RUN: MT001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: MT108I.rwl.conv LOG FILE PROCESSED: MT108I.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 DENSITY_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 3.354 0.263 0.616 3.517 0.060 0.433 2 692012 1523 1983 461 3.209 0.256 0.639 3.762 0.059 0.517 3 692021 1592 1983 392 3.703 0.443 1.441 5.074 0.053 0.808 4 692022 1626 1983 358 3.584 0.276 1.077 5.818 0.056 0.478 5 692031 1795 1983 189 3.424 0.234 0.495 3.931 0.058 0.408 6 692032 1810 1983 174 3.391 0.251 0.495 3.498 0.053 0.475 7 692041 1630 1983 354 3.504 0.316 1.215 5.931 0.066 0.444 8 692042 1654 1983 330 3.171 0.238 0.691 4.057 0.065 0.319 9 692051 1646 1983 338 3.049 0.222 1.868 10.438 0.050 0.560 10 692052 1654 1983 330 3.325 0.284 1.375 4.953 0.046 0.738 11 692061 1654 1983 330 3.245 0.204 0.309 2.797 0.042 0.652 12 692062 1635 1983 349 3.379 0.328 3.787 22.671 0.041 0.707 13 692071 1613 1983 371 3.317 0.259 0.850 4.571 0.059 0.432 14 692072 1614 1983 370 3.371 0.249 1.117 5.612 0.064 0.314 15 692081 1496 1983 488 3.410 0.293 1.913 9.387 0.049 0.664 16 692082 1510 1983 474 3.321 0.241 0.499 3.148 0.044 0.650 17 692091 1682 1983 302 3.280 0.448 2.251 8.636 0.050 0.843 18 692092 1815 1983 169 3.109 0.213 1.496 6.204 0.043 0.662 19 692101 1789 1983 195 3.325 0.300 1.186 5.160 0.059 0.540 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 692102 1780 1983 204 3.376 0.316 1.293 5.882 0.053 0.649 21 692111 1737 1983 247 3.818 0.698 1.517 5.060 0.052 0.907 22 692112 1722 1983 262 3.449 0.453 1.588 7.172 0.058 0.719 23 692121 1669 1983 315 3.563 0.277 2.141 10.815 0.058 0.391 24 692122 1660 1983 324 3.660 0.288 0.759 5.221 0.057 0.461 25 692131 1660 1983 324 3.447 0.282 1.131 7.110 0.055 0.490 26 692132 1619 1983 365 3.529 0.372 1.598 6.827 0.063 0.659 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 3.397 0.308 1.283 6.433 0.054 0.574 STANDARD DEVIATION 89 0.178 0.105 0.737 3.939 0.007 0.160 MEDIAN (50TH QUANTILE) 330 3.377 0.279 1.201 5.417 0.055 0.550 INTERQUARTILE RANGE 108 0.187 0.067 0.897 3.053 0.009 0.221 MINIMUM VALUE 169 3.049 0.204 0.309 2.797 0.041 0.314 LOWER HINGE (25TH QUANTILE) 262 3.317 0.249 0.691 4.057 0.050 0.444 UPPER HINGE (75TH QUANTILE) 370 3.504 0.316 1.588 7.110 0.059 0.664 MAXIMUM VALUE 488 3.818 0.698 3.787 22.671 0.066 0.907 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.305 0.207 0.012 -0.594 3.378 -0.312 0.793 MINIMUM CORRELATION: -0.312 SERIES 692011 AND 692111 247 YEARS MAXIMUM CORRELATION: 0.793 SERIES 692021 AND 692132 365 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 0.492 0.534 0.376 0.387 0.537 0.503 0.391 0.354 0.319 0.316 SDEV 0.137 0.155 0.130 0.208 0.137 0.164 0.185 0.206 0.172 0.202 SERR 0.079 0.063 0.053 0.066 0.026 0.020 0.015 0.016 0.013 0.014 EPS 0.783 0.827 0.760 0.841 0.939 0.946 0.924 0.916 0.907 0.909 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 0.352 0.465 0.485 0.394 0.342 0.373 0.317 SDEV 0.198 0.175 0.172 0.181 0.234 0.206 0.187 SERR 0.014 