RUN: fix002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN020L.rwl.conv LOG FILE PROCESSED: FRAN020L.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: 486 1 Pic Aubas WIDTH_LATE ABAL - 486 2 France silver fir, European fir 1800 4246-37 1784 1977 - 486 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 13 486081 MISSING VALUES FOUND: 7 IN 1 GAPS / 1841 1847 / -------------------------------------------------------------------- 14 486082 MISSING VALUES FOUND: 11 IN 2 GAPS / 1940 1944 / 1963 1968 / -------------------------------------------------------------------- 17 486101 MISSING VALUES FOUND: 5 IN 1 GAPS / 1939 1943 / -------------------------------------------------------------------- 25 486141 MISSING VALUES FOUND: 10 IN 2 GAPS / 1921 1925 / 1965 1969 / -------------------------------------------------------------------- 26 486142 MISSING VALUES FOUND: 7 IN 1 GAPS / 1967 1973 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 486011 1843 1977 135 0.282 0.280 1.954 6.162 0.329 0.882 2 486012 1831 1977 147 0.263 0.161 1.059 4.275 0.343 0.690 3 486021 1871 1977 107 0.237 0.242 2.365 7.795 0.445 0.661 4 486022 1806 1977 172 0.285 0.310 4.288 26.193 0.345 0.690 5 486031 1795 1977 183 0.235 0.161 1.154 3.902 0.275 0.869 6 486032 1814 1977 164 0.242 0.201 1.499 4.663 0.362 0.834 7 486041 1822 1977 156 0.224 0.134 1.097 4.198 0.291 0.725 8 486042 1806 1977 172 0.306 0.213 1.203 4.259 0.356 0.768 9 486051 1807 1977 171 0.243 0.136 1.210 4.465 0.314 0.702 10 486052 1792 1977 186 0.244 0.132 0.624 2.835 0.306 0.731 11 486071 1884 1977 94 0.398 0.250 0.596 2.885 0.309 0.722 12 486072 1883 1977 95 0.514 0.377 1.139 4.111 0.353 0.803 13 486081 1796 1977 182 0.265 0.236 1.991 7.018 0.374 0.690 14 486082 1801 1968 168 0.235 0.181 1.686 7.011 0.321 0.737 15 486091 1803 1977 175 0.317 0.270 3.164 16.638 0.332 0.798 16 486092 1797 1977 181 0.296 0.239 2.438 9.303 0.330 0.819 17 486101 1847 1977 131 0.358 0.337 1.952 8.131 0.368 0.790 18 486102 1836 1977 142 0.269 0.160 0.762 3.468 0.384 0.588 19 486111 1804 1977 174 0.439 0.323 1.289 4.215 0.362 0.783 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 486112 1805 1977 173 0.443 0.241 0.705 3.172 0.338 0.677 21 486121 1796 1977 182 0.226 0.145 1.030 4.430 0.422 0.729 22 486122 1811 1977 167 0.293 0.161 1.168 7.013 0.400 0.584 23 486131 1795 1977 183 0.276 0.162 1.074 3.789 0.284 0.790 24 486132 1837 1977 141 0.233 0.148 1.570 5.512 0.284 0.822 25 486141 1784 1969 186 0.226 0.165 0.844 3.667 0.295 0.786 26 486142 1796 1973 178 0.283 0.275 1.386 3.948 0.385 0.826 NUMBER OF SERIES READ IN: 26 FROM 1784 TO 1977 194 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 158 0.294 0.217 1.510 6.271 0.343 0.750 STANDARD DEVIATION 27 0.076 0.070 0.834 4.967 0.043 0.077 MEDIAN (50TH QUANTILE) 171 0.273 0.207 1.207 4.352 0.340 0.753 INTERQUARTILE RANGE 33 0.069 0.109 0.893 3.111 0.059 0.113 MINIMUM VALUE 94 0.224 0.132 0.596 2.835 0.275 0.584 LOWER HINGE (25TH QUANTILE) 142 0.237 0.161 1.059 3.902 0.309 0.690 UPPER HINGE (75TH QUANTILE) 175 0.306 0.270 1.952 7.013 0.368 0.803 MAXIMUM VALUE 186 0.514 0.377 4.288 26.193 0.445 0.882 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.578 0.137 0.008 -0.914 4.276 0.000 0.835 MINIMUM CORRELATION: 0.000 SERIES 486072 AND 486082 86 YEARS MAXIMUM CORRELATION: 0.835 SERIES 486031 AND 486142 178 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 74.02 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1840. 