378092 3 0.00000000 0.00000000 0.00173420 0.22453946 15 378101 3 0.00000000 0.00000000 -0.00252233 0.48708105 16 378102 3 0.00000000 0.00000000 -0.00081898 0.34596500 17 379111 3 0.00000000 0.00000000 0.00593261 0.14521366 18 379112 3 0.00000000 0.00000000 0.00047426 0.50423455 19 379121 3 0.00000000 0.00000000 -0.00208478 0.74981511 SERIES IDENT OPTION A B C D 20 379122 3 0.00000000 0.00000000 -0.00026699 0.53952020 21 379131 3 0.00000000 0.00000000 -0.00618562 0.86284608 22 379132 3 0.00000000 0.00000000 -0.00116925 0.37389627 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 377011 1845 1976 132 0.998 0.806 2.003 8.738 0.448 0.693 2 377012 1865 1976 112 0.983 0.652 0.820 4.159 0.468 0.555 3 377022 1837 1974 138 1.000 0.821 0.973 3.769 0.530 0.696 4 377031 1843 1976 134 0.990 0.537 0.978 4.071 0.382 0.600 5 377032 1828 1976 149 0.999 0.528 1.127 4.807 0.382 0.499 6 377051 1838 1976 139 0.998 0.489 0.711 3.384 0.358 0.545 7 377052 1837 1967 131 0.992 0.447 1.070 4.839 0.308 0.542 8 378061 1900 1976 77 0.979 0.729 1.461 4.736 0.509 0.621 9 378071 1831 1976 146 1.000 0.493 0.938 4.181 0.317 0.675 10 378072 1859 1976 118 0.979 0.446 0.790 4.070 0.388 0.406 11 378081 1851 1976 126 1.000 0.766 1.626 5.856 0.447 0.644 12 378082 1838 1976 139 1.000 0.521 1.064 4.150 0.446 0.351 13 378091 1856 1976 121 1.000 0.524 0.621 2.750 0.385 0.533 14 378092 1832 1976 145 1.012 0.764 1.822 7.307 0.437 0.616 15 378101 1853 1976 124 0.989 0.573 1.331 4.923 0.427 0.520 16 378102 1857 1976 120 1.000 0.532 1.080 4.444 0.433 0.470 17 379111 1854 1976 123 0.974 0.576 1.029 4.095 0.437 0.616 18 379112 1863 1976 114 1.000 0.602 1.441 5.749 0.406 0.564 19 379121 1853 1976 124 0.998 0.392 0.328 2.704 0.372 0.349 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 379122 1843 1976 134 1.000 0.411 0.443 2.923 0.372 0.360 21 379131 1864 1976 113 0.980 0.521 0.707 3.700 0.458 0.493 22 379132 1843 1976 134 0.996 0.499 0.549 3.499 0.420 0.561 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 127 0.994 0.574 1.041 4.493 0.415 0.541 STANDARD DEVIATION 15 0.009 0.128 0.433 1.427 0.055 0.105 MEDIAN (50TH QUANTILE) 128 0.998 0.530 1.004 4.155 0.424 0.550 INTERQUARTILE RANGE 18 0.011 0.159 0.621 1.139 0.065 0.124 MINIMUM VALUE 77 0.974 0.392 0.328 2.704 0.308 0.349 LOWER HINGE (25TH QUANTILE) 120 0.989 0.493 0.711 3.700 0.382 0.493 UPPER HINGE (75TH QUANTILE) 138 1.000 0.652 1.331 4.839 0.447 0.616 MAXIMUM VALUE 149 1.012 0.821 2.003 8.738 0.530 0.696 |------------------------ 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 377011 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 377012 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 377022 5 0.00000000 0.00000000 0.00000000 0.99999505 4 377031 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 377032 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 377051 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 377052 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 378061 -67 51 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 378071 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 378072 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 378081 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 378082 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 378091 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 378092 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 378101 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 378102 -67 80 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 379111 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 379112 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 379121 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 379122 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 379131 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 379132 -67 89 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 377011 1845 1976 132 1.038 0.848 3.675 21.788 0.449 0.497 2 377012 1865 1976 112 1.006 0.701 2.113 9.677 0.468 0.475 3 377022 1837 1974 138 1.000 0.821 0.973 3.769 0.530 0.696 4 377031 1843 1976 134 0.996 0.524 0.966 4.137 0.382 0.570 5 377032 1828 1976 149 0.995 0.503 0.954 4.264 0.383 0.447 6 377051 1838 1976 139 0.997 0.488 0.802 3.534 0.358 0.525 7 377052 1837 1967 131 0.993 