RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit024e.rwl LOG FILE PROCESSED: brit024e.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: 387 1 Glen Affric WIDTH_EARLY PISY - 387 2 Great Britain Scots pine, Scotch pine 300 5717-455 1735 1976 - 387 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 2 387012 MISSING VALUES FOUND: 14 IN 1 GAPS / 1793 1806 / -------------------------------------------------------------------- 11 388061 MISSING VALUES FOUND: 1 IN 1 GAPS / 1965 1965 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 387011 1735 1976 242 0.768 0.475 0.421 2.854 0.256 0.897 2 387012 1751 1976 226 0.828 0.505 0.855 3.310 0.224 0.889 3 387021 1766 1976 211 0.485 0.384 1.367 4.034 0.279 0.916 4 387022 1813 1976 164 0.884 0.562 0.371 2.094 0.211 0.906 5 387031 1808 1976 169 0.601 0.307 3.785 25.406 0.266 0.659 6 387032 1809 1976 168 0.593 0.260 1.746 7.764 0.265 0.658 7 387041 1787 1975 189 0.716 0.277 1.068 6.526 0.226 0.665 8 387042 1766 1976 211 0.643 0.293 1.160 5.162 0.240 0.784 9 387051 1829 1976 148 1.087 0.189 -0.319 3.239 0.127 0.621 10 387052 1808 1976 169 0.735 0.244 0.514 3.478 0.195 0.720 11 388061 1816 1975 160 0.720 0.544 0.959 3.837 0.298 0.814 12 388062 1826 1976 151 0.750 0.661 1.343 4.480 0.348 0.800 13 388071 1812 1976 165 0.767 0.333 0.638 3.255 0.239 0.777 14 388072 1785 1976 192 0.625 0.337 0.324 2.336 0.236 0.868 15 388081 1810 1976 167 0.580 0.269 0.452 2.397 0.259 0.769 16 388082 1843 1950 108 0.550 0.286 0.022 2.229 0.362 0.740 17 388091 1829 1976 148 0.686 0.405 1.064 4.757 0.222 0.838 18 388092 1827 1976 150 0.709 0.272 0.361 2.666 0.225 0.747 19 388101 1828 1976 149 0.783 0.498 1.144 4.460 0.238 0.858 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 388102 1776 1976 201 0.593 0.350 0.896 3.132 0.258 0.859 21 389111 1776 1976 201 0.637 0.293 -0.114 2.451 0.259 0.840 22 389112 1758 1976 219 0.653 0.300 0.080 2.743 0.296 0.800 23 389121 1840 1976 137 1.102 0.356 0.950 4.117 0.202 0.641 24 389131 1769 1976 208 0.545 0.294 0.264 2.364 0.269 0.851 25 389132 1825 1976 152 0.774 0.329 1.092 3.730 0.197 0.798 NUMBER OF SERIES READ IN: 25 FROM 1735 TO 1976 242 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 176 0.713 0.361 0.818 4.513 0.248 0.789 STANDARD DEVIATION 31 0.150 0.116 0.802 4.561 0.048 0.088 MEDIAN (50TH QUANTILE) 168 0.709 0.329 0.855 3.310 0.240 0.800 INTERQUARTILE RANGE 50 0.166 0.119 0.731 1.794 0.042 0.118 MINIMUM VALUE 108 0.485 0.189 -0.319 2.094 0.127 0.621 LOWER HINGE (25TH QUANTILE) 151 0.601 0.286 0.361 2.666 0.224 0.740 UPPER HINGE (75TH QUANTILE) 201 0.768 0.405 1.092 4.460 0.266 0.858 MAXIMUM VALUE 242 1.102 0.661 3.785 25.406 0.362 0.916 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 300 0.373 0.262 0.015 -0.266 2.211 -0.350 0.886 MINIMUM CORRELATION: -0.350 SERIES 387032 AND 388082 108 YEARS MAXIMUM CORRELATION: 0.886 SERIES 387011 AND 387012 226 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 65.17 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1790. 1815. 1840. 1865. 1890. 1915. 1940. CORR 3. 45. 120. 276. 300. 300. 