RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit016w.rwl LOG FILE PROCESSED: brit016w.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_RING 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 2.807 0.978 0.176 2.379 0.186 0.810 2 571012 1899 1978 80 2.926 0.858 0.136 2.409 0.185 0.737 3 571021 1868 1978 111 2.021 0.662 0.857 4.316 0.185 0.691 4 571022 1860 1978 119 1.625 0.871 1.174 4.757 0.210 0.817 5 571031 1873 1978 106 1.564 0.690 0.873 4.169 0.188 0.823 6 571032 1847 1978 132 1.412 1.152 1.372 4.094 0.232 0.928 7 571041 1866 1978 113 1.767 0.873 0.445 2.809 0.197 0.854 8 571042 1864 1966 103 1.610 0.954 1.125 4.198 0.200 0.895 9 571051 1859 1978 120 1.836 0.732 0.617 3.139 0.168 0.832 10 571052 1899 1978 80 1.452 0.630 1.116 3.954 0.204 0.848 11 571061 1891 1978 88 1.971 0.739 -0.519 2.651 0.198 0.813 12 571062 1883 1978 96 1.339 0.763 0.265 2.286 0.188 0.916 13 571071 1873 1967 95 1.704 0.583 0.424 3.161 0.151 0.805 14 571072 1876 1965 90 2.006 0.778 0.391 2.662 0.160 0.854 15 571081 1874 1978 105 1.246 0.379 -0.210 3.156 0.191 0.750 16 571082 1853 1978 126 1.501 0.638 0.919 3.991 0.192 0.817 17 571091 1866 1978 113 1.896 0.597 0.020 2.780 0.176 0.793 18 571092 1868 1978 111 1.531 0.530 0.267 2.372 0.188 0.739 19 571101 1877 1976 100 2.057 0.894 0.301 2.697 0.271 0.746 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 2.744 1.122 0.923 3.264 0.191 0.813 21 571111 1856 1978 123 2.187 1.251 1.003 3.137 0.240 0.863 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 1.867 0.794 0.556 3.256 0.195 0.816 STANDARD DEVIATION 16 0.475 0.217 0.499 0.760 0.027 0.060 MEDIAN (50TH QUANTILE) 105 1.767 0.763 0.445 3.139 0.191 0.817 INTERQUARTILE RANGE 23 0.490 0.257 0.657 1.329 0.015 0.061 MINIMUM VALUE 70 1.246 0.379 -0.519 2.286 0.151 0.691 LOWER HINGE (25TH QUANTILE) 90 1.531 0.638 0.265 2.662 0.185 0.793 UPPER HINGE (75TH QUANTILE) 113 2.021 0.894 0.923 3.991 0.200 0.854 MAXIMUM VALUE 132 2.926 1.251 1.372 4.757 0.271 0.928 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.408 0.303 0.021 -0.883 3.280 -0.509 0.863 MINIMUM CORRELATION: -0.509 SERIES 571012 AND 571042 68 YEARS MAXIMUM CORRELATION: 0.863 SERIES 571032 AND 571111 123 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 0.553 0.375 0.320 SDEV 0.255 0.297 0.288 SERR 0.029 0.022 0.025 EPS 0.959 0.926 0.905 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 2.008 0.825 1.158 4.758 0.128 0.885 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.181 0.069 0.546 61 71 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.38 0.99 1.00 1.11 2.10 5.09 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.11 0.00 0.87 0.98 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 0.878 0.796 0.754 0.760 0.728 0.656 0.634 0.639 0.618 0.548 PACF 0.878 0.109 0.157 0.254 -0.042 -0.155 0.156 0.088 -0.075 -0.142 95% C.L. 0.174 0.278 0.340 0.387 0.430 0.466 0.493 0.517 0.540 0.561 |------------------ 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 0.821 0.665 0.028 -0.025 0.278 |================== 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 2.47977066 0.06761577 0.00000000 2.30534124 2 571012 1 1.45790243 0.04177665 0.00000000 2.51430964 3 571021 1 1.91969323 0.01860780 0.00000000 1.21654737 4 571022 1 2.89766574 0.01798884 0.00000000 0.44132918 5 571031 1 2.65803242 0.12600659 0.00000000 1.37102962 6 571032 1 4.21241474 0.02511164 0.00000000 0.20261906 7 571041 1 2.14451003 0.07402620 0.00000000 1.51467574 8 571042 1 3.69718719 0.10265245 0.00000000 1.27787995 9 571051 3 0.00000000 0.00000000 -0.01233492 2.58267927 10 571052 1 2.38341689 0.13211264 0.00000000 1.24106562 11 571061 3 0.00000000 