1865. 1890. 1915. 1940. CORR 136. 210. 253. 325. 325. RBAR 0.244 0.333 0.477 0.356 0.507 SDEV 0.274 0.192 0.207 0.228 0.160 SERR 0.023 0.013 0.013 0.013 0.009 EPS 0.868 0.921 0.958 0.935 0.964 NSS 20.5 23.4 25.1 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 1784 1977 194 0.290 0.160 0.735 3.271 0.259 0.818 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.736 0.372 0.016 135 59 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.91 1.51 1.01 1.37 2.88 9.16 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.00 0.86 0.94 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 172. 39. 94. 142. 181. 186. |----------- 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 0.814 0.759 0.748 0.726 0.702 0.648 0.626 0.629 0.629 0.599 PACF 0.814 0.287 0.238 0.126 0.070 -0.068 0.015 0.094 0.103 -0.006 95% C.L. 0.144 0.219 0.268 0.308 0.341 0.370 0.393 0.413 0.432 0.451 |------------------ 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 0.730 0.454 0.133 0.191 0.142 |================== 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 486011 1 1.04802966 0.03810846 0.00000000 0.08309219 2 486012 3 0.00000000 0.00000000 -0.00257985 0.45410585 3 486021 1 0.80225670 0.05155376 0.00000000 0.09595687 4 486022 -67 115 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 486031 3 0.00000000 0.00000000 -0.00229408 0.44619226 6 486032 1 0.72871840 0.02554916 0.00000000 0.07279325 7 486041 3 0.00000000 0.00000000 -0.00189050 0.37276345 8 486042 3 0.00000000 0.00000000 -0.00324892 0.58701956 9 486051 1 0.37657377 0.02045247 0.00000000 0.13928679 10 486052 3 0.00000000 0.00000000 -0.00189152 0.42099681 11 486071 3 0.00000000 0.00000000 -0.00622136 0.69391900 12 486072 3 0.00000000 0.00000000 -0.00821851 0.90848827 13 486081 3 0.00000000 0.00000000 -0.00261110 0.50572574 14 486082 -67 112 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 486091 1 1.42847073 0.14462776 0.00000000 0.26417226 16 486092 1 1.21541500 0.08585942 0.00000000 0.22084698 17 486101 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 486102 3 0.00000000 0.00000000 -0.00284396 0.47256818 19 486111 1 0.96596581 0.03003144 0.00000000 0.25779781 SERIES IDENT OPTION A B C D 20 486112 3 0.00000000 0.00000000 -0.00353099 0.74991328 21 486121 3 0.00000000 0.00000000 -0.00195793 0.40535912 22 486122 3 0.00000000 0.00000000 -0.00179115 0.44309142 23 486131 3 0.00000000 0.00000000 -0.00236945 0.49394584 24 486132 3 0.00000000 0.00000000 -0.00238482 0.40222999 25 486141 5 0.00000000 0.00000000 0.00000000 0.21665382 26 486142 -67 119 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 486011 1843 1977 135 0.997 0.389 0.762 4.232 0.328 0.452 2 486012 1831 1977 147 0.980 0.405 0.692 3.730 0.341 0.448 3 486021 1871 1977 107 1.005 0.515 0.886 3.968 0.443 0.267 4 486022 1806 1977 172 1.001 0.493 1.646 6.141 0.343 0.456 5 486031 1795 1977 183 1.068 0.492 1.092 4.806 0.275 0.694 6 486032 1814 1977 164 1.009 0.416 0.362 4.568 0.358 0.301 7 486041 1822 1977 156 0.996 0.429 0.991 4.096 0.290 0.550 8 486042 1806 1977 172 1.056 0.546 2.243 10.251 0.356 0.532 9 486051 1807 1977 171 