RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN028L.rwl.conv LOG FILE PROCESSED: FRAN028L.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_LATE 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 0.294 0.193 1.061 3.944 0.346 0.758 2 480022 1813 1977 165 0.256 0.170 1.468 6.174 0.332 0.667 3 480031 1834 1977 144 0.311 0.139 1.561 5.725 0.250 0.678 4 480032 1857 1977 121 0.336 0.173 2.374 10.381 0.231 0.716 5 480041 1765 1977 213 0.178 0.076 0.364 2.903 0.339 0.561 6 480042 1778 1977 200 0.163 0.088 0.920 3.315 0.346 0.640 7 480051 1844 1977 134 0.473 0.238 1.985 8.229 0.265 0.743 8 480052 1866 1977 112 0.271 0.148 1.625 6.010 0.241 0.780 9 480061 1816 1977 162 0.240 0.135 2.655 12.255 0.235 0.845 10 480062 1825 1977 153 0.196 0.075 0.776 3.550 0.238 0.668 11 480071 1739 1977 239 0.274 0.143 1.618 6.259 0.271 0.745 12 480072 1817 1977 161 0.201 0.130 1.722 6.904 0.279 0.770 13 480081 1842 1977 136 0.272 0.141 0.880 3.288 0.312 0.723 14 480082 1841 1977 137 0.213 0.118 0.942 3.522 0.293 0.784 15 480091 1757 1977 221 0.129 0.079 1.642 7.686 0.354 0.695 16 480092 1772 1977 206 0.149 0.090 0.991 3.647 0.328 0.759 17 480101 1802 1977 176 0.290 0.092 0.296 3.572 0.248 0.572 18 480102 1760 1977 218 0.304 0.127 0.703 3.405 0.258 0.698 19 480111 1759 1977 219 0.243 0.147 1.026 3.552 0.323 0.697 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 480112 1749 1977 229 0.149 0.104 2.160 8.397 0.293 0.823 21 480131 1715 1977 263 0.172 0.093 1.371 4.706 0.259 0.802 22 480132 1715 1977 263 0.221 0.134 0.864 3.633 0.263 0.831 23 480141 1750 1977 228 0.134 0.125 2.625 13.268 0.405 0.810 24 480142 1732 1977 246 0.166 0.109 0.906 3.355 0.321 0.813 25 480151 1786 1977 192 0.218 0.100 0.755 3.065 0.232 0.767 26 480152 1787 1977 191 0.164 0.127 2.703 11.858 0.259 0.821 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 0.231 0.127 1.384 5.869 0.289 0.737 STANDARD DEVIATION 44 0.078 0.038 0.698 3.144 0.047 0.076 MEDIAN (50TH QUANTILE) 191 0.220 0.127 1.216 4.325 0.275 0.752 INTERQUARTILE RANGE 68 0.108 0.050 0.842 4.165 0.078 0.107 MINIMUM VALUE 112 0.129 0.075 0.296 2.903 0.231 0.561 LOWER HINGE (25TH QUANTILE) 153 0.166 0.093 0.880 3.522 0.250 0.695 UPPER HINGE (75TH QUANTILE) 221 0.274 0.143 1.722 7.686 0.328 0.802 MAXIMUM VALUE 263 0.473 0.238 2.703 13.268 0.405 0.845 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.380 0.268 0.015 -0.418 2.122 -0.235 0.859 MINIMUM CORRELATION: -0.235 SERIES 480022 AND 480061 162 YEARS MAXIMUM CORRELATION: 0.859 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 0.806 0.357 0.447 0.413 0.376 0.355 0.309 0.342 0.377 SDEV 0.000 0.076 0.178 0.250 0.205 0.243 0.257 0.226 0.185 SERR 0.000 0.031 0.027 0.026 0.016 0.015 0.014 0.013 0.010 EPS 0.945 0.844 0.918 0.927 0.932 0.933 0.921 0.931 0.940 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 0.217 0.076 0.501 2.993 0.207 0.722 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.446 0.233 0.045 138 125 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.67 1.46 1.00 1.24 2.70 23.74 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.12 0.60 0.88 1.00 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 0.719 0.661 0.616 0.560 0.497 0.466 0.394 0.387 0.350 0.377 PACF 0.719 0.298 0.155 0.048 -0.018 0.034 -0.065 0.068 0.004 0.139 95% C.L. 0.123 0.176 0.210 0.236 0.256 0.270 0.282 0.290 0.298 0.304 |------------------ 