RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN028W.rwl.conv LOG FILE PROCESSED: FRAN028W.rwl.conv_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: 480 1 Le Tournairet WIDTH_RING PCAB - 480 2 France Norway spruce 2050 4352-720 1715 1977 - 480 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES --- NO GAPS IN DATA FOUND --- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 480021 1813 1977 165 1.720 0.763 0.384 2.118 0.143 0.904 2 480022 1813 1977 165 1.601 0.886 0.913 4.184 0.154 0.900 3 480031 1834 1977 144 1.228 0.442 1.184 4.082 0.148 0.828 4 480032 1857 1977 121 1.098 0.432 1.409 4.927 0.191 0.825 5 480041 1765 1977 213 1.285 0.527 0.780 3.402 0.145 0.883 6 480042 1778 1977 200 1.083 0.649 1.223 4.194 0.179 0.931 7 480051 1844 1977 134 1.856 0.587 0.901 4.010 0.157 0.765 8 480052 1866 1977 112 1.245 0.493 0.903 3.310 0.156 0.843 9 480061 1816 1977 162 1.434 0.520 1.172 6.185 0.157 0.830 10 480062 1825 1977 153 1.273 0.360 0.118 3.088 0.147 0.786 11 480071 1739 1977 239 1.091 0.408 0.993 3.957 0.186 0.816 12 480072 1817 1977 161 0.724 0.414 1.191 4.470 0.236 0.863 13 480081 1842 1977 136 1.108 0.562 0.973 3.265 0.195 0.892 14 480082 1841 1977 137 1.029 0.419 0.790 3.256 0.165 0.847 15 480091 1757 1977 221 0.810 0.367 0.551 3.141 0.206 0.830 16 480092 1772 1977 206 1.009 0.496 0.590 2.646 0.162 0.908 17 480101 1802 1977 176 1.093 0.260 0.559 3.816 0.144 0.699 18 480102 1760 1977 218 1.047 0.305 0.202 2.429 0.166 0.756 19 480111 1759 1977 219 1.318 0.589 0.391 2.182 0.201 0.841 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 480112 1749 1977 229 0.784 0.401 1.122 3.864 0.183 0.885 21 480131 1715 1977 263 0.732 0.349 1.239 5.011 0.198 0.873 22 480132 1715 1977 263 0.852 0.474 0.527 2.578 0.218 0.902 23 480141 1750 1977 228 0.793 0.602 1.460 5.594 0.174 0.930 24 480142 1732 1977 246 0.877 0.520 0.280 2.098 0.177 0.937 25 480151 1786 1977 192 0.979 0.336 0.413 2.806 0.154 0.819 26 480152 1787 1977 191 0.784 0.410 0.704 3.113 0.170 0.891 NUMBER OF SERIES READ IN: 26 FROM 1715 TO 1977 263 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 188 1.110 0.483 0.807 3.605 0.174 0.853 STANDARD DEVIATION 44 0.301 0.141 0.382 1.058 0.025 0.058 MEDIAN (50TH QUANTILE) 191 1.087 0.458 0.845 3.356 0.168 0.855 INTERQUARTILE RANGE 68 0.421 0.161 0.645 1.378 0.037 0.074 MINIMUM VALUE 112 0.724 0.260 0.118 2.098 0.143 0.699 LOWER HINGE (25TH QUANTILE) 153 0.852 0.401 0.527 2.806 0.154 0.825 UPPER HINGE (75TH QUANTILE) 221 1.273 0.562 1.172 4.184 0.191 0.900 MAXIMUM VALUE 263 1.856 0.886 1.460 6.185 0.236 0.937 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.471 0.294 0.016 -0.728 2.469 -0.254 0.948 MINIMUM CORRELATION: -0.254 SERIES 480062 AND 480152 153 YEARS MAXIMUM CORRELATION: 0.948 SERIES 480021 AND 480022 165 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 61.74 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1740. 1770. 1795. 1820. 1845. 1870. 1895. 1920. 1945. CORR 1. 6. 45. 91. 171. 276. 325. 325. 325. RBAR 0.916 0.442 0.458 0.259 0.457 0.477 0.447 0.401 0.494 SDEV 0.000 0.177 0.199 0.255 0.238 0.286 0.272 0.277 0.205 SERR 0.000 0.072 0.030 0.027 0.018 0.017 0.015 0.015 0.011 EPS 0.979 0.885 0.922 0.863 0.950 0.959 0.955 0.946 0.962 NSS 4.2 9.7 13.9 18.1 22.6 25.3 26.0 26.0 26.0 |======================== 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 1715 1977 263 1.051 0.348 0.026 2.499 0.135 0.875 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.580 0.248 0.138 119 144 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.27 0.69 1.00 1.10 1.79 18.75 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.93 0.12 0.75 0.87 0.99 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 192. 