RUN: MT001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: MT108E.rwl.conv LOG FILE PROCESSED: MT108E.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: 692 1 Highland Fire Outlook WIDTH_EARLY PCEN - 692 2 United States of America Engelmann spruce 2730 4545-11232 1496 1983 692 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 16 692082 MISSING VALUES FOUND: 1 IN 1 GAPS / 1518 1518 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 692011 1539 1983 445 0.412 0.192 1.029 3.696 0.208 0.858 2 692012 1523 1983 461 0.408 0.210 1.371 4.742 0.209 0.856 3 692021 1592 1983 392 0.292 0.123 0.366 2.770 0.240 0.763 4 692022 1626 1983 358 0.307 0.141 0.901 3.449 0.254 0.769 5 692031 1795 1983 189 0.453 0.154 -0.163 2.873 0.256 0.661 6 692032 1810 1983 174 0.661 0.210 -0.156 2.619 0.224 0.653 7 692041 1630 1983 354 0.303 0.123 0.201 2.566 0.308 0.633 8 692042 1654 1983 330 0.362 0.152 0.063 2.083 0.275 0.699 9 692051 1646 1983 338 0.312 0.094 0.100 2.945 0.213 0.626 10 692052 1654 1983 330 0.232 0.148 1.527 6.088 0.213 0.916 11 692061 1654 1983 330 0.289 0.109 1.413 5.482 0.195 0.804 12 692062 1635 1983 349 0.265 0.089 1.475 5.588 0.187 0.742 13 692071 1613 1983 371 0.439 0.154 1.151 5.011 0.209 0.716 14 692072 1614 1983 370 0.410 0.209 1.323 4.724 0.201 0.855 15 692081 1496 1983 488 0.298 0.103 0.773 4.014 0.250 0.589 16 692082 1510 1983 474 0.398 0.183 1.295 4.306 0.245 0.793 17 692091 1682 1983 302 0.369 0.199 0.336 2.037 0.220 0.864 18 692092 1815 1983 169 0.481 0.151 0.276 2.930 0.191 0.717 19 692101 1789 1983 195 0.439 0.137 -0.169 2.846 0.226 0.615 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 692102 1780 1983 204 0.534 0.166 -0.330 2.707 0.219 0.688 21 692111 1737 1983 247 0.478 0.184 0.014 2.691 0.228 0.716 22 692112 1722 1983 262 0.546 0.188 0.190 2.617 0.236 0.664 23 692121 1669 1983 315 0.401 0.124 0.246 3.159 0.241 0.527 24 692122 1660 1983 324 0.368 0.134 0.473 3.593 0.262 0.603 25 692131 1660 1983 324 0.336 0.142 0.332 3.166 0.230 0.757 26 692132 1619 1983 365 0.331 0.124 0.385 3.059 0.242 0.663 NUMBER OF SERIES READ IN: 26 FROM 1496 TO 1983 488 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 325 0.389 0.152 0.555 3.529 0.230 0.721 STANDARD DEVIATION 89 0.098 0.036 0.591 1.123 0.028 0.099 MEDIAN (50TH QUANTILE) 330 0.384 0.150 0.351 3.109 0.227 0.716 INTERQUARTILE RANGE 108 0.132 0.060 1.051 1.599 0.036 0.139 MINIMUM VALUE 169 0.232 0.089 -0.330 2.037 0.187 0.527 LOWER HINGE (25TH QUANTILE) 262 0.307 0.124 0.100 2.707 0.209 0.653 UPPER HINGE (75TH QUANTILE) 370 0.439 0.184 1.151 4.306 0.245 0.793 MAXIMUM VALUE 488 0.661 0.210 1.527 6.088 0.308 0.916 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.264 0.321 0.018 -0.380 2.606 -0.713 0.906 MINIMUM CORRELATION: -0.713 SERIES 692052 AND 692091 302 YEARS MAXIMUM CORRELATION: 0.906 SERIES 692011 AND 692012 445 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 56.20 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1550. 1575. 1600. 1625. 1650. 1675. 1700. 1725. 1750. 1775. CORR 3. 6. 6. 10. 28. 66. 153. 171. 190. 210. RBAR 0.424 0.492 0.376 0.400 0.355 0.446 0.419 0.390 0.489 0.421 SDEV 0.179 0.267 0.306 0.283 0.296 0.235 0.228 0.205 0.175 0.182 SERR 0.103 0.109 0.125 0.089 0.056 0.029 0.018 0.016 0.013 0.013 EPS 0.733 0.801 0.760 0.848 0.880 0.933 0.932 0.927 0.952 0.940 NSS 3.7 4.2 5.2 8.3 13.2 17.3 18.9 19.8 20.8 21.7 YEAR 1800. 1825. 1850. 1875. 1900. 1925. 1950. CORR 210. 276. 325. 325. 325. 325. 