0.00000000 -0.01834904 2.78755498 12 571062 3 0.00000000 0.00000000 -0.02479069 2.54089046 13 571071 1 1.69522691 0.05291643 0.00000000 1.37788808 14 571072 1 2.71499872 0.02022485 0.00000000 0.76857650 15 571081 1 1.12082291 0.33896685 0.00000000 1.21935463 16 571082 1 2.59548807 0.20545509 0.00000000 1.41024220 17 571091 1 1.91844952 0.00912338 0.00000000 0.70472717 18 571092 3 0.00000000 0.00000000 -0.00839647 1.99834800 19 571101 1 2.02111101 0.05213588 0.00000000 1.68181777 SERIES IDENT OPTION A B C D 20 571102 1 3.70256448 0.03166536 0.00000000 1.46952331 21 571111 1 4.31533718 0.03561585 0.00000000 1.23198545 |-------------------- 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 0.293 0.125 2.869 0.183 0.722 2 571012 1899 1978 80 1.000 0.274 0.367 2.839 0.182 0.672 3 571021 1868 1978 111 1.000 0.241 0.825 4.105 0.184 0.520 4 571022 1860 1978 119 0.999 0.309 0.629 3.492 0.209 0.621 5 571031 1873 1978 106 1.000 0.373 0.574 3.398 0.185 0.793 6 571032 1847 1978 132 1.018 0.325 0.745 3.782 0.229 0.480 7 571041 1866 1978 113 0.999 0.475 1.058 5.191 0.193 0.850 8 571042 1864 1966 103 0.999 0.479 0.833 3.145 0.199 0.858 9 571051 1859 1978 120 0.995 0.341 1.909 7.918 0.166 0.794 10 571052 1899 1978 80 1.000 0.331 0.571 3.325 0.202 0.706 11 571061 1891 1978 88 0.993 0.327 -0.100 2.582 0.196 0.768 12 571062 1883 1978 96 1.021 0.381 3.352 22.472 0.190 0.462 13 571071 1873 1967 95 1.000 0.270 0.174 2.805 0.149 0.750 14 571072 1876 1965 90 0.999 0.263 0.910 4.550 0.157 0.723 15 571081 1874 1978 105 1.000 0.297 -0.191 3.433 0.189 0.744 16 571082 1853 1978 126 1.000 0.386 0.818 4.319 0.190 0.813 17 571091 1866 1978 113 1.000 0.265 0.059 3.665 0.174 0.716 18 571092 1868 1978 111 0.997 0.295 0.316 2.711 0.192 0.647 19 571101 1877 1976 100 1.000 0.392 0.297 2.994 0.268 0.682 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 1.000 0.224 -0.091 3.480 0.187 0.417 21 571111 1856 1978 123 1.001 0.354 1.075 6.120 0.238 0.655 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 1.001 0.328 0.679 4.724 0.193 0.685 STANDARD DEVIATION 16 0.006 0.069 0.787 4.261 0.026 0.125 MEDIAN (50TH QUANTILE) 105 1.000 0.325 0.574 3.480 0.190 0.716 INTERQUARTILE RANGE 23 0.001 0.099 0.660 1.326 0.016 0.121 MINIMUM VALUE 70 0.993 0.224 -0.191 2.582 0.149 0.417 LOWER HINGE (25TH QUANTILE) 90 0.999 0.274 0.174 2.994 0.183 0.647 UPPER HINGE (75TH QUANTILE) 113 1.000 0.373 0.833 4.319 0.199 0.768 MAXIMUM VALUE 132 1.021 0.479 3.352 22.472 0.268 0.858 |------------------------ 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 0.995 0.263 0.260 2.936 0.182 0.662 2 571012 1899 1978 80 0.995 0.223 0.116 2.526 0.180 0.509 3 571021 1868 1978 111 0.997 0.206 0.502 3.177 0.183 0.339 4 571022 1860 1978 119 0.996 0.285 0.416 3.223 0.209 0.573 5 571031 1873 1978 106 0.992 0.287 0.036 3.168 0.183 0.667 6 571032 1847 1978 132 0.998 0.295 0.461 2.863 0.229 0.437 7 571041 1866 1978 113 0.980 0.414 0.927 4.820 0.193 0.820 8 571042 1864 1966 103 0.981 0.365 0.214 2.688 0.198 0.778 9 571051 1859 1978 120 0.997 0.299 1.351 6.199 0.167 0.733 10 571052 1899 1978 80 0.996 0.313 0.543 3.276 0.203 0.682 11 571061 1891 1978 88 0.996 0.302 0.175 3.177 0.196 0.716 12 571062 1883 1978 96 0.995 0.302 1.152 7.848 0.189 0.523 13 571071 1873 1967 95 0.992 0.220 -0.013 2.839 0.148 0.656 14 571072 1876 1965 90 0.996 0.220 0.374 3.533 0.157 0.608 15 571081 1874 1978 105 0.995 0.279 -0.216 3.566 0.189 0.702 16 571082 1853 1978 126 0.994 0.327 0.072 3.457 0.189 0.744 17 571091 1866 1978 113 0.996 0.226 -0.645 3.847 0.174 0.620 18 571092 1868 1978 111 0.998 0.273 0.345 2.692 0.192 0.595 19 571101 1877 1976 100 0.991 0.366 0.244 2.999 