68. 112. 153. 221. 263. |----------- 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 0.872 0.816 0.753 0.674 0.598 0.532 0.492 0.424 0.381 0.371 PACF 0.872 0.232 0.018 -0.095 -0.073 -0.009 0.100 -0.082 0.007 0.144 95% C.L. 0.123 0.196 0.242 0.275 0.299 0.317 0.330 0.341 0.349 0.356 |------------------ 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 0.796 0.643 0.272 |================== 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 480021 3 0.00000000 0.00000000 -0.01398296 2.88070655 2 480022 3 0.00000000 0.00000000 -0.01591192 2.92129564 3 480031 1 1.42951941 0.00478117 0.00000000 0.19693109 4 480032 1 0.48110312 0.02639649 0.00000000 0.95530272 5 480041 3 0.00000000 0.00000000 -0.00528435 1.85035479 6 480042 1 2.17410326 0.01547098 0.00000000 0.41736010 7 480051 3 0.00000000 0.00000000 0.00318822 1.64046681 8 480052 1 1.23750019 0.04175335 0.00000000 0.98837239 9 480061 3 0.00000000 0.00000000 0.00375958 1.12735987 10 480062 3 0.00000000 0.00000000 0.00283570 1.05433095 11 480071 3 0.00000000 0.00000000 -0.00135572 1.25415075 12 480072 1 1.03870320 0.01653380 0.00000000 0.36426926 13 480081 1 1.81563592 0.02834264 0.00000000 0.65333146 14 480082 1 1.10678458 0.04618977 0.00000000 0.85890329 15 480091 3 0.00000000 0.00000000 -0.00336844 1.18367052 16 480092 3 0.00000000 0.00000000 -0.00699157 1.73255932 17 480101 3 0.00000000 0.00000000 -0.00011748 1.10346496 18 480102 1 0.62563366 0.00690818 0.00000000 0.72438544 19 480111 3 0.00000000 0.00000000 -0.00677646 2.06321859 SERIES IDENT OPTION A B C D 20 480112 1 1.26896930 0.01239378 0.00000000 0.36584175 21 480131 3 0.00000000 0.00000000 -0.00254458 1.06824195 22 480132 3 0.00000000 0.00000000 -0.00356559 1.32271099 23 480141 1 2.16557574 0.01628469 0.00000000 0.22865731 24 480142 3 0.00000000 0.00000000 -0.00625860 1.64964461 25 480151 3 0.00000000 0.00000000 -0.00378603 1.34410179 26 480152 3 0.00000000 0.00000000 -0.00565574 1.32740152 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 480021 1813 1977 165 1.014 0.266 0.907 4.021 0.142 0.775 2 480022 1813 1977 165 1.030 0.309 0.931 3.667 0.153 0.798 3 480031 1834 1977 144 1.000 0.304 0.679 2.820 0.148 0.774 4 480032 1857 1977 121 1.000 0.357 0.834 3.300 0.189 0.782 5 480041 1765 1977 213 1.004 0.315 0.273 2.696 0.144 0.797 6 480042 1778 1977 200 0.999 0.307 0.666 3.421 0.178 0.743 7 480051 1844 1977 134 1.000 0.306 0.760 3.415 0.156 0.746 8 480052 1866 1977 112 1.000 0.340 1.748 7.728 0.154 0.811 9 480061 1816 1977 162 1.001 0.329 0.454 3.852 0.157 0.795 10 480062 1825 1977 153 1.001 0.271 0.103 2.899 0.147 0.754 11 480071 1739 1977 239 0.999 0.373 1.309 4.738 0.185 0.809 12 480072 1817 1977 161 1.001 0.428 0.533 2.637 0.234 0.772 13 480081 1842 1977 136 1.000 0.337 1.172 5.042 0.194 0.781 14 480082 1841 1977 137 1.000 0.341 0.739 3.283 0.164 0.802 15 480091 1757 1977 221 0.996 0.380 0.708 3.663 0.205 0.785 16 480092 1772 1977 206 1.016 0.327 1.168 4.686 0.161 0.805 17 480101 1802 1977 176 1.000 0.237 0.527 3.767 0.143 0.695 18 480102 1760 1977 218 1.000 0.261 0.099 2.809 0.165 0.703 19 480111 1759 1977 219 1.010 0.354 0.960 4.558 0.200 0.719 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 480112 1749 1977 229 0.999 0.309 1.141 5.726 0.183 0.722 21 480131 1715 1977 263 0.996 0.343 0.474 3.615 0.197 0.754 22 480132 1715 1977 263 0.979 0.430 0.666 3.242 0.218 0.835 23 480141 