1.001 0.393 0.468 2.813 0.312 0.502 10 486052 1792 1977 186 1.002 0.357 0.958 4.404 0.305 0.363 11 486071 1884 1977 94 0.956 0.460 1.788 6.977 0.306 0.548 12 486072 1883 1977 95 0.940 0.513 1.264 4.304 0.348 0.676 13 486081 1796 1977 182 1.048 0.719 2.269 8.796 0.370 0.563 14 486082 1801 1968 168 0.994 0.352 1.167 5.352 0.321 0.212 15 486091 1803 1977 175 1.003 0.605 1.130 4.431 0.331 0.682 16 486092 1797 1977 181 1.003 0.491 0.722 4.225 0.327 0.595 17 486101 1847 1977 131 1.007 0.456 1.313 5.626 0.370 0.414 18 486102 1836 1977 142 0.988 0.452 2.123 10.919 0.381 0.179 19 486111 1804 1977 174 0.999 0.581 1.316 4.827 0.360 0.652 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 486112 1805 1977 173 1.000 0.368 0.583 3.398 0.336 0.385 21 486121 1796 1977 182 0.991 0.468 1.071 5.549 0.421 0.355 22 486122 1811 1977 167 0.985 0.486 1.454 7.912 0.397 0.483 23 486131 1795 1977 183 1.015 0.361 1.058 4.500 0.282 0.429 24 486132 1837 1977 141 1.006 0.407 0.823 3.798 0.283 0.572 25 486141 1784 1969 186 1.000 0.764 0.894 3.682 0.292 0.794 26 486142 1796 1973 178 1.007 0.567 0.997 3.870 0.380 0.555 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 159 1.002 0.480 1.157 5.276 0.341 0.487 STANDARD DEVIATION 27 0.026 0.104 0.510 2.076 0.043 0.153 MEDIAN (50TH QUANTILE) 171 1.001 0.464 1.064 4.466 0.339 0.492 INTERQUARTILE RANGE 39 0.012 0.109 0.493 1.658 0.064 0.187 MINIMUM VALUE 94 0.940 0.352 0.362 2.813 0.275 0.179 LOWER HINGE (25TH QUANTILE) 142 0.994 0.405 0.823 3.968 0.306 0.385 UPPER HINGE (75TH QUANTILE) 181 1.007 0.515 1.316 5.626 0.370 0.572 MAXIMUM VALUE 186 1.068 0.764 2.269 10.919 0.443 0.794 |------------------------ 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 486011 -67 90 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 486012 -67 98 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 486021 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 486022 -67 115 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 486031 -67 122 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 486032 -67 109 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 486041 -67 104 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 486042 -67 115 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 486051 -67 114 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 486052 -67 124 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 486071 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 486072 -67 63 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 486081 -67 121 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 486082 -67 112 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 486091 -67 117 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 486092 -67 121 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 486101 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 486102 -67 95 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 486111 -67 116 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 486112 -67 115 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 486121 -67 121 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 486122 -67 111 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 486131 -67 122 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 486132 -67 94 