0.011 0.010 0.010 0.013 0.011 0.010 EPS 0.928 0.957 0.961 0.944 0.931 0.939 0.924 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 3.426 0.251 2.626 13.827 0.042 0.673 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.049 0.023 0.183 173 315 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.48 1.22 1.00 1.12 2.34 26.21 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.93 0.12 0.00 0.88 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 0.671 0.554 0.531 0.504 0.421 0.400 0.351 0.318 0.285 0.279 PACF 0.671 0.188 0.195 0.112 -0.029 0.061 -0.027 0.010 0.000 0.038 95% C.L. 0.091 0.125 0.144 0.159 0.171 0.180 0.187 0.192 0.196 0.200 |------------------ 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 0.563 0.419 0.095 0.146 0.201 |================== 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 0.55053645 0.03062361 0.00000000 3.31444263 2 692012 3 0.00000000 0.00000000 -0.00098444 3.43653750 3 692021 1 1.55325830 0.01476689 0.00000000 3.43732858 4 692022 1 0.64568424 0.02470882 0.00000000 3.51143718 5 692031 1 0.31466705 0.02791059 0.00000000 3.36587167 6 692032 3 0.00000000 0.00000000 0.00045352 3.35112143 7 692041 1 0.70375413 0.05124064 0.00000000 3.46586108 8 692042 1 0.45575985 0.01726547 0.00000000 3.09218407 9 692051 1 0.38086337 0.01619421 0.00000000 2.98029375 10 692052 3 0.00000000 0.00000000 0.00121990 3.12277389 11 692061 1 0.57543492 0.00983131 0.00000000 3.07534075 12 692062 1 1.92738020 0.06688193 0.00000000 3.29904342 13 692071 1 0.35806507 0.00666656 0.00000000 3.18460059 14 692072 3 0.00000000 0.00000000 0.00056205 3.26641607 15 692081 1 0.96817875 0.01965928 0.00000000 3.31006217 16 692082 3 0.00000000 0.00000000 -0.00050730 3.44102478 17 692091 1 1.84201241 0.02693619 0.00000000 3.05619979 18 692092 3 0.00000000 0.00000000 -0.00199848 3.27898359 19 692101 3 0.00000000 0.00000000 -0.00137592 3.45945597 SERIES IDENT OPTION A B C D 20 692102 1 0.87804568 0.01618258 0.00000000 3.12144375 21 692111 1 2.64361477 0.01886314 0.00000000 3.26096988 22 692112 1 1.45039690 0.01179799 0.00000000 3.00416422 23 692121 1 1.52765143 0.12158693 0.00000000 3.52594972 24 692122 3 0.00000000 0.00000000 -0.00136350 3.88147688 25 692131 1 0.54382598 0.03335860 0.00000000 3.39709496 26 692132 1 1.40599549 0.02634534 0.00000000 3.38493013 |-------------------- 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 0.073 0.711 3.812 0.059 0.343 2 692012 1523 1983 461 1.000 0.068 0.796 4.177 0.059 0.332 3 692021 1592 1983 392 1.000 0.066 0.747 4.319 0.053 0.420 4 692022 1626 1983 358 1.000 0.067 0.794 4.401 0.056 0.341 5 692031 1795 1983 189 1.000 0.064 0.456 3.834 0.057 0.335 6 692032 1810 1983 174 1.000 0.074 0.599 3.832 0.053 0.468 7 692041 1630 1983 354 1.000 0.085 1.269 6.898 0.066 0.372 8 692042 1654 1983 330 1.000 0.067 1.048 5.719 0.065 0.138 9 692051 1646 1983 338 1.000 0.065 1.527 8.765 0.050 0.464 10 692052 1654 1983 330 1.000 0.077 0.786 4.192 0.046 0.670 11 692061 1654 1983 330 1.000 0.044 0.099 3.166 0.042 0.289 12 