325. RBAR 0.451 0.558 0.584 0.352 0.341 0.322 0.332 SDEV 0.208 0.167 0.141 0.257 0.231 0.209 0.229 SERR 0.014 0.010 0.008 0.014 0.013 0.012 0.013 EPS 0.951 0.970 0.973 0.934 0.931 0.925 0.928 NSS 23.7 25.5 26.0 26.0 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 1496 1983 488 0.409 0.149 1.068 4.232 0.177 0.809 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.319 0.178 0.086 113 375 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.15 0.30 1.00 1.05 1.35 4.40 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.13 0.00 0.87 1.00 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 330. 108. 169. 262. 370. 488. |----------- 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 0.807 0.750 0.733 0.718 0.672 0.649 0.620 0.599 0.575 0.561 PACF 0.807 0.282 0.219 0.149 0.002 0.041 -0.004 0.020 0.009 0.032 95% C.L. 0.091 0.137 0.168 0.192 0.213 0.230 0.244 0.257 0.268 0.278 |------------------ 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 0.715 0.464 0.134 0.150 0.167 |================== 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 692011 1 0.64271188 0.00576463 0.00000000 0.18150872 2 692012 1 0.69360477 0.00865748 0.00000000 0.23827368 3 692021 3 0.00000000 0.00000000 0.00049886 0.19404118 4 692022 1 0.10881312 0.01018165 0.00000000 0.27853569 5 692031 3 0.00000000 0.00000000 0.00056654 0.39877126 6 692032 3 0.00000000 0.00000000 0.00159082 0.52206761 7 692041 3 0.00000000 0.00000000 -0.00067576 0.42260352 8 692042 3 0.00000000 0.00000000 -0.00112314 0.54742581 9 692051 3 0.00000000 0.00000000 -0.00004181 0.31954172 10 692052 1 0.50805092 0.01051956 0.00000000 0.09136519 11 692061 1 0.40805268 0.02331108 0.00000000 0.23680747 12 692062 1 0.22745773 0.00921867 0.00000000 0.19783352 13 692071 1 0.46313277 0.01238780 0.00000000 0.33956847 14 692072 1 0.69312793 0.00939937 0.00000000 0.21796454 15 692081 1 0.15160654 0.00453419 0.00000000 0.23675953 16 692082 1 0.63758427 0.01095212 0.00000000 0.27703860 17 692091 3 0.00000000 0.00000000 0.00188146 0.08439616 18 692092 3 0.00000000 0.00000000 0.00191651 0.31762892 19 692101 3 0.00000000 0.00000000 0.00089477 0.35179964 SERIES IDENT OPTION A B C D 20 692102 3 0.00000000 0.00000000 0.00157255 0.37234280 21 692111 3 0.00000000 0.00000000 0.00180710 0.25438136 22 692112 3 0.00000000 0.00000000 0.00180052 0.30922437 23 692121 1 0.09945985 0.02245313 0.00000000 0.38728186 24 692122 1 0.25094864 0.01419201 0.00000000 0.31423420 25 692131 3 0.00000000 0.00000000 -0.00086151 0.47604421 26 692132 3 0.00000000 0.00000000 -0.00024017 0.37493768 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 692011 1539 1983 445 1.000 0.237 0.090 3.591 0.208 0.406 2 692012 1523 1983 461 1.000 0.270 0.350 3.327 0.209 0.525 3 692021 1592 1983 392 0.996 0.385 0.500 2.722 0.240 0.709 4 692022 1626 1983 358 1.000 0.454 1.033 4.007 0.254 0.755 5 692031 1795 1983 189 1.000 0.337 -0.114 2.906 0.255 0.647 6 692032 1810 1983 174 0.999 0.301 0.017 2.973 0.223 0.596 7 692041 1630 1983 354 0.996 0.339 0.140 2.869 0.307 0.434 8 692042 1654 1983 330 0.994 0.307 0.258 3.007 0.275 0.407 9 692051 1646 1983 338 1.000 0.298 0.057 2.921 0.213 0.621 10 692052 1654 1983 330 0.995 0.308 -0.015 2.837 0.213 0.662 11 692061 1654 1983 330 1.000 0.230 0.388 3.299 0.194 0.428 12 692062 1635 1983 349 1.000 0.227 0.290 4.003 0.187 0.445 13 692071 1613 1983 371 1.000 0.233 0.083 3.286 0.208 0.359 14 692072 1614 1983 370 1.000 0.263 0.281 3.028 0.201 0.531 15 692081 1496 1983 488 1.000 0.304 0.188 3.249 0.250 0.483 16 692082 1510 1983 474 1.000 0.255 0.244 2.815 0.244 0.299 