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 25 486141 5 0.00000000 0.00000000 0.00000000 1.00000024 26 486142 -67 119 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 486011 1843 1977 135 0.995 0.362 0.547 3.730 0.328 0.358 2 486012 1831 1977 147 0.997 0.391 0.584 3.316 0.342 0.363 3 486021 1871 1977 107 0.995 0.500 0.865 3.581 0.444 0.241 4 486022 1806 1977 172 0.996 0.478 1.608 5.934 0.342 0.436 5 486031 1795 1977 183 0.994 0.380 0.519 2.936 0.274 0.611 6 486032 1814 1977 164 0.997 0.392 0.172 4.457 0.358 0.277 7 486041 1822 1977 156 0.986 0.386 1.055 4.401 0.290 0.482 8 486042 1806 1977 172 0.997 0.429 1.066 4.033 0.355 0.420 9 486051 1807 1977 171 0.995 0.383 0.570 2.916 0.312 0.489 10 486052 1792 1977 186 0.998 0.348 0.966 4.445 0.305 0.338 11 486071 1884 1977 94 0.996 0.347 1.255 4.819 0.306 0.317 12 486072 1883 1977 95 0.987 0.340 1.314 6.738 0.346 0.216 13 486081 1796 1977 182 0.972 0.503 1.688 6.477 0.369 0.403 14 486082 1801 1968 168 0.998 0.341 1.056 5.107 0.321 0.176 15 486091 1803 1977 175 0.995 0.425 1.261 5.490 0.332 0.456 16 486092 1797 1977 181 0.988 0.401 0.654 3.718 0.326 0.419 17 486101 1847 1977 131 0.995 0.412 1.136 5.388 0.370 0.331 18 486102 1836 1977 142 0.998 0.443 1.848 9.062 0.381 0.147 19 486111 1804 1977 174 0.992 0.473 0.780 3.551 0.360 0.521 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 486112 1805 1977 173 0.997 0.356 0.540 3.330 0.336 0.346 21 486121 1796 1977 182 0.998 0.470 1.172 6.074 0.421 0.326 22 486122 1811 1977 167 0.988 0.437 1.376 7.382 0.397 0.366 23 486131 1795 1977 183 0.997 0.331 0.926 4.016 0.283 0.389 24 486132 1837 1977 141 0.994 0.379 0.733 3.719 0.283 0.538 25 486141 1784 1969 186 1.000 0.764 0.894 3.682 0.292 0.794 26 486142 1796 1973 178 0.990 0.527 0.925 3.872 0.380 0.544 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 159 0.994 0.423 0.981 4.699 0.340 0.396 STANDARD DEVIATION 27 0.006 0.089 0.398 1.505 0.043 0.140 MEDIAN (50TH QUANTILE) 171 0.995 0.396 0.946 4.217 0.339 0.378 INTERQUARTILE RANGE 39 0.005 0.108 0.601 1.808 0.063 0.156 MINIMUM VALUE 94 0.972 0.331 0.172 2.916 0.274 0.147 LOWER HINGE (25TH QUANTILE) 142 0.992 0.362 0.654 3.682 0.306 0.326 UPPER HINGE (75TH QUANTILE) 181 0.997 0.470 1.255 5.490 0.369 0.482 MAXIMUM VALUE 186 1.000 0.764 1.848 9.062 0.444 0.794 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.352 0.117 0.006 -0.298 3.221 -0.007 0.668 MINIMUM CORRELATION: -0.007 SERIES 486011 AND 486141 127 YEARS MAXIMUM CORRELATION: 0.668 SERIES 486021 AND 486022 107 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 74.02 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1840. 1865. 1890. 1915. 1940. CORR 136. 210. 253. 325. 325. RBAR 0.318 0.339 0.397 0.373 0.403 SDEV 0.219 0.159 0.205 0.208 0.169 SERR 0.019 0.011 0.013 0.012 0.009 EPS 0.905 0.923 0.943 0.939 0.946 NSS 20.5 23.4 25.1 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 1784 1977 194 1.033 0.366 1.332 7.348 0.296 0.453 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.222 0.075 0.236 83 111 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.19 0.44 1.00 1.08 1.52 4.75 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.00 0.88 0.94 1.00 |----------- STANDARD CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.451 0.269 0.253 0.215 0.200 