1750 1977 228 0.992 0.337 1.085 5.063 0.174 0.757 24 480142 1732 1977 246 1.039 0.488 2.093 9.196 0.178 0.831 25 480151 1786 1977 192 0.996 0.266 0.631 2.994 0.153 0.708 26 480152 1787 1977 191 1.003 0.354 1.148 4.729 0.170 0.795 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 188 1.003 0.333 0.839 4.137 0.173 0.771 STANDARD DEVIATION 44 0.012 0.056 0.454 1.533 0.025 0.039 MEDIAN (50TH QUANTILE) 191 1.000 0.333 0.750 3.665 0.168 0.778 INTERQUARTILE RANGE 68 0.005 0.048 0.608 1.487 0.036 0.052 MINIMUM VALUE 112 0.979 0.237 0.099 2.637 0.142 0.695 LOWER HINGE (25TH QUANTILE) 153 0.999 0.306 0.533 3.242 0.153 0.746 UPPER HINGE (75TH QUANTILE) 221 1.003 0.354 1.141 4.729 0.189 0.798 MAXIMUM VALUE 263 1.039 0.488 2.093 9.196 0.234 0.835 |------------------------ 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 480021 -67 110 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 480022 -67 110 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 480031 -67 96 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 480032 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 480041 -67 142 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 480042 -67 134 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 480051 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 480052 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 480061 -67 108 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 480062 -67 102 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 480071 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 480072 -67 107 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 480081 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 480082 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 480091 -67 148 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 480092 -67 138 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 480101 -67 117 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 480102 -67 146 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 480111 -67 146 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 480112 -67 153 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 480131 -67 176 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 480132 -67 176 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 480141 -67 152 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 480142 -67 164 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 25 480151 -67 128 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 26 480152 -67 127 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 480021 1813 1977 165 0.997 0.207 0.088 2.728 0.142 0.654 2 480022 1813 1977 165 0.994 0.228 0.328 3.162 0.153 0.651 3 480031 1834 1977 144 0.997 0.287 0.694 2.927 0.147 0.755 4 480032 1857 1977 121 0.996 0.339 0.872 3.448 0.189 0.765 5 480041 1765 1977 213 0.995 0.285 0.352 3.012 0.144 0.771 6 480042 1778 1977 200 0.998 0.294 0.539 3.302 0.178 0.719 7 480051 1844 1977 134 0.997 0.289 0.728 3.015 0.155 0.729 8 480052 1866 1977 112 0.994 0.294 1.291 6.056 0.153 0.769 9 480061 1816 1977 162 0.996 0.301 0.453 4.055 0.157 0.758 10 480062 1825 1977 153 0.995 0.247 0.273 3.386 0.146 0.710 11 480071 1739 1977 239 0.997 0.304 0.771 3.874 0.185 0.719 12 480072 1817 1977 161 0.991 0.403 0.542 2.658 0.234 0.752 13 480081 1842 1977 136 0.998 0.328 1.180 5.078 0.194 0.770 14 480082 1841 1977 137 0.998 0.333 0.787 3.534 0.164 0.786 15 480091 1757 1977 221 0.996 0.362 0.649 3.285 0.205 0.751 16 480092 1772 1977 206 0.996 0.275 0.444 3.334 0.161 0.741 17 480101 