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 0.589 0.440 0.234 0.172 |================== 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 -0.00338234 0.57461274 2 480022 3 0.00000000 0.00000000 -0.00284506 0.49171546 3 480031 1 0.20516327 0.01150342 0.00000000 0.21091427 4 480032 1 0.36339170 0.01624452 0.00000000 0.17876005 5 480041 1 0.17861231 0.01514828 0.00000000 0.12536742 6 480042 1 0.23715201 0.02060768 0.00000000 0.10652481 7 480051 3 0.00000000 0.00000000 0.00101959 0.40393895 8 480052 1 0.62786871 0.23656729 0.00000000 0.25033480 9 480061 3 0.00000000 0.00000000 0.00131890 0.13226287 10 480062 3 0.00000000 0.00000000 0.00051315 0.15610853 11 480071 3 0.00000000 0.00000000 0.00000510 0.27298653 12 480072 1 0.27546397 0.01451676 0.00000000 0.09566719 13 480081 1 0.40904307 0.02909105 0.00000000 0.17175214 14 480082 3 0.00000000 0.00000000 -0.00175304 0.33417132 15 480091 1 0.20017862 0.02799957 0.00000000 0.09676472 16 480092 3 0.00000000 0.00000000 -0.00115322 0.26838693 17 480101 3 0.00000000 0.00000000 0.00046224 0.24892142 18 480102 1 0.35527727 0.01649971 0.00000000 0.20858358 19 480111 3 0.00000000 0.00000000 -0.00128691 0.38420802 SERIES IDENT OPTION A B C D 20 480112 1 0.34122753 0.02347306 0.00000000 0.08646313 21 480131 3 0.00000000 0.00000000 -0.00075527 0.27144486 22 480132 3 0.00000000 0.00000000 -0.00112078 0.36912113 23 480141 1 0.49768922 0.03373677 0.00000000 0.07014193 24 480142 3 0.00000000 0.00000000 -0.00125890 0.32140931 25 480151 3 0.00000000 0.00000000 -0.00117915 0.33165303 26 480152 1 0.63494897 0.07597824 0.00000000 0.12212870 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 480021 1813 1977 165 1.127 0.695 2.656 10.856 0.345 0.466 2 480022 1813 1977 165 1.060 0.443 1.172 4.484 0.330 0.342 3 480031 1834 1977 144 1.000 0.408 1.210 4.350 0.249 0.638 4 480032 1857 1977 121 1.000 0.388 1.494 5.926 0.230 0.598 5 480041 1765 1977 213 1.000 0.353 -0.026 3.419 0.338 0.337 6 480042 1778 1977 200 1.000 0.404 0.741 4.818 0.344 0.461 7 480051 1844 1977 134 0.999 0.478 1.752 7.309 0.263 0.719 8 480052 1866 1977 112 1.000 0.505 1.884 8.173 0.239 0.758 9 480061 1816 1977 162 1.009 0.432 1.284 6.234 0.234 0.749 10 480062 1825 1977 153 1.000 0.362 0.603 3.225 0.236 0.608 11 480071 1739 1977 239 1.000 0.522 1.615 6.249 0.270 0.742 12 480072 1817 1977 161 1.000 0.522 1.349 5.699 0.278 0.676 13 480081 1842 1977 136 1.000 0.399 0.869 4.279 0.309 0.543 14 480082 1841 1977 137 0.997 0.450 1.226 4.917 0.291 0.669 15 480091 1757 1977 221 1.000 0.520 1.744 11.063 0.353 0.602 16 480092 1772 1977 206 1.024 0.418 0.608 3.549 0.328 0.458 17 480101 1802 1977 176 1.000 0.309 0.347 3.766 0.247 0.535 18 480102 1760 1977 218 1.000 0.300 0.161 3.865 0.257 0.450 19 480111 1759 1977 219 1.010 0.571 1.978 7.879 0.322 0.535 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 480112 1749 1977 229 1.001 0.387 1.155 4.713 0.293 0.489 21 480131 1715 1977 263 1.005 0.400 1.435 8.170 0.258 0.539 22 480132 1715 1977 263 0.979 0.420 1.017 4.198 0.262 0.678 23 480141 1750 1977 228 0.996 0.516 2.113 12.952 0.404 0.383 24 480142 1732 1977 246 1.124 0.738 2.822 12.051 0.321 0.630 25 480151 1786 1977 192 0.992 0.322 0.685 3.269 0.231 0.601 26 480152 1787 1977 191 0.999 0.481 1.497 7.476 0.258 0.686 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 188 1.012 0.452 1.284 6.265 0.288 0.573 STANDARD DEVIATION 44 0.036 0.105 0.697 2.844 0.047 