RUN: 4DIG001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM047W.rwl.conv LOG FILE PROCESSED: GERM047W.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: 028 1 Sirnitz SW (D), EU-Pr. WIDTH_RING ABAL - 028 2 Germany silver fir, European fir 930 4748-745 1844 1995 - 028 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 6 028033 MISSING VALUES FOUND: 3 IN 1 GAPS / 1974 1976 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 028021 1844 1995 152 1.988 1.149 0.749 3.054 0.203 0.898 2 028023 1844 1995 152 2.177 1.406 1.038 4.172 0.232 0.913 3 028025 1844 1995 152 1.738 1.159 1.076 3.521 0.243 0.914 4 028027 1844 1995 152 1.729 1.203 1.291 4.503 0.242 0.899 5 028031 1855 1995 141 2.248 1.162 0.305 2.634 0.221 0.879 6 028033 1857 1995 139 2.803 1.320 0.380 3.087 0.234 0.827 7 028035 1857 1995 139 1.818 0.988 0.583 3.195 0.213 0.870 8 028037 1855 1995 141 1.509 0.607 0.613 3.078 0.219 0.757 9 028051 1851 1995 145 2.634 1.597 0.720 3.281 0.213 0.897 10 028053 1851 1995 145 2.472 1.517 0.887 3.179 0.229 0.871 11 028055 1851 1995 145 1.905 0.882 0.320 2.492 0.238 0.811 12 028057 1851 1995 145 1.955 1.025 0.362 2.293 0.241 0.837 13 028071 1850 1995 146 2.731 1.757 2.231 7.343 0.181 0.934 14 028073 1852 1995 144 2.104 0.670 0.764 4.386 0.196 0.664 15 028075 1850 1995 146 1.972 0.852 0.743 3.072 0.211 0.801 16 028077 1850 1995 146 2.511 1.919 2.277 7.257 0.201 0.938 17 028091 1845 1995 151 2.163 1.052 1.019 3.520 0.195 0.878 18 028093 1845 1995 151 2.459 1.370 1.201 3.977 0.194 0.915 19 028095 1845 1995 151 2.288 1.277 1.362 4.442 0.208 0.884 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 028097 1845 1995 151 2.405 1.306 1.580 5.690 0.204 0.897 NUMBER OF SERIES READ IN: 20 FROM 1844 TO 1995 152 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 147 2.180 1.211 0.975 3.909 0.216 0.864 STANDARD DEVIATION 4 0.358 0.336 0.565 1.412 0.018 0.066 MEDIAN (50TH QUANTILE) 146 2.170 1.182 0.825 3.400 0.213 0.881 INTERQUARTILE RANGE 6 0.536 0.382 0.648 1.339 0.031 0.074 MINIMUM VALUE 136 1.509 0.607 0.305 2.293 0.181 0.664 LOWER HINGE (25TH QUANTILE) 144 1.930 1.006 0.598 3.075 0.202 0.832 UPPER HINGE (75TH QUANTILE) 151 2.465 1.388 1.246 4.414 0.233 0.906 MAXIMUM VALUE 152 2.803 1.919 2.277 7.343 0.243 0.938 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.331 0.385 0.028 -0.567 2.340 -0.547 0.896 MINIMUM CORRELATION: -0.547 SERIES 028021 AND 028035 139 YEARS MAXIMUM CORRELATION: 0.896 SERIES 028071 AND 028077 146 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 94.81 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1869. 1900. 1925. 1950. CORR 6. 190. 190. 190. RBAR 0.883 0.584 0.540 0.258 SDEV 0.032 0.263 0.203 0.437 SERR 0.013 0.019 0.015 0.032 EPS 0.993 0.966 0.959 0.874 NSS 17.9 20.0 20.0 20.0 |======================== 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 1844 1995 152 2.081 0.755 0.476 2.653 0.170 0.829 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.777 0.568 -0.282 71 81 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.47 0.84 1.00 1.15 1.99 9.61 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.07 0.76 0.85 0.92 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 146. 6. 139. 144. 151. 152. |----------- 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 0.823 0.811 0.740 0.716 0.672 0.626 0.544 0.553 0.505 0.505 PACF 0.823 0.415 0.030 0.071 0.024 -0.048 -0.173 0.169 0.028 0.056 95% C.L. 0.162 0.249 0.311 0.354 0.390 0.420 0.444 0.461 0.478 0.492 |------------------ RAW DATA CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 2 0.750 0.458 0.447 |================== 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 028021 3 0.00000000 0.00000000 0.02105359 0.37782153 2 028023 3 0.00000000 0.00000000 0.02665824 0.13728911 3 028025 3 0.00000000 