0.055 0.043 0.099 0.129 0.026 PACF 0.451 0.082 0.132 0.059 0.068 -0.121 0.008 0.066 0.079 -0.088 95% C.L. 0.144 0.170 0.179 0.186 0.191 0.195 0.196 0.196 0.197 0.199 |------------------ 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 0.213 0.455 |======================= 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 0.245 0.087 0.089 0.070 0.153 0.014 0.001 0.106 0.139 0.016 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 0.245 2 0.238 0.029 3 0.236 0.014 0.065 4 0.234 0.013 0.057 0.034 5 0.230 0.006 0.055 0.003 0.131 6 0.238 0.006 0.059 0.004 0.145 -0.064 7 0.238 0.006 0.059 0.004 0.145 -0.063 -0.004 8 0.238 0.013 0.045 0.004 0.140 -0.064 -0.028 0.098 9 0.229 0.015 0.051 -0.010 0.139 -0.068 -0.029 0.075 0.096 10 0.235 0.020 0.049 -0.014 0.149 -0.069 -0.025 0.076 0.112 -0.069 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) 1701.48 1691.43 1693.27 1694.45 1696.22 1694.89 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1696.08 1698.07 1698.20 1698.41 1699.50 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 0.245 R-SQUARED DUE TO POOLED AUTOREGRESSION: 6.02 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 106.40 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.245 0.060 0.015 0.004 0.001 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 486011 1 0.150 0.365 2 486012 1 0.140 0.374 3 486021 1 0.061 0.245 4 486022 1 0.213 0.457 5 486031 1 0.401 0.611 6 486032 1 0.094 0.278 7 486041 1 0.297 0.483 8 486042 1 0.188 0.420 9 486051 1 0.245 0.492 10 486052 1 0.121 0.338 11 486071 1 0.112 0.320 12 486072 1 0.047 0.216 13 486081 1 0.186 0.405 14 486082 1 0.046 0.177 15 486091 1 0.221 0.456 16 486092 1 0.179 0.423 17 486101 1 0.122 0.337 18 486102 1 0.027 0.148 19 486111 1 0.296 0.522 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 486112 1 0.122 0.349 21 486121 1 0.108 0.329 22 486122 1 0.137 0.370 23 486131 1 0.175 0.389 24 486132 1 0.326 0.541 25 486141 1 0.683 0.798 26 486142 1 0.327 0.552 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.193 0.400 STANDARD DEVIATION 0 0.138 0.141 MEDIAN 1 0.162 0.381 INTERQUARTILE RANGE 0 0.133 0.155 MINIMUM VALUE 1 0.027 0.148 LOWER HINGE 1 0.112 0.329 UPPER HINGE 1 0.245 0.483 MAXIMUM VALUE 1 0.683 0.798 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 486011 1843 1977 135 1.000 0.337 0.357 3.339 0.397 -0.042 2 486012 1831 1977 147 1.000 0.362 0.523 3.446 0.396 -0.007 3 486021 1871 1977 107 1.000 0.485 0.883 3.510 0.501 -0.005 4 486022 1806 1977 172 1.000 0.421 1.466 6.438 0.426 -0.052 5 486031 1795 1977 183 1.000 0.301 0.443 3.367 0.364 -0.127 6 486032 1814 1977 164 1.000 0.375 0.395 5.109 0.411 -0.037 7 486041 1822 1977 156 1.000 0.337 1.073 4.671 0.374 -0.139 8 486042 1806 1977 172 1.000 0.389 0.858 4.109 0.443 -0.050 9 486051 1807 1977 171 1.000 0.333 0.379 2.505 0.392 -0.028 10 486052 1792 1977 186 1.000 0.328 0.803 4.257 0.361 -0.029 11 486071 1884 1977 94 1.000 0.328 1.306 6.216 0.346 0.033 12 486072 1883 1977 95 1.000 0.332 1.184 5.890 0.371 -0.001 13 486081 1796 1977 182 1.000 0.459 1.425 6.269 0.446 -0.062 14 486082 1801 1968 168 1.000 0.336 1.155 5.274 0.347 -0.021 15 486091 1803 1977 175 1.000 0.378 1.194 5.242 0.410 -0.059 16 486092 1797 1977 181 1.000 0.363 0.959 4.233 0.377 0.004 17 486101 1847 1977 131 1.000 0.388 