RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit016l.rwl LOG FILE PROCESSED: brit016l.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: 571 1 Shieldaig WIDTH_LATE PISY - 571 2 Great Britain Scots pine, Scotch pine 12 5730-537 1847 1978 - 571 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 5 571031 MISSING VALUES FOUND: 1 IN 1 GAPS / 1924 1924 / -------------------------------------------------------------------- 7 571041 MISSING VALUES FOUND: 1 IN 1 GAPS / 1959 1959 / -------------------------------------------------------------------- 18 571092 MISSING VALUES FOUND: 1 IN 1 GAPS / 1889 1889 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 571011 1909 1978 70 0.733 0.282 0.125 2.566 0.377 0.374 2 571012 1899 1978 80 0.733 0.213 0.484 2.994 0.315 0.182 3 571021 1868 1978 111 0.631 0.224 1.000 3.900 0.311 0.316 4 571022 1860 1978 119 0.509 0.262 0.844 3.773 0.346 0.563 5 571031 1873 1978 106 0.591 0.286 0.995 4.130 0.317 0.578 6 571032 1847 1978 132 0.401 0.366 1.666 5.338 0.469 0.827 7 571041 1866 1978 113 0.782 0.460 0.758 3.324 0.336 0.711 8 571042 1864 1966 103 0.666 0.433 0.910 3.195 0.318 0.771 9 571051 1859 1978 120 0.534 0.320 2.029 10.496 0.303 0.602 10 571052 1899 1978 80 0.472 0.248 1.646 7.185 0.334 0.552 11 571061 1891 1978 88 0.952 0.390 -0.243 2.581 0.302 0.638 12 571062 1883 1978 96 0.568 0.336 0.146 1.950 0.308 0.831 13 571071 1873 1967 95 0.499 0.191 0.523 3.206 0.280 0.585 14 571072 1876 1965 90 0.560 0.221 1.183 4.990 0.329 0.358 15 571081 1874 1978 105 0.419 0.169 0.380 2.827 0.306 0.568 16 571082 1853 1978 126 0.532 0.279 1.183 5.899 0.336 0.689 17 571091 1866 1978 113 0.610 0.219 0.291 3.060 0.302 0.447 18 571092 1868 1978 111 0.502 0.217 0.376 3.107 0.319 0.589 19 571101 1877 1976 100 0.759 0.358 0.183 2.420 0.417 0.487 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 0.839 0.342 1.038 4.652 0.325 0.397 21 571111 1856 1978 123 0.744 0.356 0.882 3.419 0.313 0.622 NUMBER OF SERIES READ IN: 21 FROM 1847 TO 1978 132 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 0.621 0.294 0.781 4.048 0.331 0.557 STANDARD DEVIATION 16 0.145 0.081 0.573 1.950 0.043 0.168 MEDIAN (50TH QUANTILE) 105 0.591 0.282 0.844 3.324 0.318 0.578 INTERQUARTILE RANGE 23 0.224 0.135 0.662 1.657 0.028 0.191 MINIMUM VALUE 70 0.401 0.169 -0.243 1.950 0.280 0.182 LOWER HINGE (25TH QUANTILE) 90 0.509 0.221 0.376 2.994 0.308 0.447 UPPER HINGE (75TH QUANTILE) 113 0.733 0.356 1.038 4.652 0.336 0.638 MAXIMUM VALUE 132 0.952 0.460 2.029 10.496 0.469 0.831 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.364 0.227 0.016 -0.566 2.633 -0.243 0.788 MINIMUM CORRELATION: -0.243 SERIES 571011 AND 571041 70 YEARS MAXIMUM CORRELATION: 0.788 SERIES 571041 AND 571042 101 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 69.52 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 78. 190. 136. RBAR 0.498 0.414 0.404 SDEV 0.192 0.232 0.226 SERR 0.022 0.017 0.019 EPS 0.949 0.936 0.932 NSS 18.8 20.8 20.2 |======================== 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 1847 1978 132 0.619 0.239 1.397 5.849 0.238 0.568 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.495 0.239 0.120 46 86 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.22 0.64 1.00 1.10 1.74 6.24 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.00 0.86 0.93 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 105. 23. 70. 90. 113. 