0.00000000 0.01744189 0.40398484 4 028027 3 0.00000000 0.00000000 0.01640653 0.47378182 5 028031 1 0.18201484 0.01502735 0.00000000 2.17272091 6 028033 1 2.85044122 0.00272364 0.00000000 0.38387832 7 028035 3 0.00000000 0.00000000 -0.01782189 3.06537390 8 028037 1 1.19610393 0.02862046 0.00000000 1.22236037 9 028051 3 0.00000000 0.00000000 0.02260648 0.98358905 10 028053 3 0.00000000 0.00000000 0.01170548 1.61729312 11 028055 3 0.00000000 0.00000000 0.00277240 1.70230460 12 028057 3 0.00000000 0.00000000 0.00978531 1.24036205 13 028071 3 0.00000000 0.00000000 0.02930385 0.57712609 14 028073 3 0.00000000 0.00000000 0.00946966 1.41719985 15 028075 3 0.00000000 0.00000000 0.01330298 0.99380636 16 028077 3 0.00000000 0.00000000 0.03089146 0.24029945 17 028091 3 0.00000000 0.00000000 0.01674831 0.89057219 18 028093 3 0.00000000 0.00000000 0.02360812 0.66498804 19 028095 3 0.00000000 0.00000000 0.01980234 0.78343314 SERIES IDENT OPTION A B C D 20 028097 3 0.00000000 0.00000000 0.02191492 0.73903573 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 028021 1844 1995 152 1.055 0.520 2.709 15.525 0.203 0.727 2 028023 1844 1995 152 1.173 0.966 4.457 26.438 0.234 0.737 3 028025 1844 1995 152 1.033 0.536 1.046 4.975 0.242 0.779 4 028027 1844 1995 152 1.031 0.557 1.235 6.240 0.240 0.795 5 028031 1855 1995 141 1.000 0.522 0.372 2.713 0.220 0.874 6 028033 1857 1995 139 1.000 0.514 0.824 4.117 0.234 0.850 7 028035 1857 1995 139 0.982 0.369 0.505 2.898 0.212 0.719 8 028037 1855 1995 141 1.000 0.366 0.766 3.823 0.218 0.689 9 028051 1851 1995 145 1.030 0.653 1.698 6.291 0.213 0.891 10 028053 1851 1995 145 1.000 0.572 0.657 2.451 0.227 0.865 11 028055 1851 1995 145 1.000 0.470 0.544 3.090 0.236 0.807 12 028057 1851 1995 145 1.007 0.567 1.432 5.676 0.239 0.849 13 028071 1850 1995 146 1.086 0.549 1.781 5.649 0.179 0.847 14 028073 1852 1995 144 1.002 0.275 1.147 5.095 0.195 0.540 15 028075 1850 1995 146 1.018 0.390 1.098 4.226 0.210 0.769 16 028077 1850 1995 146 1.262 1.159 3.161 13.676 0.201 0.892 17 028091 1845 1995 151 1.028 0.446 2.488 13.563 0.195 0.793 18 028093 1845 1995 151 1.050 0.528 3.001 14.213 0.193 0.823 19 028095 1845 1995 151 1.028 0.469 1.823 7.652 0.207 0.797 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 028097 1845 1995 151 1.045 0.484 2.629 13.614 0.202 0.796 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 147 1.042 0.546 1.669 8.096 0.215 0.792 STANDARD DEVIATION 4 0.067 0.199 1.090 6.156 0.018 0.083 MEDIAN (50TH QUANTILE) 146 1.028 0.521 1.333 5.663 0.212 0.797 INTERQUARTILE RANGE 6 0.047 0.105 1.764 9.619 0.032 0.096 MINIMUM VALUE 139 0.982 0.275 0.372 2.451 0.179 0.540 LOWER HINGE (25TH QUANTILE) 144 1.000 0.457 0.795 3.970 0.202 0.753 UPPER HINGE (75TH QUANTILE) 151 1.047 0.562 2.558 13.589 0.234 0.849 MAXIMUM VALUE 152 1.262 1.159 4.457 26.438 0.242 0.892 |------------------------ 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 028021 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 028023 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 028025 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 028027 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 028031 -67 94 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 028033 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 028035 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 028037 -67 94 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 028051 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 028053 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 028055 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 028057 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 028071 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 028073 -67 96 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 