17 692091 1682 1983 302 1.027 0.446 2.449 13.006 0.219 0.771 18 692092 1815 1983 169 1.003 0.266 0.468 3.506 0.190 0.592 19 692101 1789 1983 195 0.998 0.298 0.022 2.734 0.225 0.573 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 692102 1780 1983 204 0.996 0.270 -0.063 3.417 0.218 0.539 21 692111 1737 1983 247 0.991 0.289 0.208 3.304 0.227 0.514 22 692112 1722 1983 262 0.999 0.246 0.107 2.594 0.235 0.323 23 692121 1669 1983 315 1.000 0.306 0.230 3.027 0.240 0.507 24 692122 1660 1983 324 1.000 0.338 0.700 5.006 0.261 0.495 25 692131 1660 1983 324 1.004 0.361 -0.002 3.169 0.229 0.669 26 692132 1619 1983 365 0.999 0.362 0.268 3.004 0.241 0.638 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 325 1.000 0.305 0.315 3.600 0.229 0.536 STANDARD DEVIATION 90 0.006 0.061 0.501 1.984 0.028 0.128 MEDIAN (50TH QUANTILE) 330 1.000 0.300 0.219 3.098 0.226 0.528 INTERQUARTILE RANGE 108 0.002 0.076 0.294 0.512 0.036 0.204 MINIMUM VALUE 169 0.991 0.227 -0.114 2.594 0.187 0.299 LOWER HINGE (25TH QUANTILE) 262 0.998 0.263 0.057 2.906 0.209 0.434 UPPER HINGE (75TH QUANTILE) 370 1.000 0.338 0.350 3.417 0.244 0.638 MAXIMUM VALUE 488 1.027 0.454 2.449 13.006 0.307 0.771 |------------------------ 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 692011 -67 298 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 692012 -67 308 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 692021 -67 262 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 692022 -67 239 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 692031 -67 126 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 692032 -67 116 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 692041 -67 237 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 692042 -67 221 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 692051 -67 226 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 692052 -67 221 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 692061 -67 221 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 692062 -67 233 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 692071 -67 248 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 692072 -67 247 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 692081 -67 326 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 692082 -67 317 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 692091 -67 202 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 692092 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 692101 -67 130 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 692102 -67 136 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 692111 -67 165 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 692112 -67 175 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 692121 -67 211 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 692122 -67 217 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 25 692131 -67 217 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 26 692132 -67 244 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 692011 1539 1983 445 1.000 0.234 0.022 3.550 0.208 0.394 2 692012 1523 1983 461 0.999 0.265 0.420 3.568 0.209 0.506 3 692021 1592 1983 392 0.990 0.318 0.482 2.947 0.240 0.560 4 692022 1626 1983 358 0.988 0.352 0.580 3.267 0.254 0.599 5 692031 1795 1983 189 0.996 0.305 -0.277 3.362 0.255 0.546 6 692032 1810 1983 174 0.997 0.265 -0.154 3.682 0.223 0.448 7 692041 1630 1983 354 0.997 0.316 0.018 3.098 0.307 0.349 8 692042 1654 1983 330 0.999 0.296 0.219 3.179 