276. RBAR 0.595 0.412 0.214 0.239 0.170 0.173 0.370 SDEV 0.325 0.420 0.279 0.231 0.266 0.305 0.283 SERR 0.188 0.063 0.025 0.014 0.015 0.018 0.017 EPS 0.931 0.916 0.860 0.887 0.836 0.839 0.935 NSS 9.2 15.6 22.4 24.9 25.0 25.0 24.7 |======================== 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 1735 1976 242 0.622 0.259 0.232 2.288 0.165 0.864 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.502 0.244 0.113 91 151 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.16 0.30 1.00 1.07 1.37 11.96 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.10 0.00 0.84 0.95 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 168. 50. 108. 151. 201. 242. |----------- 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 0.861 0.832 0.819 0.768 0.772 0.749 0.713 0.713 0.683 0.641 PACF 0.861 0.353 0.228 -0.030 0.160 0.034 -0.040 0.069 -0.019 -0.109 95% C.L. 0.129 0.203 0.253 0.293 0.325 0.354 0.379 0.401 0.421 0.439 |------------------ 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 3 0.798 0.476 0.221 0.238 |================== 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 387011 3 0.00000000 0.00000000 0.00149897 0.58543706 2 387012 3 0.00000000 0.00000000 0.00023867 0.76106054 3 387021 3 0.00000000 0.00000000 -0.00221944 0.71981043 4 387022 3 0.00000000 0.00000000 -0.01049772 1.75026929 5 387031 1 1.01271343 0.11134584 0.00000000 0.55036587 6 387032 1 1.10663259 0.18607152 0.00000000 0.56112409 7 387041 3 0.00000000 0.00000000 0.00055860 0.66317683 8 387042 3 0.00000000 0.00000000 0.00188681 0.44260529 9 387051 3 0.00000000 0.00000000 0.00018752 1.07298946 10 387052 3 0.00000000 0.00000000 -0.00015541 0.74823964 11 388061 3 0.00000000 0.00000000 -0.00703929 1.28371572 12 388062 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 388071 3 0.00000000 0.00000000 -0.00338976 1.04868364 14 388072 3 0.00000000 0.00000000 -0.00060493 0.68321991 15 388081 3 0.00000000 0.00000000 -0.00284488 0.81932902 16 388082 3 0.00000000 0.00000000 -0.00511661 0.82913291 17 388091 3 0.00000000 0.00000000 -0.00783826 1.26955879 18 388092 3 0.00000000 0.00000000 -0.00395314 1.00792837 19 388101 3 0.00000000 0.00000000 -0.00912839 1.46764922 SERIES IDENT OPTION A B C D 20 388102 3 0.00000000 0.00000000 -0.00177018 0.77187264 21 389111 3 0.00000000 0.00000000 0.00025938 0.61116618 22 389112 3 0.00000000 0.00000000 0.00025007 0.62555152 23 389121 3 0.00000000 0.00000000 -0.00392102 1.37266743 24 389131 3 0.00000000 0.00000000 -0.00214750 0.76975054 25 389132 1 0.83294296 0.00540809 0.00000000 0.20741872 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 387011 1735 1976 242 0.995 0.640 0.643 3.038 0.255 0.885 2 387012 1751 1976 226 1.000 0.657 0.897 3.344 0.221 0.900 3 387021 1766 1976 211 0.974 0.629 0.957 3.276 0.278 0.873 4 387022 1813 1976 164 1.079 0.621 4.023 20.967 0.210 0.769 5 387031 1808 1976 169 1.000 0.382 0.997 4.048 0.265 0.600 6 387032 1809 1976 168 1.000 0.377 0.896 3.974 0.263 0.560 7 387041 1787 1975 189 1.000 0.389 1.216 7.290 0.225 0.653 8 387042 1766 1976 211 0.996 0.415 1.197 5.026 0.238 0.701 9 387051 1829 1976 148 1.000 0.174 -0.299 3.171 0.126 0.619 10 387052 1808 1976 169 1.000 0.330 0.461 3.415 0.194 0.711 11 388061 1816 1975 160 0.936 0.543 0.909 3.870 0.300 0.732 12 388062 1826 1976 151 1.008 0.381 1.049 4.325 0.346 0.282 13 388071 1812 1976 165 0.992 0.360 0.340 2.595 0.238 0.699 14 388072 1785 1976 192 0.999 0.533 0.286 2.232 0.235 0.861 15 388081 1810 1976 167 0.991 0.360 0.025 2.475 0.258 0.652 16 388082 1843 1950 108 0.982 0.417 -0.076 2.591 0.359 0.539 17 388091 1829 1976 148 1.025 0.326 0.619 3.442 