0.423 0.968 4.625 0.309 0.512 8 378061 1900 1976 77 0.979 0.564 0.882 3.658 0.510 0.381 9 378071 1831 1976 146 0.989 0.450 0.907 4.268 0.319 0.581 10 378072 1859 1976 118 0.995 0.412 0.923 4.581 0.390 0.313 11 378081 1851 1976 126 0.971 0.619 1.041 3.767 0.451 0.554 12 378082 1838 1976 139 0.996 0.508 0.993 3.901 0.446 0.321 13 378091 1856 1976 121 0.991 0.478 0.984 5.241 0.386 0.417 14 378092 1832 1976 145 0.965 0.546 0.882 3.716 0.436 0.531 15 378101 1853 1976 124 0.993 0.513 0.966 3.955 0.427 0.429 16 378102 1857 1976 120 0.998 0.524 1.035 4.316 0.433 0.456 17 379111 1854 1976 123 0.989 0.546 0.803 3.789 0.436 0.549 18 379112 1863 1976 114 0.996 0.547 1.437 6.107 0.407 0.445 19 379121 1853 1976 124 0.998 0.369 0.263 2.676 0.372 0.247 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 379122 1843 1976 134 0.997 0.390 0.698 4.237 0.371 0.267 21 379131 1864 1976 113 0.996 0.524 0.989 4.492 0.457 0.414 22 379132 1843 1976 134 0.993 0.475 0.709 3.946 0.420 0.476 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 127 0.994 0.535 1.089 5.202 0.415 0.459 STANDARD DEVIATION 15 0.014 0.122 0.664 3.943 0.055 0.109 MEDIAN (50TH QUANTILE) 128 0.995 0.518 0.966 4.187 0.423 0.466 INTERQUARTILE RANGE 18 0.007 0.071 0.111 0.812 0.067 0.117 MINIMUM VALUE 77 0.965 0.369 0.263 2.676 0.309 0.247 LOWER HINGE (25TH QUANTILE) 120 0.991 0.475 0.882 3.769 0.382 0.414 UPPER HINGE (75TH QUANTILE) 138 0.997 0.547 0.993 4.581 0.449 0.531 MAXIMUM VALUE 149 1.038 0.848 3.675 21.788 0.530 0.696 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.358 0.145 0.010 -0.064 3.066 -0.150 0.754 MINIMUM CORRELATION: -0.150 SERIES 377022 AND 378092 138 YEARS MAXIMUM CORRELATION: 0.754 SERIES 377031 AND 377051 134 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 79.19 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1880. 1905. 1930. CORR 105. 210. 231. RBAR 0.308 0.342 0.317 SDEV 0.194 0.192 0.193 SERR 0.019 0.013 0.013 EPS 0.901 0.918 0.911 NSS 20.4 21.6 22.0 |======================== 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 1828 1976 149 0.970 0.308 0.593 4.493 0.265 0.367 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.635 0.304 0.093 51 98 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.23 1.14 1.00 1.08 2.22 7.02 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.06 0.00 0.87 0.94 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 0.365 0.200 0.049 0.013 -0.035 -0.054 0.006 -0.070 -0.121 -0.060 PACF 0.365 0.077 -0.055 -0.004 -0.037 -0.034 0.053 -0.090 -0.096 0.036 95% C.L. 0.164 0.184 0.190 0.190 0.190 0.191 0.191 0.191 0.192 0.194 |------------------ 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 0.155 0.384 |======================= 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 0.399 0.220 0.051 0.030 -0.019 -0.048 0.015 -0.050 -0.098 -0.064 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 0.399 2 0.370 0.073 3 0.375 0.099 -0.071 4 0.377 0.097 -0.078 0.020 5 0.377 0.094 -0.075 0.032 -0.031 6 0.376 0.096 -0.079 0.036 -0.015 -0.042 7 0.379 0.097 -0.081 0.041 -0.021 -0.067 0.067 8 0.384 0.092 -0.083 0.044 -0.028 -0.060 0.097 -0.078 9 0.377 0.100 -0.088 0.042 -0.024 -0.067 0.104 -0.045 -0.085 10 0.380 0.101 -0.090 0.044 -0.023 -0.068 0.107 -0.048 -0.094 0.026 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) 1306.05 1282.21 1283.42 1284.67 1286.61 1288.47 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1290.21 1291.53 1292.62 1293.55 1295.45 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 0.399 R-SQUARED DUE TO POOLED AUTOREGRESSION: 15.92 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 118.94 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.399 0.159 0.064 0.025 0.010 0.004 0.002 0.001 0.000 0.0001 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 377011 1 0.370 0.608 2 377012 1 0.267 0.515 3 377022 1 0.573 0.700 4 377031 1 0.335 0.578 5 377032 1 0.208 0.456 6 377051 1 0.285 0.532 7 377052 1 0.273 0.517 8 378061 1 0.169 0.409 9 378071 1 0.373 0.611 10 378072 1 0.107 0.319 11 378081 1 0.325 0.566 12 378082 1 0.106 0.326 13 378091 1 0.174 0.417 14 378092 1 0.305 0.534 15 378101 1 0.189 0.431 16 378102 1 0.216 0.463 17 379111 1 0.312 0.556 18 379112 1 0.208 0.453 19 379121 1 0.111 0.252 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 379122 