0.267 0.647 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 0.999 0.218 -0.069 3.452 0.187 0.391 21 571111 1856 1978 123 0.992 0.311 0.634 4.757 0.238 0.592 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 0.994 0.285 0.328 3.669 0.193 0.619 STANDARD DEVIATION 16 0.005 0.055 0.450 1.288 0.027 0.124 MEDIAN (50TH QUANTILE) 105 0.995 0.287 0.260 3.223 0.189 0.647 INTERQUARTILE RANGE 23 0.004 0.085 0.430 0.631 0.016 0.128 MINIMUM VALUE 70 0.980 0.206 -0.645 2.526 0.148 0.339 LOWER HINGE (25TH QUANTILE) 90 0.992 0.226 0.072 2.936 0.182 0.573 UPPER HINGE (75TH QUANTILE) 113 0.996 0.311 0.502 3.566 0.198 0.702 MAXIMUM VALUE 132 0.999 0.414 1.351 7.848 0.267 0.820 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.359 0.202 0.014 -0.668 3.106 -0.195 0.775 MINIMUM CORRELATION: -0.195 SERIES 571012 AND 571031 80 YEARS MAXIMUM CORRELATION: 0.775 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 0.552 0.449 0.280 SDEV 0.107 0.227 0.193 SERR 0.012 0.016 0.017 EPS 0.959 0.944 0.887 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 0.984 0.175 -0.187 3.402 0.122 0.647 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.268 0.127 0.085 31 101 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.21 0.49 1.00 1.08 1.56 2.95 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.00 0.87 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 0.642 0.414 0.252 0.134 0.124 0.093 0.023 -0.028 -0.061 0.003 PACF 0.642 0.004 -0.027 -0.031 0.094 -0.017 -0.084 -0.034 -0.013 0.118 95% C.L. 0.174 0.235 0.256 0.264 0.266 0.267 0.268 0.269 0.269 0.269 |------------------ 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 0.415 0.644 |======================= 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 0.709 0.471 0.281 0.173 0.192 0.107 0.032 -0.004 -0.041 -0.029 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 0.709 2 0.754 -0.064 3 0.751 -0.018 -0.060 4 0.752 -0.018 -0.082 0.029 5 0.747 -0.003 -0.079 -0.101 0.172 6 0.779 -0.022 -0.094 -0.101 0.311 -0.186 7 0.773 -0.011 -0.098 -0.105 0.310 -0.158 -0.037 8 0.774 -0.003 -0.113 -0.099 0.315 -0.157 -0.075 0.049 9 0.776 -0.006 -0.119 -0.088 0.312 -0.161 -0.075 0.078 -0.037 10 0.776 -0.005 -0.120 -0.090 0.315 -0.162 -0.076 0.078 -0.027 -0.012 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) 960.54 870.23 871.70 873.21 875.10 873.13 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 870.48 872.30 873.98 875.80 877.78 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 0.709 R-SQUARED DUE TO POOLED AUTOREGRESSION: 50.31 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 201.23 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.709 0.503 0.357 0.253 0.179 0.127 0.090 0.064 0.045 0.0322 0.023 0.016 0.011 0.008 0.006 0.004 0.003 0.002 0.001 0.0010 0.001 0.001 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 1 0.459 0.665 2 571012 1 0.295 0.516 3 571021 1 0.119 0.345 4 571022 1 0.336 0.575 5 571031 1 0.488 0.680 6 571032 1 0.194 0.439 7 571041 1 0.683 0.822 8 571042 1 0.616 0.785 9 571051 1 0.549 0.741 10 571052 1 0.470 0.686 11 571061 1 0.546 0.724 12 571062 1 0.370 0.598 13 571071 1 0.457 0.663 14 571072 1 0.412 0.620 15 571081 1 0.534 0.702 16 571082 1 0.557 0.745 17 571091 1 0.412 0.625 18 571092 1 0.369 0.607 19 571101 1 0.428 0.649 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 571102 1 0.164 0.399 21 571111 1 0.357 0.593 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.420 0.628 STANDARD DEVIATION 0 0.145 0.122 MEDIAN 1 0.428 0.649 INTERQUARTILE RANGE 0 0.177 0.109 MINIMUM VALUE 1 0.119 0.345 LOWER HINGE 1 0.357 0.593 UPPER HINGE 1 0.534 0.702 MAXIMUM VALUE 1 0.683 0.822 |------------------- 