0.221 0.587 18 388092 1827 1976 150 0.997 0.296 0.186 2.644 0.224 0.604 19 388101 1828 1976 149 1.029 0.387 0.923 3.890 0.237 0.711 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 388102 1776 1976 201 0.991 0.530 0.760 3.111 0.257 0.843 21 389111 1776 1976 201 1.000 0.464 -0.065 2.442 0.257 0.839 22 389112 1758 1976 219 1.000 0.463 0.119 2.730 0.294 0.798 23 389121 1840 1976 137 0.999 0.279 0.606 2.892 0.201 0.582 24 389131 1769 1976 208 0.982 0.489 0.466 2.572 0.268 0.828 25 389132 1825 1976 152 1.000 0.398 1.516 5.279 0.196 0.783 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 176 0.999 0.434 0.746 4.185 0.247 0.704 STANDARD DEVIATION 32 0.024 0.122 0.824 3.670 0.048 0.142 MEDIAN (50TH QUANTILE) 168 1.000 0.398 0.643 3.276 0.238 0.711 INTERQUARTILE RANGE 50 0.007 0.170 0.671 1.330 0.044 0.223 MINIMUM VALUE 108 0.936 0.174 -0.299 2.232 0.126 0.282 LOWER HINGE (25TH QUANTILE) 151 0.992 0.360 0.286 2.644 0.221 0.604 UPPER HINGE (75TH QUANTILE) 201 1.000 0.530 0.957 3.974 0.265 0.828 MAXIMUM VALUE 242 1.079 0.657 4.023 20.967 0.359 0.900 |------------------------ 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 387011 -67 162 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 387012 -67 151 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 387021 -67 141 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 387022 -67 109 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 387031 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 387032 -67 112 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 387041 -67 126 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 387042 -67 141 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 387051 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 387052 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 388061 -67 107 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 388062 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 388071 -67 110 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 388072 -67 128 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 388081 -67 111 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 388082 -67 72 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 388091 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 388092 -67 100 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 388101 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 388102 -67 134 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 389111 -67 134 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 389112 -67 146 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 389121 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 389131 -67 139 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 25 389132 -67 101 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 387011 1735 1976 242 0.963 0.509 0.556 4.551 0.254 0.789 2 387012 1751 1976 226 1.001 0.543 1.399 6.967 0.223 0.823 3 387021 1766 1976 211 0.999 0.519 2.243 13.435 0.280 0.698 4 387022 1813 1976 164 0.993 0.342 0.763 4.482 0.209 0.667 5 387031 1808 1976 169 0.992 0.324 1.046 5.279 0.265 0.447 6 387032 1809 1976 168 0.990 0.322 0.947 4.395 0.263 0.427 7 387041 1787 1975 189 0.995 0.355 1.623 10.150 0.225 0.573 8 387042 1766 1976 211 0.991 0.346 1.243 5.474 0.238 0.569 9 387051 1829 1976 148 0.998 0.157 -0.317 3.307 0.126 