1802 1977 176 0.999 0.228 0.466 3.500 0.143 0.670 18 480102 1760 1977 218 0.999 0.255 0.082 2.872 0.165 0.689 19 480111 1759 1977 219 0.997 0.331 1.385 7.650 0.200 0.692 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 480112 1749 1977 229 0.996 0.262 0.770 4.383 0.182 0.619 21 480131 1715 1977 263 0.994 0.328 0.614 3.845 0.197 0.728 22 480132 1715 1977 263 0.991 0.368 0.629 3.216 0.217 0.749 23 480141 1750 1977 228 0.995 0.304 0.928 4.873 0.174 0.702 24 480142 1732 1977 246 0.983 0.324 0.889 4.857 0.177 0.764 25 480151 1786 1977 192 0.997 0.236 0.558 2.817 0.153 0.622 26 480152 1787 1977 191 0.996 0.337 1.158 4.705 0.170 0.778 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 188 0.995 0.298 0.672 3.830 0.173 0.724 STANDARD DEVIATION 44 0.003 0.048 0.337 1.153 0.025 0.048 MEDIAN (50TH QUANTILE) 191 0.996 0.297 0.639 3.417 0.168 0.735 INTERQUARTILE RANGE 68 0.003 0.069 0.418 1.368 0.037 0.072 MINIMUM VALUE 112 0.983 0.207 0.082 2.658 0.142 0.619 LOWER HINGE (25TH QUANTILE) 153 0.995 0.262 0.453 3.015 0.153 0.692 UPPER HINGE (75TH QUANTILE) 221 0.997 0.331 0.872 4.383 0.189 0.764 MAXIMUM VALUE 263 0.999 0.403 1.385 7.650 0.234 0.786 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.438 0.153 0.008 -0.209 2.704 0.006 0.820 MINIMUM CORRELATION: 0.006 SERIES 480051 AND 480092 134 YEARS MAXIMUM CORRELATION: 0.820 SERIES 480061 AND 480062 153 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 61.74 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1740. 1770. 1795. 1820. 1845. 1870. 1895. 1920. 1945. CORR 1. 6. 45. 91. 171. 276. 325. 325. 325. RBAR 0.923 0.439 0.452 0.272 0.472 0.495 0.440 0.447 0.580 SDEV 0.000 0.142 0.188 0.260 0.255 0.254 0.260 0.251 0.167 SERR 0.000 0.058 0.028 0.027 0.019 0.015 0.014 0.014 0.009 EPS 0.980 0.884 0.920 0.871 0.953 0.961 0.953 0.955 0.973 NSS 4.2 9.7 13.9 18.1 22.6 25.3 26.0 26.0 26.0 |======================== 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 1715 1977 263 0.971 0.232 0.094 3.073 0.139 0.756 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.573 0.252 -0.040 79 184 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.20 0.58 1.00 1.10 1.67 8.31 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.08 0.75 0.88 0.96 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 0.753 0.673 0.551 0.418 0.297 0.145 0.071 -0.037 -0.111 -0.122 PACF 0.753 0.245 -0.038 -0.127 -0.089 -0.163 0.027 -0.068 -0.043 0.090 95% C.L. 0.123 0.180 0.215 0.236 0.247 0.252 0.253 0.253 0.254 0.254 |------------------ 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 0.607 0.559 0.265 |======================= 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 0.715 0.635 0.466 0.310 0.158 -0.025 -0.115 -0.221 -0.296 -0.309 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 0.715 2 0.534 0.253 3 0.564 0.316 -0.118 4 0.546 0.364 -0.033 -0.151 5 0.528 0.360 0.010 -0.086 -0.119 6 0.505 0.343 0.012 -0.016 -0.016 -0.195 7 0.503 0.343 0.012 -0.016 -0.013 -0.190 -0.009 8 0.503 0.335 0.011 -0.017 -0.012 -0.175 0.013 -0.043 9 0.499 0.336 -0.004 -0.018 -0.014 -0.174 0.042 0.000 -0.086 10 0.501 0.336 -0.005 -0.013 -0.014 -0.174 0.042 -0.009 -0.098 0.025 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) 2225.31 2039.25 2023.82 2022.11 2018.05 2016.31 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 2008.16 2010.14 2011.65 2011.71 2013.55 SELECTED AUTOREGRESSION ORDER: 6 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 0.505 0.343 0.012 -0.016 -0.016 -0.195 R-SQUARED DUE TO POOLED AUTOREGRESSION: 58.16 