1 0.084 0.288 21 379131 1 0.195 0.438 22 379132 1 0.249 0.496 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.247 0.476 STANDARD DEVIATION 0 0.113 0.113 MEDIAN 1 0.233 0.480 INTERQUARTILE RANGE 0 0.138 0.138 MINIMUM VALUE 1 0.084 0.252 LOWER HINGE 1 0.174 0.417 UPPER HINGE 1 0.312 0.556 MAXIMUM VALUE 1 0.573 0.700 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 377011 1845 1976 132 1.004 0.665 2.885 14.869 0.605 0.126 2 377012 1865 1976 112 1.001 0.599 2.178 10.885 0.581 0.021 3 377022 1837 1974 138 1.002 0.582 1.561 6.549 0.580 -0.261 4 377031 1843 1976 134 1.000 0.427 1.167 5.231 0.454 -0.018 5 377032 1828 1976 149 1.000 0.448 1.260 5.196 0.440 0.003 6 377051 1838 1976 139 1.001 0.411 0.973 4.382 0.425 0.033 7 377052 1837 1967 131 1.000 0.361 0.687 3.833 0.394 -0.049 8 378061 1900 1976 77 1.000 0.515 0.943 3.869 0.553 0.044 9 378071 1831 1976 146 1.000 0.356 0.634 3.880 0.383 0.014 10 378072 1859 1976 118 1.000 0.390 1.122 5.518 0.415 -0.017 11 378081 1851 1976 126 1.000 0.510 1.090 4.065 0.533 -0.039 12 378082 1838 1976 139 1.002 0.475 1.052 4.535 0.493 0.018 13 378091 1856 1976 121 1.000 0.434 1.196 6.335 0.427 0.003 14 378092 1832 1976 145 1.001 0.460 0.976 3.971 0.485 -0.084 15 378101 1853 1976 124 1.000 0.463 1.329 5.305 0.472 -0.024 16 378102 1857 1976 120 1.000 0.464 0.887 3.896 0.517 -0.014 17 379111 1854 1976 123 1.000 0.452 1.011 5.033 0.501 -0.046 18 379112 1863 1976 114 1.003 0.479 1.386 5.710 0.453 0.040 19 379121 1853 1976 124 1.000 0.357 0.376 2.816 0.394 0.059 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 379122 1843 1976 134 1.000 0.373 0.741 3.793 0.403 0.021 21 379131 1864 1976 113 1.000 0.471 1.071 4.518 0.490 0.049 22 379132 1843 1976 134 1.000 0.413 0.690 4.080 0.461 0.051 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 127 1.001 0.459 1.146 5.376 0.475 -0.003 STANDARD DEVIATION 15 0.001 0.080 0.535 2.664 0.065 0.073 MEDIAN (50TH QUANTILE) 128 1.000 0.456 1.062 4.526 0.467 0.009 INTERQUARTILE RANGE 18 0.001 0.067 0.373 1.623 0.092 0.064 MINIMUM VALUE 77 1.000 0.356 0.376 2.816 0.383 -0.261 LOWER HINGE (25TH QUANTILE) 120 1.000 0.411 0.887 3.896 0.425 -0.024 UPPER HINGE (75TH QUANTILE) 138 1.001 0.479 1.260 5.518 0.517 0.040 MAXIMUM VALUE 149 1.004 0.665 2.885 14.869 0.605 0.126 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.396 0.110 0.007 0.168 3.249 0.075 0.750 MINIMUM CORRELATION: 0.075 SERIES 377022 AND 378092 138 YEARS MAXIMUM CORRELATION: 0.750 SERIES 377031 AND 377051 134 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 79.19 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1880. 1905. 1930. CORR 105. 210. 231. RBAR 0.377 0.397 0.407 SDEV 0.144 0.149 0.135 SERR 0.014 0.010 0.009 EPS 0.925 0.934 0.938 NSS 20.4 21.6 22.0 |======================== 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 1828 1976 149 0.977 0.279 0.721 3.834 0.308 -0.111 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.609 0.288 0.034 57 92 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.20 0.50 1.01 1.07 1.57 10.33 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.00 0.87 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 -0.110 0.093 -0.044 0.006 -0.026 -0.059 0.082 -0.045 -0.103 0.012 PACF -0.110 0.082 -0.026 -0.009 -0.020 -0.065 0.075 -0.021 -0.131 0.000 95% C.L. 0.164 0.166 0.167 0.168 0.168 0.168 0.168 0.169 0.170 0.171 |------------------ 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 0.007 0.073 -0.034 -0.003 -0.032 -0.054 0.073 -0.045 -0.107 -0.005 PACF 0.007 0.073 -0.035 -0.008 -0.027 -0.054 0.079 -0.042 -0.123 0.009 95% C.L. 0.164 0.164 0.165 0.165 0.165 0.165 0.166 0.166 0.167 0.169 |----------------- 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 0.006 0.007 |========================= 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 1828 1976 149 0.972 0.303 0.680 4.659 0.255 0.387 |------------ 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 0.384 0.172 0.030 -0.009 -0.039 -0.044 0.024 -0.050 -0.109 -0.068 PACF 0.384 0.029 -0.053 -0.010 -0.029 -0.020 0.063 -0.088 -0.089 0.019 95% C.L. 0.164 0.186 0.191 0.191 0.191 0.191 0.191 0.191 0.192 0.193 |------------------- 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 1 0.166 0.405 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 1.50 MINUTES