692062 1635 1983 349 1.000 0.056 3.206 33.774 0.040 0.342 13 692071 1613 1983 371 1.000 0.073 0.747 3.926 0.059 0.357 14 692072 1614 1983 370 1.000 0.072 1.348 6.548 0.064 0.274 15 692081 1496 1983 488 1.000 0.063 0.744 4.659 0.049 0.430 16 692082 1510 1983 474 1.000 0.069 0.293 3.150 0.044 0.614 17 692091 1682 1983 302 1.000 0.063 1.715 13.582 0.050 0.399 18 692092 1815 1983 169 1.000 0.060 1.365 6.866 0.043 0.551 19 692101 1789 1983 195 1.000 0.086 0.964 5.548 0.058 0.501 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 692102 1780 1983 204 1.000 0.064 0.441 3.644 0.053 0.352 21 692111 1737 1983 247 1.000 0.062 0.271 3.398 0.052 0.424 22 692112 1722 1983 262 1.000 0.071 1.769 10.247 0.058 0.240 23 692121 1669 1983 315 1.000 0.063 1.226 6.892 0.058 0.113 24 692122 1660 1983 324 1.000 0.070 0.674 4.750 0.057 0.340 25 692131 1660 1983 324 1.000 0.076 1.296 8.724 0.055 0.414 26 692132 1619 1983 365 1.000 0.068 0.595 4.880 0.062 0.265 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 325 1.000 0.068 0.980 6.681 0.054 0.377 STANDARD DEVIATION 90 0.000 0.009 0.632 6.055 0.007 0.126 MEDIAN (50TH QUANTILE) 330 1.000 0.068 0.790 4.705 0.055 0.354 INTERQUARTILE RANGE 108 0.000 0.010 0.696 3.059 0.009 0.097 MINIMUM VALUE 169 1.000 0.044 0.099 3.150 0.040 0.113 LOWER HINGE (25TH QUANTILE) 262 1.000 0.063 0.599 3.834 0.050 0.332 UPPER HINGE (75TH QUANTILE) 370 1.000 0.073 1.296 6.892 0.059 0.430 MAXIMUM VALUE 488 1.000 0.086 3.206 33.774 0.066 0.670 |------------------------ 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 0.065 0.779 4.412 0.059 0.167 2 692012 1523 1983 461 1.000 0.067 0.861 4.345 0.059 0.307 3 692021 1592 1983 392 1.000 0.063 0.725 4.423 0.053 0.363 4 692022 1626 1983 358 1.000 0.065 0.809 4.646 0.056 0.305 5 692031 1795 1983 189 1.000 0.060 0.623 4.292 0.057 0.234 6 692032 1810 1983 174 1.000 0.063 0.655 4.207 0.053 0.303 7 692041 1630 1983 354 1.000 0.081 1.207 6.601 0.066 0.305 8 692042 1654 1983 330 1.000 0.066 1.123 6.062 0.065 0.098 9 692051 1646 1983 338 1.000 0.064 1.593 9.013 0.050 0.437 10 692052 1654 1983 330 1.000 0.068 0.745 4.436 0.046 0.585 11 692061 1654 1983 330 1.000 0.043 0.109 3.170 0.042 0.274 12 692062 1635 1983 349 1.000 0.053 3.858 42.957 0.040 0.261 13 692071 1613 1983 371 1.000 0.069 0.841 4.244 0.059 0.290 14 692072 1614 1983 370 1.000 0.070 1.322 6.402 0.064 0.246 15 692081 1496 1983 488 1.000 0.060 0.799 4.897 0.049 0.379 16 692082 1510 1983 474 1.000 0.058 0.567 4.932 0.044 0.448 17 692091 1682 1983 302 1.000 0.061 1.748 14.027 0.050 0.371 18 692092 1815 1983 169 1.000 0.052 1.098 6.290 0.043 0.417 19 692101 1789 1983 195 1.000 0.083 1.166 6.257 0.058 0.461 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 692102 1780 1983 204 1.000 0.058 0.591 4.438 0.053 0.233 21 692111 1737 1983 247 1.000 0.057 0.190 3.283 0.052 0.319 22 692112 1722 1983 262 1.000 0.069 1.980 11.894 0.058 0.175 23 692121 1669 1983 315 1.000 0.062 1.342 7.434 0.058 0.091 24 692122 1660 1983 324 1.000 0.067 0.883 5.657 0.057 