0.275 0.361 9 692051 1646 1983 338 0.995 0.270 -0.098 3.152 0.213 0.529 10 692052 1654 1983 330 0.993 0.281 0.081 3.293 0.213 0.584 11 692061 1654 1983 330 0.999 0.220 0.328 3.377 0.194 0.361 12 692062 1635 1983 349 1.000 0.222 0.185 3.993 0.187 0.422 13 692071 1613 1983 371 0.998 0.222 -0.067 3.291 0.208 0.301 14 692072 1614 1983 370 0.997 0.247 0.219 3.132 0.201 0.472 15 692081 1496 1983 488 0.999 0.298 0.120 3.216 0.250 0.460 16 692082 1510 1983 474 0.999 0.251 0.220 2.754 0.244 0.280 17 692091 1682 1983 302 0.986 0.295 0.747 4.069 0.219 0.600 18 692092 1815 1983 169 0.996 0.233 0.206 3.221 0.190 0.478 19 692101 1789 1983 195 0.995 0.245 0.048 2.683 0.225 0.385 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 692102 1780 1983 204 0.998 0.230 0.059 3.955 0.218 0.292 21 692111 1737 1983 247 0.996 0.246 0.176 3.110 0.227 0.336 22 692112 1722 1983 262 0.999 0.242 0.127 2.699 0.235 0.297 23 692121 1669 1983 315 0.998 0.290 0.486 4.021 0.240 0.429 24 692122 1660 1983 324 0.995 0.314 1.328 9.008 0.261 0.370 25 692131 1660 1983 324 0.990 0.327 0.150 3.805 0.229 0.592 26 692132 1619 1983 365 0.991 0.299 0.145 3.387 0.241 0.473 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 325 0.996 0.272 0.222 3.570 0.229 0.439 STANDARD DEVIATION 90 0.004 0.038 0.321 1.176 0.028 0.103 MEDIAN (50TH QUANTILE) 330 0.997 0.268 0.163 3.292 0.226 0.438 INTERQUARTILE RANGE 108 0.004 0.057 0.281 0.551 0.036 0.168 MINIMUM VALUE 169 0.986 0.220 -0.277 2.683 0.187 0.280 LOWER HINGE (25TH QUANTILE) 262 0.995 0.242 0.048 3.132 0.209 0.361 UPPER HINGE (75TH QUANTILE) 370 0.999 0.299 0.328 3.682 0.244 0.529 MAXIMUM VALUE 488 1.000 0.352 1.328 9.008 0.307 0.600 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.380 0.127 0.007 0.294 4.020 -0.053 0.819 MINIMUM CORRELATION: -0.053 SERIES 692051 AND 692091 302 YEARS MAXIMUM CORRELATION: 0.819 SERIES 692131 AND 692132 324 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 56.20 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1550. 1575. 1600. 1625. 1650. 1675. 1700. 1725. 1750. 1775. CORR 3. 6. 6. 10. 28. 66. 153. 171. 190. 210. RBAR 0.417 0.383 0.360 0.447 0.455 0.472 0.421 0.396 0.471 0.451 SDEV 0.222 0.339 0.283 0.161 0.197 0.178 0.178 0.189 0.173 0.156 SERR 0.128 0.139 0.116 0.051 0.037 0.022 0.014 0.014 0.013 0.011 EPS 0.727 0.721 0.747 0.871 0.917 0.939 0.932 0.929 0.949 0.947 NSS 3.7 4.2 5.2 8.3 13.2 17.3 18.9 19.8 20.8 21.7 YEAR 1800. 1825. 1850. 1875. 1900. 1925. 1950. CORR 210. 276. 325. 325. 325. 325. 325. RBAR 0.478 0.604 0.591 0.364 0.347 0.329 0.353 SDEV 0.168 0.118 0.146 0.229 0.225 0.201 0.210 SERR 0.012 0.007 0.008 0.013 0.012 0.011 0.012 EPS 0.956 0.975 0.974 0.937 0.932 0.927 0.934 NSS 23.7 25.5 26.0 26.0 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 1496 1983 488 0.982 0.199 -0.186 3.532 0.185 0.352 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.252 0.103 0.098 120 368 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.16 0.28 1.00 1.06 1.34 5.91 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.12 0.00 0.88 1.00 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 0.351 0.224 0.199 0.251 0.129 0.103 -0.019 0.045 0.025 0.027 PACF 0.351 0.115 0.103 0.160 -0.028 0.010 -0.122 0.034 -0.002 0.016 95% C.L. 0.091 0.101 0.105 0.108 0.113 0.114 0.115 0.115 0.115 0.115 |------------------ 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 4 0.175 0.278 0.072 0.060 0.173 |======================= 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 0.237 0.142 0.107 0.230 0.063 