132. |----------- 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 0.563 0.457 0.354 0.243 0.343 0.283 0.254 0.112 0.049 0.127 PACF 0.563 0.205 0.051 -0.036 0.245 0.013 -0.003 -0.182 -0.023 0.144 95% C.L. 0.174 0.223 0.249 0.264 0.271 0.284 0.292 0.299 0.300 0.300 |------------------ 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 0.358 0.446 0.217 |================== 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 571011 1 0.28909028 0.05647314 0.00000000 0.66313857 2 571012 1 0.03777814 0.03235548 0.00000000 0.71984416 3 571021 3 0.00000000 0.00000000 -0.00189549 0.73704833 4 571022 3 0.00000000 0.00000000 -0.00459386 0.78428715 5 571031 3 0.00000000 0.00000000 -0.00181363 0.68500966 6 571032 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 571041 1 0.96659070 0.08463505 0.00000000 0.68380058 8 571042 1 1.17558742 0.14315300 0.00000000 0.59205616 9 571051 3 0.00000000 0.00000000 -0.00391881 0.77092159 10 571052 1 0.70388818 0.20975153 0.00000000 0.43379807 11 571061 3 0.00000000 0.00000000 -0.00728726 1.27666926 12 571062 3 0.00000000 0.00000000 -0.00970340 1.03905261 13 571071 3 0.00000000 0.00000000 -0.00104927 0.54889137 14 571072 1 0.30897662 0.08904820 0.00000000 0.52337289 15 571081 3 0.00000000 0.00000000 0.00089042 0.37223625 16 571082 3 0.00000000 0.00000000 0.00328075 0.32325968 17 571091 3 0.00000000 0.00000000 -0.00150492 0.69622314 18 571092 3 0.00000000 0.00000000 -0.00241939 0.63606685 19 571101 1 0.39497659 0.06720649 0.00000000 0.70255148 SERIES IDENT OPTION A B C D 20 571102 1 1.21162641 0.01097163 0.00000000 0.05145451 21 571111 1 1.01842105 0.05211970 0.00000000 0.58988941 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 571011 1909 1978 70 1.000 0.379 0.247 2.818 0.372 0.330 2 571012 1899 1978 80 1.000 0.291 0.489 2.938 0.311 0.181 3 571021 1868 1978 111 1.000 0.343 1.158 4.728 0.309 0.285 4 571022 1860 1978 119 0.993 0.428 1.442 6.432 0.344 0.377 5 571031 1873 1978 106 0.999 0.487 1.261 5.150 0.310 0.591 6 571032 1847 1978 132 0.997 0.528 0.965 4.613 0.467 0.348 7 571041 1866 1978 113 0.999 0.582 1.276 5.480 0.332 0.713 8 571042 1864 1966 103 1.000 0.642 1.322 4.793 0.316 0.773 9 571051 1859 1978 120 0.989 0.592 3.506 19.566 0.300 0.558 10 571052 1899 1978 80 0.999 0.504 2.244 11.622 0.331 0.462 11 571061 1891 1978 88 0.994 0.391 0.135 2.729 0.300 0.615 12 571062 1883 1978 96 0.982 0.401 0.691 4.071 0.308 0.472 13 571071 1873 1967 95 1.000 0.389 0.809 3.745 0.277 0.587 14 571072 1876 1965 90 1.000 0.391 1.563 6.557 0.324 0.335 15 571081 1874 1978 105 1.000 0.394 0.300 2.786 0.303 0.533 16 571082 1853 1978 126 1.001 0.461 0.677 4.387 0.334 0.573 17 571091 1866 1978 113 0.999 0.354 0.543 3.848 0.299 0.469 18 571092 1868 1978 111 0.997 0.417 0.701 4.093 0.321 0.537 19 571101 1877 1976 100 1.000 0.471 0.325 2.625 0.413 0.481 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 1.000 0.326 0.821 3.758 0.321 0.038 21 571111 1856 1978 123 0.999 0.399 1.266 6.604 0.309 0.503 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 0.998 0.437 1.035 5.397 0.329 0.465 STANDARD DEVIATION 16 0.005 0.092 0.766 3.818 0.043 0.172 MEDIAN (50TH QUANTILE) 105 0.999 0.401 0.821 4.387 0.316 0.481 INTERQUARTILE RANGE 23 0.003 0.099 0.734 1.735 0.024 0.225 MINIMUM VALUE 70 0.982 0.291 0.135 2.625 0.277 0.038 LOWER HINGE (25TH QUANTILE) 90 0.997 0.389 0.543 3.745 0.308 0.348 UPPER HINGE (75TH QUANTILE) 113 1.000 0.487 1.276 5.480 0.332 0.573 MAXIMUM VALUE 132 1.001 0.642 3.506 19.566 0.467 0.773 |------------------------ 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 