0.267 25 692131 1660 1983 324 1.000 0.071 1.358 8.570 0.055 0.329 26 692132 1619 1983 365 1.000 0.065 0.594 4.807 0.062 0.183 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 325 1.000 0.064 1.060 7.373 0.054 0.302 STANDARD DEVIATION 90 0.000 0.008 0.720 7.687 0.007 0.114 MEDIAN (50TH QUANTILE) 330 1.000 0.064 0.851 4.914 0.055 0.304 INTERQUARTILE RANGE 108 0.000 0.008 0.666 2.190 0.009 0.137 MINIMUM VALUE 169 1.000 0.043 0.109 3.170 0.040 0.091 LOWER HINGE (25TH QUANTILE) 262 1.000 0.060 0.655 4.412 0.050 0.234 UPPER HINGE (75TH QUANTILE) 370 1.000 0.068 1.322 6.601 0.059 0.371 MAXIMUM VALUE 488 1.000 0.083 3.858 42.957 0.066 0.585 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.340 0.119 0.007 -0.006 3.476 0.002 0.700 MINIMUM CORRELATION: 0.002 SERIES 692052 AND 692131 324 YEARS MAXIMUM CORRELATION: 0.700 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 0.360 0.615 0.432 0.419 0.507 0.476 0.426 0.367 0.330 0.321 SDEV 0.276 0.112 0.128 0.181 0.122 0.148 0.165 0.180 0.168 0.186 SERR 0.159 0.046 0.052 0.057 0.023 0.018 0.013 0.014 0.012 0.013 EPS 0.676 0.869 0.800 0.857 0.932 0.940 0.933 0.920 0.911 0.911 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 0.360 0.474 0.504 0.394 0.355 0.390 0.325 SDEV 0.192 0.168 0.157 0.159 0.204 0.207 0.183 SERR 0.013 0.010 0.009 0.009 0.011 0.011 0.010 EPS 0.930 0.958 0.964 0.944 0.935 0.943 0.926 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 0.998 0.045 0.488 3.515 0.043 0.211 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.301 0.152 -0.106 168 320 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.21 0.64 1.00 1.08 1.72 72.36 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.94 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 0.211 0.038 0.072 0.115 -0.024 0.033 -0.018 0.028 -0.017 0.041 PACF 0.211 -0.007 0.069 0.091 -0.071 0.051 -0.050 0.038 -0.025 0.045 95% C.L. 0.091 0.094 0.095 0.095 0.096 0.096 0.096 0.096 0.096 0.096 |------------------ STANDARD CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.045 0.213 |======================= 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 0.101 -0.038 -0.020 0.052 -0.105 0.024 -0.026 0.032 -0.034 0.056 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 0.101 2 0.106 -0.049 3 0.105 -0.047 -0.011 4 0.106 -0.045 -0.017 0.054 5 0.112 -0.047 -0.022 0.067 -0.119 6 0.119 -0.050 -0.021 0.069 -0.125 0.054 7 0.121 -0.056 -0.018 0.068 -0.127 0.059 -0.043 8 0.123 -0.058 -0.014 0.066 -0.127 0.061 -0.047 0.037 9 0.124 -0.059 -0.012 0.062 -0.125 0.061 -0.049 0.041 -0.031 10 0.125 -0.061 -0.009 0.059 -0.118 0.058 -0.048 0.044 -0.037 0.050 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) 2736.02 2733.02 2733.87 2735.81 2736.38 2731.40 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 2731.97 2733.07 2734.41 2735.94 2736.73 SELECTED AUTOREGRESSION ORDER: 1 AR ORDER SELECTION CRITERION: IPP=0 FIRST-MINIMUM AIC SELECTION THE AIC TRACE SHOULD BE CHECKED TO SEE IF AR ORDER SELECTION CRITERION IS ADEQUATE. E.G. IF AR-ORDERS