0.123 MEDIAN (50TH QUANTILE) 191 1.000 0.426 1.255 5.308 0.274 0.599 INTERQUARTILE RANGE 68 0.005 0.128 1.003 3.681 0.079 0.210 MINIMUM VALUE 112 0.979 0.300 -0.026 3.225 0.230 0.337 LOWER HINGE (25TH QUANTILE) 153 1.000 0.388 0.741 4.198 0.249 0.466 UPPER HINGE (75TH QUANTILE) 221 1.005 0.516 1.744 7.879 0.328 0.676 MAXIMUM VALUE 263 1.127 0.738 2.822 12.952 0.404 0.758 |------------------------ 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 0.994 0.353 0.133 3.350 0.344 0.195 2 480022 1813 1977 165 0.997 0.333 0.196 3.124 0.330 0.199 3 480031 1834 1977 144 0.995 0.387 1.160 4.064 0.249 0.609 4 480032 1857 1977 121 0.997 0.376 1.496 5.962 0.229 0.585 5 480041 1765 1977 213 0.999 0.344 -0.119 3.484 0.338 0.323 6 480042 1778 1977 200 0.997 0.390 0.664 4.488 0.344 0.411 7 480051 1844 1977 134 0.991 0.396 1.277 4.958 0.263 0.621 8 480052 1866 1977 112 0.984 0.414 1.977 8.904 0.238 0.681 9 480061 1816 1977 162 0.996 0.382 0.988 5.642 0.234 0.701 10 480062 1825 1977 153 0.993 0.334 0.550 3.226 0.236 0.573 11 480071 1739 1977 239 0.991 0.402 0.995 5.060 0.270 0.590 12 480072 1817 1977 161 0.986 0.470 1.107 4.393 0.277 0.627 13 480081 1842 1977 136 0.997 0.386 0.759 3.956 0.309 0.513 14 480082 1841 1977 137 0.998 0.438 1.080 4.625 0.291 0.643 15 480091 1757 1977 221 0.999 0.509 1.578 9.869 0.353 0.592 16 480092 1772 1977 206 0.997 0.374 0.334 3.477 0.328 0.404 17 480101 1802 1977 176 0.997 0.299 0.441 3.672 0.247 0.492 18 480102 1760 1977 218 0.999 0.298 0.112 3.801 0.257 0.440 19 480111 1759 1977 219 0.996 0.548 2.122 9.120 0.322 0.544 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 480112 1749 1977 229 0.996 0.345 0.916 3.961 0.293 0.360 21 480131 1715 1977 263 0.994 0.366 1.298 7.394 0.258 0.499 22 480132 1715 1977 263 0.992 0.367 1.052 4.367 0.262 0.561 23 480141 1750 1977 228 0.997 0.480 2.000 14.616 0.404 0.320 24 480142 1732 1977 246 0.994 0.393 0.992 5.300 0.320 0.458 25 480151 1786 1977 192 0.997 0.291 0.448 2.607 0.231 0.486 26 480152 1787 1977 191 0.992 0.405 1.211 5.735 0.259 0.601 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 188 0.995 0.388 0.953 5.352 0.288 0.501 STANDARD DEVIATION 44 0.004 0.062 0.596 2.683 0.047 0.137 MEDIAN (50TH QUANTILE) 191 0.996 0.384 0.993 4.440 0.274 0.529 INTERQUARTILE RANGE 68 0.004 0.060 0.829 2.063 0.079 0.190 MINIMUM VALUE 112 0.984 0.291 -0.119 2.607 0.229 0.195 LOWER HINGE (25TH QUANTILE) 153 0.993 0.345 0.448 3.672 0.249 0.411 UPPER HINGE (75TH QUANTILE) 221 0.997 0.405 1.277 5.735 0.328 0.601 MAXIMUM VALUE 263 0.999 0.548 2.122 14.616 0.404 0.701 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.366 0.130 0.007 0.094 3.000 -0.019 0.765 MINIMUM CORRELATION: -0.019 SERIES 480032 AND 480091 121 YEARS MAXIMUM CORRELATION: 0.765 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 0.802 0.382 0.390 0.435 0.352 0.362 0.341 0.363 0.461 SDEV 0.000 0.151 0.163 0.192 0.200 0.222 0.238 0.215 0.155 SERR 0.000 0.062 0.024 0.020 0.015 0.013 0.013 0.012 0.009 EPS 0.944 0.858 0.899 0.933 0.925 0.935 0.931 0.937 0.957 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 0.965 0.240 0.274 3.094 0.208 0.447 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.505 0.229 0.031 104 159 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.36 0.78 1.00 1.14 1.92 13.71 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.10 0.60 0.88 0.99 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 