0.070 -0.066 0.033 -0.014 0.083 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 0.237 2 0.216 0.091 3 0.210 0.078 0.058 4 0.199 0.063 0.017 0.196 5 0.207 0.063 0.020 0.205 -0.042 6 0.208 0.059 0.019 0.203 -0.047 0.023 7 0.211 0.053 0.044 0.206 -0.040 0.049 -0.122 8 0.214 0.052 0.045 0.201 -0.041 0.048 -0.126 0.021 9 0.214 0.049 0.046 0.200 -0.037 0.048 -0.125 0.026 -0.019 10 0.216 0.047 0.057 0.196 -0.034 0.031 -0.129 0.021 -0.038 0.089 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) 4228.32 4202.07 4200.05 4200.39 4183.21 4184.33 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 4186.06 4180.80 4182.57 4184.40 4182.49 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 0.216 0.091 R-SQUARED DUE TO POOLED AUTOREGRESSION: 6.40 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 106.83 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.216 0.137 0.049 0.023 0.009 0.004 0.002 0.001 0.000 0.0001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 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 692011 2 0.193 0.317 0.197 2 692012 2 0.295 0.415 0.179 3 692021 2 0.346 0.471 0.162 4 692022 2 0.387 0.510 0.149 5 692031 2 0.388 0.356 0.351 6 692032 2 0.257 0.330 0.263 7 692041 2 0.166 0.278 0.209 8 692042 2 0.153 0.306 0.155 9 692051 2 0.345 0.403 0.241 10 692052 2 0.379 0.496 0.157 11 692061 2 0.148 0.317 0.125 12 692062 2 0.212 0.349 0.181 13 692071 2 0.127 0.242 0.196 14 692072 2 0.251 0.394 0.168 15 692081 2 0.246 0.409 0.119 16 692082 2 0.086 0.259 0.077 17 692091 2 0.424 0.450 0.250 18 692092 2 0.285 0.380 0.215 19 692101 2 0.158 0.354 0.082 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 692102 2 0.106 0.318 -0.075 21 692111 2 0.124 0.314 0.068 22 692112 2 0.116 0.262 0.120 23 692121 2 0.191 0.406 0.057 24 692122 2 0.144 0.344 0.071 25 692131 2 0.410 0.491 0.172 26 692132 2 0.278 0.408 0.138 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.239 0.368 0.155 STANDARD DEVIATION 0 0.106 0.075 0.083 MEDIAN 2 0.229 0.355 0.159 INTERQUARTILE RANGE 0 0.197 0.092 0.078 MINIMUM VALUE 2 0.086 0.242 -0.075 LOWER HINGE 2 0.148 0.317 0.119 UPPER HINGE 2 0.345 0.409 0.197 MAXIMUM VALUE 2 0.424 0.510 0.351 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 692011 1539 1983 445 1.000 0.211 -0.111 4.460 0.238 -0.014 2 692012 1523 1983 461 1.000 0.225 0.346 4.777 0.249 -0.027 3 692021 1592 1983 392 1.000 0.260 0.477 4.358 0.289 -0.023 4 692022 1626 1983 358 1.000 0.279 0.679 5.776 0.307 -0.021 5 692031 1795 1983 189 1.000 0.238 -0.106 3.248 0.274 -0.011 6 692032 1810 1983 174 1.000 0.228 0.264 4.347 0.245 0.000 7 692041 1630 1983 354 1.000 0.289 -0.059 3.583 0.338 -0.012 8 692042 1654 1983 330 1.000 0.272 0.131 3.425 0.312 -0.003 9 692051 1646 1983 338 1.000 0.222 -0.066 3.874 0.256 -0.044 10 692052 1654 1983 330 1.000 0.224 0.198 4.044 0.260 -0.024 11 692061 1654 1983 330 1.000 0.203 0.314 3.456 0.223 -0.008 12 692062 1635 1983 349 1.000 0.197 0.279 4.566 0.218 -0.016 13 692071 1613 1983 371 1.000 0.207 -0.019 3.530 0.230 -0.008 14 692072 1614 1983 370 1.000 0.214 0.247 4.111 0.236 -0.014 15 692081 1496 1983 488 1.000 0.261 0.217 2.993 0.300 -0.023 16 692082 1510 1983 474 1.000 0.240 0.271 3.205 0.270 -0.004 17 692091 1682 1983 302 1.000 0.228 0.256 3.746 0.264 -0.052 18 692092 1815 1983 169 1.000 0.198 0.008 3.603 0.227 -0.038 19 692101 1789 1983 195 1.000 0.226 0.152 2.913 0.263 -0.005 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 692102 1780 1983 204 1.000 0.219 0.171 4.493 0.243 0.008 21 692111 1737 1983 