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 239.00 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 6) PROCESS OUT TO ORDER 50: 1.0000 0.505 0.598 0.487 0.441 0.373 0.134 0.085 -0.038 -0.096 -.1547 -0.188 -0.176 -0.169 -0.137 -0.105 -0.066 -0.029 0.001 0.026 0.0425 0.052 0.055 0.051 0.044 0.034 0.023 0.012 0.002 -0.006 -.0116 -0.015 -0.016 -0.016 -0.014 -0.011 -0.008 -0.004 -0.001 0.001 0.0031 0.004 0.005 0.005 0.004 0.004 0.003 0.002 0.001 0.000 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 480021 6 0.457 0.613 0.054 0.018 0.035 0.065 -0.181 2 480022 6 0.451 0.634 0.016 0.009 0.048 0.096 -0.184 3 480031 6 0.634 0.580 0.246 0.102 -0.037 -0.108 -0.140 4 480032 6 0.640 0.657 0.306 -0.120 -0.023 -0.112 -0.006 5 480041 6 0.655 0.557 0.331 0.097 -0.064 -0.099 -0.065 6 480042 6 0.558 0.522 0.270 0.057 0.016 -0.086 -0.011 7 480051 6 0.560 0.695 0.016 0.102 -0.019 -0.054 -0.119 8 480052 6 0.621 0.678 0.235 -0.051 -0.078 -0.029 -0.033 9 480061 6 0.626 0.664 0.171 -0.001 -0.033 0.154 -0.248 10 480062 6 0.576 0.581 0.258 -0.060 -0.006 0.195 -0.262 11 480071 6 0.541 0.624 0.240 -0.037 -0.151 -0.018 0.064 12 480072 6 0.592 0.722 0.083 -0.092 0.225 -0.205 -0.011 13 480081 6 0.616 0.706 0.193 -0.105 0.010 -0.066 -0.052 14 480082 6 0.699 0.608 0.369 -0.017 -0.221 0.067 -0.172 15 480091 6 0.638 0.534 0.353 0.054 -0.047 -0.043 -0.143 16 480092 6 0.595 0.600 0.363 -0.141 -0.095 0.062 -0.053 17 480101 6 0.507 0.510 0.242 0.105 -0.051 -0.037 -0.067 18 480102 6 0.542 0.480 0.278 0.089 0.068 -0.110 -0.161 19 480111 6 0.546 0.577 0.298 -0.154 0.029 -0.091 -0.096 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 480112 6 0.450 0.459 0.297 -0.014 -0.012 0.092 -0.167 21 480131 6 0.579 0.543 0.200 0.077 0.133 -0.097 -0.081 22 480132 6 0.601 0.560 0.278 -0.006 0.046 0.019 -0.131 23 480141 6 0.538 0.530 0.186 0.177 -0.022 -0.070 -0.106 24 480142 6 0.631 0.590 0.237 0.001 0.079 -0.046 -0.045 25 480151 6 0.427 0.568 0.107 -0.041 0.096 0.062 -0.144 26 480152 6 0.635 0.671 0.168 -0.029 0.085 0.013 -0.180 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 6 0.574 0.595 0.223 0.001 0.000 -0.017 -0.108 STANDARD DEVIATION 0 0.070 0.070 0.101 0.085 0.090 0.094 0.078 MEDIAN 6 0.585 0.585 0.241 -0.003 -0.009 -0.040 -0.113 INTERQUARTILE RANGE 0 0.090 0.115 0.126 0.129 0.095 0.153 0.114 MINIMUM VALUE 6 0.427 0.459 0.016 -0.154 -0.221 -0.205 -0.262 LOWER HINGE 6 0.541 0.543 0.171 -0.051 -0.047 -0.091 -0.167 UPPER HINGE 6 0.631 0.657 0.297 0.077 0.048 0.062 -0.052 MAXIMUM VALUE 6 0.699 0.722 0.369 0.177 0.225 0.195 0.064 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 480021 1813 1977 165 1.000 0.153 0.167 3.216 0.175 0.003 2 480022 1813 1977 165 1.000 0.168 -0.027 3.882 0.195 -0.009 3 480031 1834 1977 144 1.000 0.174 0.641 4.888 0.178 0.011 4 480032 1857 1977 121 1.000 0.206 0.589 4.112 0.221 0.002 5 480041 1765 1977 213 1.000 0.166 0.525 3.716 0.181 -0.010 6 480042 1778 1977 200 1.000 0.196 0.261 3.447 0.216 -0.002 7 480051 1844 1977 134 1.000 0.192 0.359 3.997 0.210 -0.004 8 480052 1866 1977 112 1.000 0.181 0.448 4.061 0.192 -0.001 9 480061 1816 1977 162 1.000 0.184 -0.162 5.856 0.195 0.015 10 480062 1825 1977 153 1.000 0.161 0.042 2.811 0.184 0.004 11 480071 1739 1977 239 1.000 0.206 0.230 3.091 0.232 -0.001 12 480072 1817 1977 161 1.000 0.257 0.471 3.597 0.297 0.002 13 480081 1842 1977 136 1.000 0.203 0.247 2.688 0.235 -0.003 14 480082 1841 1977 137 1.000 0.183 0.636 6.101 0.187 0.013 15 480091 1757 1977 221 1.000 0.218 0.008 3.787 0.246 -0.019 16 480092 1772 1977 206 1.000 0.175 0.043 