OF THE FIRST-MINIMUM AND THE FULL-MINIMUM AIC ARE CLOSE, AN ARSTAN RUN WITH FULL-MINIMUM AIC ORDER SELECTION MIGHT BE TRIED AUTOREGRESSION COEFFICIENTS: T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 0.101 R-SQUARED DUE TO POOLED AUTOREGRESSION: 1.02 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 101.03 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.101 0.010 0.001 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 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 1 0.052 0.167 2 692012 1 0.117 0.307 3 692021 1 0.137 0.364 4 692022 1 0.110 0.307 5 692031 1 0.102 0.235 6 692032 1 0.093 0.304 7 692041 1 0.124 0.306 8 692042 1 0.010 0.099 9 692051 1 0.194 0.438 10 692052 1 0.356 0.594 11 692061 1 0.077 0.277 12 692062 1 0.073 0.262 13 692071 1 0.106 0.293 14 692072 1 0.085 0.246 15 692081 1 0.151 0.382 16 692082 1 0.211 0.449 17 692091 1 0.139 0.372 18 692092 1 0.185 0.422 19 692101 1 0.225 0.462 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 692102 1 0.094 0.236 21 692111 1 0.144 0.322 22 692112 1 0.037 0.177 23 692121 1 0.010 0.092 24 692122 1 0.076 0.269 25 692131 1 0.123 0.330 26 692132 1 0.034 0.183 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.118 0.304 STANDARD DEVIATION 0 0.075 0.115 MEDIAN 1 0.108 0.305 INTERQUARTILE RANGE 0 0.069 0.136 MINIMUM VALUE 1 0.010 0.092 LOWER HINGE 1 0.076 0.236 UPPER HINGE 1 0.144 0.372 MAXIMUM VALUE 1 0.356 0.594 |------------------- 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 0.064 0.814 4.723 0.065 -0.027 2 692012 1523 1983 461 1.000 0.064 0.739 4.652 0.068 -0.048 3 692021 1592 1983 392 1.000 0.058 0.689 4.332 0.063 -0.025 4 692022 1626 1983 358 1.000 0.062 0.948 5.197 0.065 -0.041 5 692031 1795 1983 189 1.000 0.058 0.752 4.493 0.065 -0.052 6 692032 1810 1983 174 1.000 0.060 0.676 4.838 0.061 -0.004 7 692041 1630 1983 354 1.000 0.077 1.215 7.030 0.078 -0.057 8 692042 1654 1983 330 1.000 0.065 1.113 5.966 0.068 -0.001 9 692051 1646 1983 338 1.000 0.057 1.152 7.991 0.062 -0.020 10 692052 1654 1983 330 1.000 0.054 0.325 4.063 0.060 -0.049 11 692061 1654 1983 330 1.000 0.041 0.244 3.088 0.047 0.006 12 692062 1635 1983 349 1.000 0.051 3.899 44.959 0.046 -0.017 13 692071 1613 1983 371 1.000 0.066 0.887 4.976 0.069 -0.045 14 692072 1614 1983 370 1.000 0.068 1.304 6.429 0.073 -0.040 15 692081 1496 1983 488 1.000 0.055 0.803 4.895 0.059 -0.031 16 692082 1510 1983 474 1.000 0.052 0.661 7.020 0.054 -0.050 17 692091 1682 1983 302 1.000 0.057 1.592 12.165 0.058 0.010 18 692092 1815 1983 169 1.000 0.047 0.886 6.436 0.052 -0.040 19 692101 1789 1983 195 1.000 0.074 1.357 7.821 0.074 -0.053 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 692102 1780 1983 204 1.000 0.057 0.793 5.467 0.059 -0.048 21 692111 1737 1983 247 1.000 0.054 0.142 3.211 0.062 -0.069 22 692112 1722 1983 262 1.000 0.068 2.157 13.251 0.063 -0.014 23 692121 1669 1983 315 1.000 0.062 1.336 7.506 0.060 0.004 24 692122 1660 1983 324 1.000 0.064 0.933 6.608 0.065 -0.017 25 692131 1660 1983 324 1.000 