0.531 10 387052 1808 1976 169 0.988 0.246 0.501 3.224 0.193 0.510 11 388061 1816 1975 160 0.984 0.438 0.995 4.344 0.301 0.582 12 388062 1826 1976 151 0.999 0.370 0.904 3.794 0.346 0.274 13 388071 1812 1976 165 0.991 0.284 0.122 2.645 0.238 0.522 14 388072 1785 1976 192 0.994 0.396 1.094 6.937 0.238 0.676 15 388081 1810 1976 167 0.993 0.318 0.278 2.741 0.257 0.548 16 388082 1843 1950 108 0.992 0.394 0.812 5.933 0.358 0.283 17 388091 1829 1976 148 0.992 0.260 0.162 2.609 0.221 0.434 18 388092 1827 1976 150 0.996 0.268 0.199 3.287 0.224 0.519 19 388101 1828 1976 149 0.998 0.355 0.950 4.271 0.236 0.692 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 388102 1776 1976 201 0.995 0.414 0.646 3.816 0.256 0.689 21 389111 1776 1976 201 1.001 0.410 1.146 9.166 0.258 0.705 22 389112 1758 1976 219 0.983 0.396 -0.128 3.008 0.294 0.732 23 389121 1840 1976 137 0.996 0.250 0.425 2.783 0.200 0.482 24 389131 1769 1976 208 0.997 0.336 0.175 3.232 0.267 0.578 25 389132 1825 1976 152 0.993 0.360 1.260 4.565 0.195 0.740 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 176 0.992 0.356 0.762 4.976 0.247 0.580 STANDARD DEVIATION 32 0.008 0.089 0.583 2.630 0.048 0.143 MEDIAN (50TH QUANTILE) 168 0.993 0.355 0.812 4.344 0.238 0.573 INTERQUARTILE RANGE 50 0.005 0.078 0.815 2.242 0.042 0.182 MINIMUM VALUE 108 0.963 0.157 -0.317 2.609 0.126 0.274 LOWER HINGE (25TH QUANTILE) 151 0.991 0.318 0.278 3.232 0.223 0.510 UPPER HINGE (75TH QUANTILE) 201 0.997 0.396 1.094 5.474 0.265 0.692 MAXIMUM VALUE 242 1.001 0.543 2.243 13.435 0.358 0.823 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 300 0.151 0.161 0.009 0.468 3.397 -0.268 0.689 MINIMUM CORRELATION: -0.268 SERIES 387041 AND 388082 108 YEARS MAXIMUM CORRELATION: 0.689 SERIES 388071 AND 388072 165 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 65.17 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1790. 1815. 1840. 1865. 1890. 1915. 1940. CORR 3. 45. 120. 276. 300. 300. 276. RBAR 0.632 0.320 0.144 0.181 0.132 0.165 0.196 SDEV 0.279 0.372 0.227 0.227 0.199 0.210 0.219 SERR 0.161 0.055 0.021 0.014 0.012 0.012 0.013 EPS 0.940 0.880 0.790 0.847 0.792 0.832 0.858 NSS 9.2 15.6 22.4 24.9 25.0 25.0 24.7 |======================== 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 1735 1976 242 1.024 0.357 0.437 4.533 0.216 0.713 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.230 0.166 0.172 72 170 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.19 0.48 1.00 1.08 1.56 70.05 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.09 0.00 0.85 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 0.710 0.624 0.553 0.436 0.449 0.374 0.363 0.388 0.339 0.280 PACF 0.710 0.241 0.097 -0.078 0.170 -0.043 0.076 0.110 -0.012 -0.122 95% C.L. 0.129 0.182 0.215 0.237 0.250 0.263 0.272 0.279 0.288 0.295 |------------------ 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 3 0.555 0.521 0.189 0.100 |======================= 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 0.557 0.391 0.362 0.237 0.240 0.124 0.098 0.145 0.095 0.061 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 0.557 2 0.491 0.118 3 0.473 0.042 0.153 4 0.482 0.045 0.179 -0.055 5 0.488 0.026 0.174 -0.106 0.106 6 0.500 0.013 0.195 -0.103 0.165 -0.121 7 0.505 0.006 0.200 -0.111 0.164 -0.142 0.042 8 0.503 0.016 0.188 -0.103 0.150 -0.142 0.006 0.071 9 0.503 0.016 0.187 -0.102 0.149 -0.141 0.006 0.074 -0.007 10 0.503 0.019 0.187 -0.107 0.155 -0.145 0.013 0.075 0.013 -0.039 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) 1881.50 1793.68 1792.31 1788.57 1789.84 1789.12 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1787.55 1789.13 1789.90 1791.89 1793.53 SELECTED AUTOREGRESSION ORDER: 3 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 0.473 0.042 0.153 R-SQUARED DUE TO POOLED AUTOREGRESSION: 33.55 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 150.50 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.473 0.266 0.299 0.225 0.160 0.131 0.103 0.079 0.062 0.0484 0.038 0.029 0.023 0.018 0.014 0.011 0.008 0.007 0.005 0.0040 0.003 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.000 0.0003 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 387011 3 0.684 0.551 0.191 0.135 2 387012 3 0.733 0.681 0.164 0.038 3 387021 3 0.585 0.666 0.151 -0.032 4 387022 3 0.484 0.571 0.164 -0.001 5 387031 3 0.236 0.424 0.083 -0.043 6 387032 3 0.280 0.257 0.271 0.131 7 387041 3 0.329 0.580 -0.016 0.010 8 387042 3 0.366 0.607 -0.030 0.026 9 387051 3 0.315 0.444 0.131 0.044 10 387052 3 0.267 0.496 -0.011 0.076 11 388061 3 0.372 0.703 -0.216 0.056 12 388062 3 0.094 0.302 -0.101 -0.063 13 388071 3 0.337 0.405 0.035 0.258 14 388072 3 0.557 0.543 0.096 0.177 15 388081 3 0.310 0.555 -0.051 0.084 16 388082 3 0.095 0.320 -0.097 0.063 17 388091 3 0.243 0.336 0.163 0.109 18 388092 3 0.286 0.484 0.140 -0.110 19 388101 3 0.507 0.741 0.029 -0.145 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 388102 3 0.513 0.636 0.078 0.030 21 389111 3 0.584 0.610 0.160 0.034 22 389112 3 0.583 0.512 0.142 0.183 23 389121 3 0.253 0.439 0.123 -0.019 24 389131 3 0.396 0.498 0.019 0.176 25 389132 3 0.557 0.770 0.019 -0.082 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.399 0.525 0.065 0.045 STANDARD DEVIATION 0 0.171 0.138 0.112 0.098 MEDIAN 3 0.366 0.543 0.083 0.038 INTERQUARTILE RANGE 0 0.276 0.171 0.162 0.128 MINIMUM VALUE 3 0.094 0.257 -0.216 -0.145 LOWER HINGE 3 0.280 0.439 -0.011 -0.019 UPPER HINGE 3 0.557 0.610 0.151 0.109 MAXIMUM VALUE 3 0.733 0.770 0.271 0.258 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 387011 1735 1976 242 1.002 0.274 1.227 8.524 0.251 0.041 2 387012 1751 1976 226 1.000 0.275 1.274 8.128 0.286 -0.029 3 387021 1766 1976 211 1.001 0.314 0.588 4.571 0.347 -0.075 4 387022 1813 1976 164 1.000 0.247 1.219 7.315 0.265 0.018 5 387031 1808 1976 169 1.000 0.288 1.192 7.793 0.321 0.005 6 387032 1809 1976 168 1.001 0.271 0.106 4.068 0.306 -0.004 7 387041 1787 1975 189 1.000 0.291 1.741 10.777 0.277 -0.001 8 387042 1766 1976 211 1.000 0.272 0.473 4.462 0.299 -0.027 9 387051 1829 1976 148 1.000 0.131 -0.113 2.662 0.150 0.005 10 387052 1808 1976 169 1.000 0.211 0.231 3.176 0.234 0.002 11 388061 1816 1975 160 1.000 0.348 0.871 4.284 0.360 0.009 12 388062 1826 1976 151 1.000 0.352 1.040 4.501 0.376 0.002 13 388071 1812 1976 165 1.000 0.232 -0.210 3.578 0.266 0.011 14 388072 1785 1976 192 1.000 0.256 0.263 3.979 0.279 -0.032 15 388081 1810 1976 167 1.000 0.264 -0.078 2.573 0.305 -0.006 16 388082 1843 1950 108 1.000 0.374 0.733 5.522 0.401 -0.009 17 388091 1829 1976 148 1.000 0.224 0.010 2.673 0.251 -0.017 18 388092 1827 1976 150 1.000 0.227 -0.156 3.120 0.266 0.005 19 388101 1828 1976 149 1.000 0.250 0.423 3.279 0.282 -0.021 