0.868 4.825 0.437 0.037 18 486102 1836 1977 142 1.000 0.437 1.775 8.971 0.404 0.013 19 486111 1804 1977 174 1.000 0.403 1.169 4.224 0.432 -0.092 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 486112 1805 1977 173 1.000 0.334 0.693 3.383 0.376 0.005 21 486121 1796 1977 182 1.002 0.437 1.303 8.146 0.473 0.015 22 486122 1811 1977 167 1.000 0.406 1.413 8.289 0.453 0.004 23 486131 1795 1977 183 1.000 0.305 0.630 3.620 0.346 -0.064 24 486132 1837 1977 141 1.000 0.318 0.655 3.968 0.373 -0.114 25 486141 1784 1969 186 1.006 0.443 1.458 7.232 0.445 -0.266 26 486142 1796 1973 178 1.001 0.436 0.959 4.467 0.468 -0.089 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 159 1.000 0.376 0.974 5.039 0.407 -0.045 STANDARD DEVIATION 27 0.001 0.052 0.391 1.701 0.043 0.065 MEDIAN (50TH QUANTILE) 171 1.000 0.369 0.959 4.569 0.401 -0.033 INTERQUARTILE RANGE 39 0.000 0.088 0.647 2.596 0.070 0.068 MINIMUM VALUE 94 1.000 0.301 0.357 2.505 0.346 -0.266 LOWER HINGE (25TH QUANTILE) 142 1.000 0.333 0.655 3.620 0.373 -0.064 UPPER HINGE (75TH QUANTILE) 181 1.000 0.421 1.303 6.216 0.443 0.004 MAXIMUM VALUE 186 1.006 0.485 1.775 8.971 0.501 0.037 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.418 0.091 0.005 -0.142 3.735 0.095 0.702 MINIMUM CORRELATION: 0.095 SERIES 486021 AND 486141 99 YEARS MAXIMUM CORRELATION: 0.702 SERIES 486021 AND 486022 107 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 74.02 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1840. 1865. 1890. 1915. 1940. CORR 136. 210. 253. 325. 325. RBAR 0.327 0.382 0.438 0.459 0.497 SDEV 0.154 0.134 0.160 0.138 0.126 SERR 0.013 0.009 0.010 0.008 0.007 EPS 0.909 0.935 0.951 0.957 0.963 NSS 20.5 23.4 25.1 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 1784 1977 194 0.996 0.277 0.652 4.445 0.321 -0.112 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.386 0.139 0.115 77 117 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.28 0.72 1.00 1.13 1.85 6.10 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 0.00 0.87 0.94 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 -0.111 -0.081 0.066 0.012 0.100 -0.078 -0.027 0.030 0.110 -0.044 PACF -0.111 -0.094 0.047 0.018 0.116 -0.055 -0.028 -0.001 0.118 -0.021 95% C.L. 0.144 0.145 0.146 0.147 0.147 0.148 0.149 0.149 0.149 0.151 |------------------ RESIDUAL CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.022 -0.112 |---------- 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 -0.011 -0.089 0.060 0.032 0.097 -0.072 -0.033 0.040 0.111 -0.042 PACF -0.011 -0.089 0.058 0.026 0.109 -0.070 -0.019 0.014 0.113 -0.041 95% C.L. 0.144 0.144 0.145 0.145 0.145 0.147 0.147 0.148 0.148 0.150 |----------------- 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 0.008 -0.011 |========================= 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 1784 1977 194 0.997 0.282 0.809 4.505 0.273 0.216 |------------ 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 0.215 -0.018 0.065 0.070 0.096 -0.052 -0.027 0.055 0.104 -0.032 PACF 0.215 -0.067 0.088 0.037 0.084 -0.097 0.010 0.039 0.091 -0.078 95% C.L. 0.144 0.150 0.150 0.151 0.151 0.153 0.153 0.153 0.154 0.155 |------------------- 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 1 0.051 0.217 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 2.26 MINUTES