3.505 0.201 -0.001 17 480101 1802 1977 176 1.000 0.159 0.201 3.151 0.179 -0.008 18 480102 1760 1977 218 1.000 0.173 -0.024 3.509 0.197 -0.012 19 480111 1759 1977 219 1.000 0.223 0.772 4.759 0.242 0.008 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 480112 1749 1977 229 1.000 0.194 0.723 4.510 0.213 -0.008 21 480131 1715 1977 263 1.000 0.212 0.257 3.825 0.239 -0.003 22 480132 1715 1977 263 1.000 0.232 0.291 3.823 0.255 -0.002 23 480141 1750 1977 228 1.000 0.207 1.390 8.482 0.213 -0.010 24 480142 1732 1977 246 1.000 0.197 0.473 6.056 0.210 0.005 25 480151 1786 1977 192 1.000 0.177 0.372 3.157 0.195 -0.009 26 480152 1787 1977 191 1.000 0.203 0.784 4.790 0.215 -0.006 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 188 1.000 0.192 0.374 4.185 0.212 -0.002 STANDARD DEVIATION 44 0.000 0.025 0.336 1.276 0.029 0.008 MEDIAN (50TH QUANTILE) 191 1.000 0.193 0.325 3.824 0.210 -0.002 INTERQUARTILE RANGE 68 0.000 0.032 0.421 1.313 0.040 0.011 MINIMUM VALUE 112 1.000 0.153 -0.162 2.688 0.175 -0.019 LOWER HINGE (25TH QUANTILE) 153 1.000 0.174 0.167 3.447 0.192 -0.008 UPPER HINGE (75TH QUANTILE) 221 1.000 0.206 0.589 4.759 0.232 0.003 MAXIMUM VALUE 263 1.000 0.257 1.390 8.482 0.297 0.015 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.418 0.109 0.006 0.154 3.088 0.124 0.749 MINIMUM CORRELATION: 0.124 SERIES 480052 AND 480141 112 YEARS MAXIMUM CORRELATION: 0.749 SERIES 480131 AND 480132 263 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 61.74 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1740. 1770. 1795. 1820. 1845. 1870. 1895. 1920. 1945. CORR 1. 6. 45. 91. 171. 276. 325. 325. 325. RBAR 0.683 0.413 0.441 0.464 0.446 0.443 0.435 0.437 0.482 SDEV 0.000 0.136 0.134 0.151 0.161 0.155 0.157 0.138 0.129 SERR 0.000 0.056 0.020 0.016 0.012 0.009 0.009 0.008 0.007 EPS 0.900 0.872 0.916 0.940 0.948 0.953 0.952 0.953 0.960 NSS 4.2 9.7 13.9 18.1 22.6 25.3 26.0 26.0 26.0 |======================== 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 1715 1977 263 0.996 0.134 0.226 2.794 0.158 -0.044 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.280 0.114 0.021 74 189 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.20 0.50 1.00 1.07 1.57 8.25 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.09 0.55 0.88 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 -0.044 0.026 0.079 0.039 -0.005 -0.074 0.072 -0.047 -0.097 0.012 PACF -0.044 0.024 0.082 0.046 -0.005 -0.084 0.059 -0.038 -0.092 0.002 95% C.L. 0.123 0.124 0.124 0.124 0.125 0.125 0.125 0.126 0.126 0.127 |------------------ 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 0.005 -0.002 -0.012 -0.004 0.004 0.004 0.049 -0.040 -0.072 0.010 PACF 0.005 -0.002 -0.012 -0.004 0.004 0.004 0.049 -0.041 -0.072 0.012 95% C.L. 0.123 0.123 0.123 0.123 0.123 0.123 0.123 0.124 0.124 0.124 |----------------- REWHITENED CHRONOLOGY AUTOREGRESSIVE MODEL -----------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 6 0.003 0.005 -0.002 -0.012 -0.005 0.004 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 1715 1977 263 0.997 0.212 0.269 2.816 0.131 0.730 |------------ 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 0.727 0.646 0.476 0.317 0.167 -0.021 -0.118 -0.247 -0.313 -0.330 PACF 0.727 0.249 -0.132 -0.161 -0.104 -0.206 -0.017 -0.091 -0.054 0.045 95% C.L. 0.123 0.177 0.210 0.226 0.232 0.234 0.234 0.235 0.239 0.245 |------------------- 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 6 0.611 0.508 0.357 0.019 -0.017 -0.005 -0.217 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.32 MINUTES