0.067 1.776 12.100 0.064 -0.041 26 692132 1619 1983 365 1.000 0.064 0.703 4.921 0.067 -0.001 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 325 1.000 0.060 1.073 7.851 0.063 -0.030 STANDARD DEVIATION 90 0.000 0.008 0.733 8.008 0.008 0.022 MEDIAN (50TH QUANTILE) 330 1.000 0.061 0.887 5.717 0.063 -0.035 INTERQUARTILE RANGE 108 0.000 0.010 0.601 2.784 0.008 0.035 MINIMUM VALUE 169 1.000 0.041 0.142 3.088 0.046 -0.069 LOWER HINGE (25TH QUANTILE) 262 1.000 0.055 0.703 4.723 0.059 -0.048 UPPER HINGE (75TH QUANTILE) 370 1.000 0.065 1.304 7.506 0.067 -0.014 MAXIMUM VALUE 488 1.000 0.077 3.899 44.959 0.078 0.010 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.391 0.104 0.006 0.487 3.222 0.159 0.735 MINIMUM CORRELATION: 0.159 SERIES 692041 AND 692102 204 YEARS MAXIMUM CORRELATION: 0.735 SERIES 692071 AND 692072 370 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 0.322 0.596 0.522 0.467 0.492 0.489 0.445 0.399 0.370 0.376 SDEV 0.183 0.116 0.145 0.157 0.150 0.148 0.162 0.161 0.151 0.163 SERR 0.106 0.047 0.059 0.050 0.028 0.018 0.013 0.012 0.011 0.011 EPS 0.639 0.860 0.851 0.880 0.928 0.943 0.938 0.929 0.924 0.929 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 0.395 0.515 0.547 0.424 0.413 0.411 0.355 SDEV 0.175 0.143 0.134 0.139 0.162 0.180 0.176 SERR 0.012 0.009 0.007 0.008 0.009 0.010 0.010 EPS 0.939 0.964 0.969 0.950 0.948 0.948 0.935 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 0.999 0.042 0.495 3.563 0.047 -0.088 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.264 0.146 -0.106 161 327 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.23 0.69 1.00 1.07 1.77 13.35 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.93 0.11 0.00 0.89 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 -0.088 -0.063 0.019 0.130 -0.080 0.028 -0.047 0.041 -0.043 0.055 PACF -0.088 -0.071 0.007 0.129 -0.056 0.032 -0.057 0.023 -0.029 0.046 95% C.L. 0.091 0.091 0.092 0.092 0.093 0.094 0.094 0.094 0.094 0.094 |------------------ 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 0.013 -0.095 -0.073 |---------- 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 -0.006 -0.070 0.025 0.126 -0.067 0.017 -0.042 0.034 -0.035 0.051 PACF -0.006 -0.070 0.024 0.122 -0.063 0.033 -0.058 0.026 -0.027 0.049 95% C.L. 0.091 0.091 0.091 0.091 0.092 0.093 0.093 0.093 0.093 0.093 |----------------- REWHITENED CHRONOLOGY AUTOREGRESSIVE MODEL -----------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.005 -0.006 |========================= 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 0.999 0.042 0.521 3.527 0.043 0.088 |------------ 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 0.088 -0.058 0.031 0.122 -0.053 0.008 -0.037 0.027 -0.026 0.047 PACF 0.088 -0.066 0.043 0.113 -0.072 0.034 -0.058 0.029 -0.024 0.051 95% C.L. 0.091 0.091 0.092 0.092 0.093 0.093 0.093 0.093 0.093 0.093 |------------------- 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 0.014 0.095 -0.065 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.43 MINUTES