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 0.196 0.121 3.252 0.224 0.112 2 571012 1899 1978 80 1.000 0.191 -0.079 2.848 0.210 0.107 3 571021 1868 1978 111 1.000 0.193 0.439 3.135 0.214 -0.006 4 571022 1860 1978 119 1.000 0.233 0.229 2.703 0.271 -0.052 5 571031 1873 1978 106 1.000 0.210 0.357 2.695 0.253 -0.134 6 571032 1847 1978 132 1.000 0.265 0.486 3.242 0.295 -0.022 7 571041 1866 1978 113 1.000 0.235 0.959 5.513 0.259 -0.118 8 571042 1864 1966 103 1.000 0.226 0.283 3.119 0.244 0.030 9 571051 1859 1978 120 1.000 0.201 0.732 4.721 0.221 -0.010 10 571052 1899 1978 80 1.000 0.227 0.680 3.494 0.241 -0.008 11 571061 1891 1978 88 1.000 0.207 -0.269 3.045 0.226 0.149 12 571062 1883 1978 96 1.000 0.242 1.958 12.883 0.206 0.144 13 571071 1873 1967 95 1.000 0.164 0.035 2.757 0.182 0.120 14 571072 1876 1965 90 1.000 0.173 0.568 2.912 0.197 -0.118 15 571081 1874 1978 105 1.000 0.199 0.011 3.332 0.205 0.198 16 571082 1853 1978 126 1.000 0.218 0.098 4.202 0.230 0.054 17 571091 1866 1978 113 1.000 0.177 -0.684 4.135 0.207 0.120 18 571092 1868 1978 111 1.000 0.216 0.206 2.946 0.240 0.009 19 571101 1877 1976 100 1.000 0.278 0.464 3.124 0.305 0.072 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 1.000 0.200 0.293 3.391 0.221 -0.024 21 571111 1856 1978 123 1.000 0.251 0.606 3.681 0.267 0.055 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 1.000 0.214 0.357 3.863 0.234 0.032 STANDARD DEVIATION 16 0.000 0.030 0.518 2.185 0.032 0.094 MEDIAN (50TH QUANTILE) 105 1.000 0.210 0.293 3.242 0.226 0.030 INTERQUARTILE RANGE 23 0.000 0.037 0.470 0.735 0.043 0.134 MINIMUM VALUE 70 1.000 0.164 -0.684 2.695 0.182 -0.134 LOWER HINGE (25TH QUANTILE) 90 1.000 0.196 0.098 2.946 0.210 -0.022 UPPER HINGE (75TH QUANTILE) 113 1.000 0.233 0.568 3.681 0.253 0.112 MAXIMUM VALUE 132 1.000 0.278 1.958 12.883 0.305 0.198 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.319 0.122 0.008 -0.244 3.092 -0.108 0.642 MINIMUM CORRELATION: -0.108 SERIES 571012 AND 571031 80 YEARS MAXIMUM CORRELATION: 0.642 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 0.428 0.374 0.284 SDEV 0.133 0.143 0.121 SERR 0.015 0.010 0.010 EPS 0.934 0.926 0.889 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 0.996 0.129 0.167 2.953 0.143 0.058 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.310 0.164 0.008 23 109 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.08 0.52 1.00 1.04 1.57 3.35 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.09 0.00 0.87 0.96 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 0.058 0.021 -0.017 -0.099 0.085 0.011 -0.052 -0.021 -0.117 0.074 PACF 0.058 0.018 -0.019 -0.098 0.098 0.004 -0.062 -0.022 -0.095 0.083 95% C.L. 0.174 0.175 0.175 0.175 0.176 0.178 0.178 0.178 0.178 0.181 |------------------ 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 0.018 -0.012 -0.104 0.091 0.009 -0.052 -0.012 -0.120 0.085 PACF -0.001 0.018 -0.012 -0.104 0.092 0.013 -0.060 -0.020 -0.100 0.081 95% C.L. 0.174 0.174 0.174 0.174 0.176 0.177 0.177 0.178 0.178 0.180 |----------------- 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 0.000 -0.001 |========================= 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 0.994 0.182 -0.193 3.115 0.115 0.705 |------------ 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 0.700 0.484 0.309 0.178 0.146 0.066 -0.014 -0.056 -0.098 -0.063 PACF 0.700 -0.011 -0.050 -0.033 0.096 -0.102 -0.076 -0.002 -0.038 0.072 95% C.L. 0.174 0.245 0.272 0.283 0.286 0.288 0.289 0.289 0.289 0.290 |------------------- 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 0.493 0.702 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.28 MINUTES