0.445 0.388 0.263 0.172 0.051 -0.033 -0.141 -0.118 -0.169 -0.138 PACF 0.445 0.236 0.035 -0.023 -0.097 -0.090 -0.130 0.012 -0.046 0.007 95% C.L. 0.123 0.146 0.161 0.167 0.170 0.170 0.170 0.172 0.173 0.176 |------------------ 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 0.252 0.337 0.249 |======================= 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 0.449 0.396 0.294 0.170 0.028 -0.104 -0.169 -0.193 -0.235 -0.240 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 0.449 2 0.339 0.245 3 0.323 0.222 0.066 4 0.326 0.235 0.085 -0.057 5 0.318 0.247 0.118 -0.011 -0.140 6 0.295 0.245 0.137 0.030 -0.087 -0.168 7 0.279 0.236 0.140 0.043 -0.063 -0.139 -0.096 8 0.277 0.233 0.139 0.044 -0.060 -0.134 -0.089 -0.022 9 0.276 0.229 0.132 0.041 -0.058 -0.127 -0.078 -0.009 -0.048 10 0.273 0.229 0.129 0.035 -0.061 -0.125 -0.072 0.002 -0.035 -0.046 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) 2322.47 2265.40 2251.19 2252.03 2253.17 2249.95 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 2244.46 2244.04 2245.91 2247.31 2248.74 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 0.339 0.245 R-SQUARED DUE TO POOLED AUTOREGRESSION: 24.89 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 133.14 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.339 0.359 0.205 0.157 0.103 0.073 0.050 0.035 0.024 0.0167 0.012 0.008 0.006 0.004 0.003 0.002 0.001 0.001 0.001 0.0004 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 480021 2 0.048 0.203 -0.028 2 480022 2 0.086 0.173 0.143 3 480031 2 0.402 0.501 0.185 4 480032 2 0.363 0.492 0.163 5 480041 2 0.153 0.254 0.225 6 480042 2 0.222 0.310 0.249 7 480051 2 0.413 0.567 0.094 8 480052 2 0.483 0.576 0.158 9 480061 2 0.533 0.571 0.199 10 480062 2 0.469 0.325 0.439 11 480071 2 0.363 0.535 0.104 12 480072 2 0.454 0.437 0.307 13 480081 2 0.282 0.435 0.154 14 480082 2 0.441 0.510 0.207 15 480091 2 0.434 0.390 0.345 16 480092 2 0.193 0.339 0.162 17 480101 2 0.266 0.417 0.157 18 480102 2 0.230 0.350 0.205 19 480111 2 0.322 0.458 0.161 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 480112 2 0.157 0.303 0.159 21 480131 2 0.293 0.400 0.207 22 480132 2 0.339 0.465 0.173 23 480141 2 0.140 0.261 0.184 24 480142 2 0.286 0.324 0.300 25 480151 2 0.265 0.484 0.023 26 480152 2 0.400 0.480 0.210 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.309 0.406 0.188 STANDARD DEVIATION 0 0.130 0.114 0.094 MEDIAN 2 0.307 0.426 0.178 INTERQUARTILE RANGE 0 0.190 0.168 0.052 MINIMUM VALUE 2 0.048 0.173 -0.028 LOWER HINGE 2 0.222 0.324 0.157 UPPER HINGE 2 0.413 0.492 0.210 MAXIMUM VALUE 2 0.533 0.576 0.439 |------------------- 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 0.345 0.126 3.636 0.382 0.004 2 480022 1813 1977 165 1.000 0.322 0.109 3.407 0.362 -0.027 3 480031 1834 1977 144 1.000 0.300 0.912 5.272 0.312 -0.007 4 480032 1857 1977 121 1.000 0.300 1.352 7.128 0.294 0.004 5 480041 1765 1977 213 1.002 0.310 -0.260 4.215 0.360 0.018 6 480042 1778 1977 200 1.000 0.344 0.642 4.678 0.370 0.006 7 480051 1844 1977 134 1.001 0.305 0.687 4.999 0.336 -0.011 8 480052 1866 1977 112 1.000 0.298 1.425 6.057 0.299 0.012 9 480061 1816 1977 162 1.000 0.262 0.474 3.899 0.286 0.024 10 480062 1825 1977 153 1.000 0.244 -0.181 4.647 0.283 0.047 11 480071 1739 1977 239 1.000 0.319 0.776 5.272 0.333 0.012 12 480072 1817 1977 161 1.000 0.347 1.491 6.939 0.334 0.007 13 480081 1842 1977 136 1.000 