571011 -67 46 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 571012 -67 53 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 571021 -67 74 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 571022 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 571031 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 571032 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 571041 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 571042 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 571051 -67 80 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 571052 -67 53 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 571061 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 571062 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 571071 -67 63 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 571072 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 571081 -67 70 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 571082 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 571091 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 571092 -67 74 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 571101 -67 67 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 571102 -67 56 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 571111 -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 571011 1909 1978 70 0.994 0.357 0.363 2.900 0.372 0.230 2 571012 1899 1978 80 0.997 0.274 0.440 2.816 0.311 0.085 3 571021 1868 1978 111 0.995 0.304 0.741 3.486 0.309 0.142 4 571022 1860 1978 119 0.995 0.396 1.131 5.109 0.344 0.313 5 571031 1873 1978 106 0.984 0.380 0.551 3.463 0.309 0.442 6 571032 1847 1978 132 0.997 0.521 0.940 4.525 0.466 0.332 7 571041 1866 1978 113 0.973 0.499 0.960 4.478 0.332 0.652 8 571042 1864 1966 103 0.966 0.458 0.825 3.665 0.314 0.634 9 571051 1859 1978 120 0.994 0.478 2.657 14.424 0.301 0.463 10 571052 1899 1978 80 0.992 0.454 1.911 10.231 0.330 0.421 11 571061 1891 1978 88 0.997 0.357 0.020 2.606 0.301 0.547 12 571062 1883 1978 96 0.993 0.386 0.914 4.796 0.308 0.393 13 571071 1873 1967 95 0.987 0.314 0.275 2.842 0.277 0.442 14 571072 1876 1965 90 0.994 0.349 1.084 4.620 0.323 0.223 15 571081 1874 1978 105 0.995 0.375 0.275 2.754 0.302 0.514 16 571082 1853 1978 126 0.994 0.434 0.425 3.673 0.333 0.541 17 571091 1866 1978 113 0.996 0.303 -0.063 3.240 0.298 0.283 18 571092 1868 1978 111 0.997 0.388 0.646 3.510 0.321 0.474 19 571101 1877 1976 100 0.990 0.443 0.217 2.437 0.414 0.443 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 0.998 0.320 0.851 3.851 0.321 0.003 21 571111 1856 1978 123 0.991 0.356 0.909 5.349 0.309 0.418 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 0.991 0.388 0.765 4.513 0.328 0.381 STANDARD DEVIATION 16 0.008 0.069 0.621 2.811 0.043 0.172 MEDIAN (50TH QUANTILE) 105 0.994 0.380 0.741 3.665 0.314 0.421 INTERQUARTILE RANGE 23 0.005 0.094 0.577 1.720 0.024 0.191 MINIMUM VALUE 70 0.966 0.274 -0.063 2.437 0.277 0.003 LOWER HINGE (25TH QUANTILE) 90 0.991 0.349 0.363 2.900 0.308 0.283 UPPER HINGE (75TH QUANTILE) 113 0.996 0.443 0.940 4.620 0.332 0.474 MAXIMUM VALUE 132 0.998 0.521 2.657 14.424 0.466 0.652 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.414 0.159 0.011 -0.497 2.943 0.007 0.749 MINIMUM CORRELATION: 0.007 SERIES 571011 AND 571041 70 YEARS MAXIMUM CORRELATION: 0.749 SERIES 571041 AND 571042 101 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 69.52 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 78. 