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 388102 1776 1976 201 1.000 0.288 0.598 4.748 0.320 -0.020 21 389111 1776 1976 201 1.000 0.254 -0.007 3.619 0.292 -0.052 22 389112 1758 1976 219 1.000 0.255 0.268 3.178 0.296 -0.009 23 389121 1840 1976 137 1.000 0.214 0.181 2.962 0.243 -0.008 24 389131 1769 1976 208 1.000 0.267 0.213 3.445 0.309 -0.040 25 389132 1825 1976 152 1.000 0.241 0.911 4.993 0.255 -0.009 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 176 1.000 0.265 0.520 4.717 0.289 -0.010 STANDARD DEVIATION 32 0.000 0.050 0.540 2.147 0.051 0.024 MEDIAN (50TH QUANTILE) 168 1.000 0.264 0.423 4.068 0.286 -0.008 INTERQUARTILE RANGE 50 0.000 0.047 0.805 1.815 0.044 0.026 MINIMUM VALUE 108 1.000 0.131 -0.210 2.573 0.150 -0.075 LOWER HINGE (25TH QUANTILE) 151 1.000 0.241 0.106 3.178 0.265 -0.021 UPPER HINGE (75TH QUANTILE) 201 1.000 0.288 0.911 4.993 0.309 0.005 MAXIMUM VALUE 242 1.002 0.374 1.741 10.777 0.401 0.041 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 300 0.192 0.111 0.006 0.309 4.039 -0.174 0.633 MINIMUM CORRELATION: -0.174 SERIES 387041 AND 388082 108 YEARS MAXIMUM CORRELATION: 0.633 SERIES 387031 AND 387032 168 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 65.17 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1790. 1815. 1840. 1865. 1890. 1915. 1940. CORR 3. 45. 120. 276. 300. 300. 276. RBAR 0.390 0.240 0.170 0.181 0.160 0.224 0.295 SDEV 0.363 0.157 0.146 0.158 0.157 0.141 0.149 SERR 0.210 0.023 0.013 0.009 0.009 0.008 0.009 EPS 0.855 0.832 0.821 0.846 0.827 0.878 0.912 NSS 9.2 15.6 22.4 24.9 25.0 25.0 24.7 |======================== 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 1735 1976 242 0.988 0.212 0.500 4.959 0.233 -0.102 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.189 0.097 0.117 84 158 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.26 0.71 1.00 1.11 1.82 89.70 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.10 0.00 0.87 0.97 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 -0.102 -0.001 0.081 -0.112 0.107 -0.032 -0.012 0.076 -0.004 -0.046 PACF -0.102 -0.012 0.081 -0.098 0.090 -0.022 0.000 0.052 0.031 -0.059 95% C.L. 0.129 0.130 0.130 0.131 0.132 0.134 0.134 0.134 0.135 0.135 |------------------ RESIDUAL CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.011 -0.103 |---------- REWHITENED CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS -----------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.010 -0.010 -0.009 -0.087 0.090 -0.030 0.005 0.071 0.002 -0.051 PACF 0.010 -0.010 -0.009 -0.087 0.092 -0.034 0.007 0.065 0.015 -0.064 95% C.L. 0.129 0.129 0.129 0.129 0.130 0.131 0.131 0.131 0.131 0.131 |----------------- 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 3 0.009 0.010 -0.010 -0.009 |========================= 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 1735 1976 242 0.991 0.257 0.310 3.851 0.185 0.555 |------------ 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 0.553 0.381 0.339 0.228 0.237 0.159 0.134 0.141 0.078 0.016 PACF 0.553 0.110 0.132 -0.035 0.110 -0.059 0.036 0.028 -0.038 -0.078 95% C.L. 0.129 0.163 0.177 0.188 0.192 0.197 0.199 0.201 0.202 0.203 |------------------- ARSTAN CHRONOLOGY AUTOREGRESSIVE MODEL -------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 3 0.330 0.485 0.041 0.130 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 1.62 MINUTES