0.326 0.353 3.787 0.371 0.002 14 480082 1841 1977 137 1.000 0.328 0.326 4.418 0.369 0.012 15 480091 1757 1977 221 1.000 0.382 1.752 12.105 0.382 0.017 16 480092 1772 1977 206 1.000 0.337 0.125 3.744 0.389 -0.017 17 480101 1802 1977 176 1.000 0.256 0.242 3.411 0.293 -0.005 18 480102 1760 1977 218 1.000 0.262 0.054 5.139 0.291 -0.011 19 480111 1759 1977 219 1.000 0.452 2.201 11.247 0.398 0.021 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 480112 1749 1977 229 1.000 0.318 0.684 4.255 0.342 -0.011 21 480131 1715 1977 263 1.000 0.309 1.551 10.983 0.302 -0.013 22 480132 1715 1977 263 1.000 0.298 0.934 4.448 0.320 -0.011 23 480141 1750 1977 228 1.000 0.446 2.557 19.820 0.442 0.016 24 480142 1732 1977 246 1.000 0.331 0.863 5.442 0.355 -0.012 25 480151 1786 1977 192 1.000 0.252 0.324 3.099 0.283 -0.010 26 480152 1787 1977 191 1.000 0.314 1.086 8.364 0.325 -0.005 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 188 1.000 0.320 0.792 6.170 0.339 0.002 STANDARD DEVIATION 44 0.000 0.050 0.720 3.727 0.042 0.016 MEDIAN (50TH QUANTILE) 191 1.000 0.316 0.686 4.839 0.335 0.003 INTERQUARTILE RANGE 68 0.000 0.039 1.110 3.041 0.072 0.023 MINIMUM VALUE 112 1.000 0.244 -0.260 3.099 0.283 -0.027 LOWER HINGE (25TH QUANTILE) 153 1.000 0.298 0.242 3.899 0.299 -0.011 UPPER HINGE (75TH QUANTILE) 221 1.000 0.337 1.352 6.939 0.370 0.012 MAXIMUM VALUE 263 1.002 0.452 2.557 19.820 0.442 0.047 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.379 0.109 0.006 0.137 2.909 0.087 0.692 MINIMUM CORRELATION: 0.087 SERIES 480032 AND 480091 121 YEARS MAXIMUM CORRELATION: 0.692 SERIES 480101 AND 480102 176 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 0.709 0.370 0.419 0.501 0.396 0.359 0.365 0.374 0.382 SDEV 0.000 0.145 0.149 0.155 0.161 0.152 0.155 0.155 0.155 SERR 0.000 0.059 0.022 0.016 0.012 0.009 0.009 0.009 0.009 EPS 0.911 0.851 0.909 0.948 0.937 0.934 0.937 0.940 0.941 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 0.985 0.197 0.044 3.801 0.233 -0.060 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.391 0.182 0.029 103 160 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.33 0.57 1.01 1.10 1.67 26.65 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.11 0.70 0.88 0.99 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 -0.060 0.014 0.083 0.029 -0.011 -0.021 -0.125 -0.038 -0.100 -0.007 PACF -0.060 0.011 0.085 0.039 -0.009 -0.031 -0.135 -0.056 -0.101 0.004 95% C.L. 0.123 0.124 0.124 0.125 0.125 0.125 0.125 0.127 0.127 0.128 |------------------ 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 0.005 0.087 0.034 -0.010 -0.029 -0.128 -0.052 -0.103 -0.013 PACF -0.001 0.005 0.087 0.034 -0.011 -0.037 -0.135 -0.054 -0.099 0.010 95% C.L. 0.123 0.123 0.123 0.124 0.124 0.124 0.125 0.126 0.127 0.128 |----------------- 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 0.008 -0.001 0.005 |========================= 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 0.987 0.229 0.304 3.061 0.191 0.460 |------------ 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 0.458 0.400 0.282 0.175 0.056 -0.038 -0.144 -0.137 -0.184 -0.141 PACF 0.458 0.241 0.043 -0.040 -0.100 -0.099 -0.128 -0.003 -0.044 0.029 95% C.L. 0.123 0.147 0.163 0.170 0.173 0.173 0.173 0.175 0.177 0.179 |------------------- 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 0.264 0.345 0.251 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.29 MINUTES