190. 136. RBAR 0.518 0.504 0.406 SDEV 0.118 0.168 0.158 SERR 0.013 0.012 0.014 EPS 0.953 0.955 0.933 NSS 18.8 20.8 20.2 |======================== 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 1847 1978 132 0.967 0.269 0.547 4.050 0.228 0.368 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.457 0.197 0.087 34 98 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.14 0.41 1.00 1.04 1.45 3.98 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.10 0.00 0.85 0.95 1.00 |----------- STANDARD CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.365 0.299 0.171 0.079 0.186 0.097 0.069 -0.057 -0.085 0.037 PACF 0.365 0.191 0.016 -0.039 0.162 -0.008 -0.033 -0.130 -0.047 0.121 95% C.L. 0.174 0.196 0.209 0.213 0.214 0.219 0.220 0.221 0.222 0.223 |------------------ 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 0.171 0.295 0.200 |======================= 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 0.376 0.336 0.156 0.088 0.230 0.085 0.093 -0.027 -0.067 0.051 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 0.376 2 0.291 0.227 3 0.299 0.237 -0.034 4 0.298 0.244 -0.024 -0.032 5 0.305 0.250 -0.080 -0.100 0.229 6 0.319 0.244 -0.085 -0.085 0.247 -0.061 7 0.316 0.253 -0.088 -0.088 0.257 -0.048 -0.039 8 0.313 0.249 -0.068 -0.095 0.250 -0.029 -0.014 -0.078 9 0.310 0.249 -0.070 -0.082 0.245 -0.032 -0.002 -0.062 -0.050 10 0.315 0.255 -0.070 -0.079 0.220 -0.024 0.005 -0.088 -0.081 0.103 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) 1056.32 1038.15 1033.18 1035.03 1036.90 1031.81 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1033.33 1035.13 1036.33 1038.01 1038.61 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 0.291 0.227 R-SQUARED DUE TO POOLED AUTOREGRESSION: 18.58 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 122.82 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.291 0.311 0.157 0.116 0.069 0.047 0.029 0.019 0.012 0.0079 0.005 0.003 0.002 0.001 0.001 0.001 0.000 0.000 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 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 571011 2 0.059 0.239 -0.031 2 571012 2 0.013 0.087 -0.011 3 571021 2 0.022 0.140 0.020 4 571022 2 0.113 0.274 0.126 5 571031 2 0.237 0.358 0.199 6 571032 2 0.123 0.301 0.100 7 571041 2 0.485 0.452 0.310 8 571042 2 0.430 0.526 0.169 9 571051 2 0.282 0.334 0.285 10 571052 2 0.235 0.327 0.227 11 571061 2 0.314 0.543 0.026 12 571062 2 0.182 0.412 0.019 13 571071 2 0.234 0.349 0.212 14 571072 2 0.152 0.163 0.279 15 571081 2 0.277 0.542 -0.045 16 571082 2 0.303 0.487 0.103 17 571091 2 0.113 0.251 0.121 18 571092 2 0.257 0.510 -0.053 19 571101 2 0.222 0.372 0.162 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 571102 2 0.003 0.003 0.039 21 571111 2 0.207 0.338 0.194 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.203 0.334 0.117 STANDARD DEVIATION 0 0.128 0.152 0.114 MEDIAN 2 0.222 0.338 0.121 INTERQUARTILE RANGE 0 0.163 0.201 0.179 MINIMUM VALUE 2 0.003 0.003 -0.053 LOWER HINGE 2 0.113 0.251 0.020 UPPER HINGE 2 0.277 0.452 0.199 MAXIMUM VALUE 2 0.485 0.543 0.310 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 571011 1909 1978 70 1.000 0.347 0.354 2.744 0.409 0.000 2 571012 1899 1978 80 1.000 0.273 0.422 2.761 0.323 0.000 3 571021 1868 1978 111 1.000 0.301 0.724 3.427 0.331 -0.001 4 571022 1860 1978 119 1.000 0.373 1.036 4.281 0.394 -0.002 5 571031 1873 1978 106 1.000 0.332 0.420 3.017 0.365 -0.017 6 571032 1847 1978 132 1.000 0.488 1.103 5.326 0.520 0.003 