247 1.000 0.231 0.211 3.097 0.259 -0.006 22 692112 1722 1983 262 1.000 0.229 0.111 2.699 0.264 -0.014 23 692121 1669 1983 315 1.000 0.261 0.726 5.530 0.279 -0.004 24 692122 1660 1983 324 1.000 0.291 1.562 11.402 0.296 -0.004 25 692131 1660 1983 324 1.000 0.259 0.632 5.181 0.280 -0.044 26 692132 1619 1983 365 1.000 0.261 0.183 3.831 0.284 -0.031 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 325 1.000 0.237 0.272 4.240 0.265 -0.017 STANDARD DEVIATION 90 0.000 0.028 0.345 1.661 0.030 0.015 MEDIAN (50TH QUANTILE) 330 1.000 0.229 0.214 3.852 0.263 -0.014 INTERQUARTILE RANGE 108 0.000 0.042 0.202 1.068 0.041 0.019 MINIMUM VALUE 169 1.000 0.197 -0.111 2.699 0.218 -0.052 LOWER HINGE (25TH QUANTILE) 262 1.000 0.219 0.111 3.425 0.243 -0.024 UPPER HINGE (75TH QUANTILE) 370 1.000 0.261 0.314 4.493 0.284 -0.005 MAXIMUM VALUE 488 1.000 0.291 1.562 11.402 0.338 0.008 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.487 0.099 0.005 0.289 4.159 0.210 0.810 MINIMUM CORRELATION: 0.210 SERIES 692052 AND 692102 204 YEARS MAXIMUM CORRELATION: 0.810 SERIES 692011 AND 692012 445 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 56.20 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1550. 1575. 1600. 1625. 1650. 1675. 1700. 1725. 1750. 1775. CORR 3. 6. 6. 10. 28. 66. 153. 171. 190. 210. RBAR 0.419 0.508 0.519 0.479 0.499 0.489 0.408 0.478 0.558 0.554 SDEV 0.192 0.226 0.177 0.181 0.141 0.116 0.149 0.142 0.125 0.116 SERR 0.111 0.092 0.072 0.057 0.027 0.014 0.012 0.011 0.009 0.008 EPS 0.728 0.811 0.850 0.884 0.930 0.943 0.929 0.948 0.963 0.964 NSS 3.7 4.2 5.2 8.3 13.2 17.3 18.9 19.8 20.8 21.7 YEAR 1800. 1825. 1850. 1875. 1900. 1925. 1950. CORR 210. 276. 325. 325. 325. 325. 325. RBAR 0.558 0.642 0.643 0.469 0.489 0.446 0.464 SDEV 0.117 0.107 0.111 0.152 0.154 0.156 0.158 SERR 0.008 0.006 0.006 0.008 0.009 0.009 0.009 EPS 0.968 0.979 0.979 0.958 0.961 0.954 0.957 NSS 23.7 25.5 26.0 26.0 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 1496 1983 488 0.993 0.175 0.059 3.956 0.203 -0.064 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.189 0.073 0.085 133 355 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.19 0.38 1.00 1.06 1.44 6.77 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.13 0.00 0.87 1.00 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 -0.063 -0.112 0.016 0.154 0.000 0.049 -0.099 0.029 0.009 0.015 PACF -0.063 -0.117 0.001 0.145 0.024 0.085 -0.096 0.007 -0.016 0.003 95% C.L. 0.091 0.091 0.092 0.092 0.094 0.094 0.094 0.095 0.095 0.095 |------------------ 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 2 0.018 -0.072 -0.119 |---------- 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 0.000 0.019 0.012 0.154 0.006 0.064 -0.096 0.031 -0.001 0.016 PACF 0.000 0.019 0.012 0.153 0.006 0.060 -0.102 0.006 -0.003 0.001 95% C.L. 0.091 0.091 0.091 0.091 0.093 0.093 0.093 0.094 0.094 0.094 |----------------- 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 0.001 0.000 0.019 |========================= 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 1496 1983 488 0.992 0.180 -0.146 3.500 0.176 0.254 |------------ 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 0.253 0.187 0.108 0.188 0.059 0.075 -0.060 0.024 0.000 0.014 PACF 0.253 0.131 0.037 0.144 -0.033 0.024 -0.110 0.024 0.006 0.003 95% C.L. 0.091 0.096 0.099 0.100 0.103 0.103 0.104 0.104 0.104 0.104 |------------------- 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 0.084 0.221 0.136 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.39 MINUTES