7 571041 1866 1978 113 1.000 0.358 0.748 4.308 0.373 0.003 8 571042 1864 1966 103 1.000 0.349 0.689 3.750 0.364 0.023 9 571051 1859 1978 120 1.000 0.405 1.978 12.467 0.359 0.013 10 571052 1899 1978 80 1.000 0.400 1.798 10.019 0.371 0.028 11 571061 1891 1978 88 1.000 0.296 -0.249 2.553 0.349 0.006 12 571062 1883 1978 96 1.000 0.350 1.050 5.548 0.349 0.028 13 571071 1873 1967 95 1.000 0.275 0.319 3.227 0.306 -0.008 14 571072 1876 1965 90 1.000 0.326 0.986 4.039 0.347 -0.040 15 571081 1874 1978 105 1.000 0.319 0.168 2.815 0.365 -0.008 16 571082 1853 1978 126 1.000 0.362 0.493 4.356 0.370 0.003 17 571091 1866 1978 113 1.000 0.289 0.003 3.593 0.319 0.015 18 571092 1868 1978 111 1.000 0.338 0.496 3.459 0.382 -0.005 19 571101 1877 1976 100 1.000 0.391 0.291 2.482 0.446 0.009 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 1.000 0.320 0.853 3.846 0.322 -0.004 21 571111 1856 1978 123 1.000 0.317 0.994 5.201 0.342 0.001 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 1.000 0.343 0.699 4.439 0.367 0.002 STANDARD DEVIATION 16 0.000 0.050 0.537 2.461 0.048 0.015 MEDIAN (50TH QUANTILE) 105 1.000 0.338 0.689 3.750 0.364 0.001 INTERQUARTILE RANGE 23 0.000 0.045 0.640 1.339 0.030 0.012 MINIMUM VALUE 70 1.000 0.273 -0.249 2.482 0.306 -0.040 LOWER HINGE (25TH QUANTILE) 90 1.000 0.317 0.354 3.017 0.342 -0.004 UPPER HINGE (75TH QUANTILE) 113 1.000 0.362 0.994 4.356 0.373 0.009 MAXIMUM VALUE 132 1.000 0.488 1.978 12.467 0.520 0.028 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.432 0.115 0.008 -0.240 3.125 0.111 0.743 MINIMUM CORRELATION: 0.111 SERIES 571012 AND 571071 69 YEARS MAXIMUM CORRELATION: 0.743 SERIES 571081 AND 571082 105 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 69.52 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 78. 190. 136. RBAR 0.483 0.489 0.475 SDEV 0.124 0.138 0.107 SERR 0.014 0.010 0.009 EPS 0.946 0.952 0.948 NSS 18.8 20.8 20.2 |======================== 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 1847 1978 132 0.989 0.242 0.631 3.827 0.259 -0.066 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.428 0.164 0.078 35 97 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.11 0.60 1.00 1.05 1.64 5.20 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.09 0.00 0.86 0.95 1.00 |----------- RESIDUAL CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF -0.066 0.050 -0.013 -0.078 0.139 0.038 0.057 -0.106 -0.105 0.127 PACF -0.066 0.046 -0.007 -0.082 0.132 0.063 0.049 -0.110 -0.106 0.123 95% C.L. 0.174 0.175 0.175 0.175 0.176 0.180 0.180 0.180 0.182 0.184 |------------------ 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 0.001 0.004 -0.018 -0.075 0.136 0.059 0.052 -0.118 -0.100 0.114 PACF 0.001 0.004 -0.018 -0.075 0.137 0.059 0.049 -0.123 -0.082 0.114 95% C.L. 0.174 0.174 0.174 0.174 0.175 0.178 0.179 0.179 0.182 0.183 |----------------- 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 0.000 0.001 0.004 |========================= 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 1847 1978 132 0.987 0.271 0.408 3.734 0.221 0.391 |------------ 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 0.388 0.342 0.193 0.110 0.190 0.100 0.059 -0.068 -0.098 0.011 PACF 0.388 0.226 0.003 -0.032 0.150 -0.014 -0.059 -0.137 -0.054 0.120 95% C.L. 0.174 0.199 0.216 0.221 0.223 0.227 0.229 0.229 0.230 0.231 |------------------- 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 0.203 0.299 0.238 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 1.92 MINUTES