028075 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 028077 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 028091 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 028093 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 028095 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 028097 -67 101 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 028021 1844 1995 152 0.986 0.314 0.198 3.304 0.202 0.668 2 028023 1844 1995 152 0.990 0.359 0.403 3.968 0.232 0.672 3 028025 1844 1995 152 0.972 0.358 0.024 2.501 0.240 0.686 4 028027 1844 1995 152 0.979 0.412 0.259 3.140 0.239 0.761 5 028031 1855 1995 141 0.976 0.461 0.126 2.635 0.220 0.853 6 028033 1857 1995 139 0.974 0.417 0.167 2.644 0.233 0.784 7 028035 1857 1995 139 0.994 0.343 0.711 3.370 0.212 0.646 8 028037 1855 1995 141 0.994 0.337 0.409 2.758 0.217 0.667 9 028051 1851 1995 145 0.958 0.363 0.440 2.768 0.210 0.764 10 028053 1851 1995 145 0.965 0.449 0.644 2.749 0.226 0.788 11 028055 1851 1995 145 0.970 0.354 0.246 2.621 0.237 0.690 12 028057 1851 1995 145 0.965 0.409 0.864 3.868 0.237 0.764 13 028071 1850 1995 146 0.996 0.263 0.399 3.345 0.180 0.628 14 028073 1852 1995 144 0.999 0.258 1.031 5.212 0.195 0.516 15 028075 1850 1995 146 0.996 0.290 0.808 5.294 0.210 0.630 16 028077 1850 1995 146 1.009 0.332 0.418 2.863 0.201 0.761 17 028091 1845 1995 151 0.997 0.304 0.400 4.133 0.194 0.708 18 028093 1845 1995 151 0.994 0.314 0.497 2.952 0.192 0.727 19 028095 1845 1995 151 0.991 0.343 0.492 2.945 0.206 0.719 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 028097 1845 1995 151 0.996 0.290 0.113 4.155 0.202 0.652 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 147 0.985 0.348 0.432 3.361 0.214 0.704 STANDARD DEVIATION 4 0.014 0.057 0.269 0.829 0.018 0.075 MEDIAN (50TH QUANTILE) 146 0.991 0.343 0.406 3.046 0.211 0.699 INTERQUARTILE RANGE 6 0.023 0.077 0.348 1.164 0.031 0.104 MINIMUM VALUE 139 0.958 0.258 0.024 2.501 0.180 0.516 LOWER HINGE (25TH QUANTILE) 144 0.973 0.309 0.222 2.754 0.201 0.659 UPPER HINGE (75TH QUANTILE) 151 0.996 0.386 0.570 3.918 0.233 0.763 MAXIMUM VALUE 152 1.009 0.461 1.031 5.294 0.240 0.853 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.403 0.193 0.014 -0.180 2.933 -0.112 0.877 MINIMUM CORRELATION: -0.112 SERIES 028025 AND 028031 141 YEARS MAXIMUM CORRELATION: 0.877 SERIES 028073 AND 028075 144 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 94.81 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1869. 1900. 1925. 1950. CORR 6. 190. 190. 190. RBAR 0.895 0.607 0.471 0.307 SDEV 0.024 0.180 0.247 0.277 SERR 0.010 0.013 0.018 0.020 EPS 0.993 0.969 0.947 0.899 NSS 17.9 20.0 20.0 20.0 |======================== 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 1844 1995 152 0.991 0.244 0.612 3.541 0.171 0.625 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.191 0.070 0.198 42 110 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.15 0.36 1.00 1.06 1.42 5.22 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.05 0.76 0.86 0.92 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 0.621 0.541 0.379 0.310 0.232 0.126 0.011 -0.011 -0.098 -0.071 PACF 0.621 0.253 -0.050 0.018 0.003 -0.100 -0.131 0.036 -0.086 0.050 95% C.L. 0.162 0.216 0.249 0.264 0.273 0.278 0.280 0.280 0.280 0.281 |------------------ 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 0.459 0.471 0.269 |======================= 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 0.622 0.534 0.392 0.317 0.222 0.109 -0.042 -0.043 -0.135 -0.082 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 0.622 2 0.472 0.241 3 0.476 0.249 -0.018 4 0.477 0.245 -0.025 0.015 5 0.477 0.244 -0.016 0.032 -0.037 6 0.473 0.248 -0.017 0.059 0.016 -0.110 7 0.453 0.251 -0.006 0.056 0.062 -0.021 -0.187 8 0.465 0.252 -0.010 0.052 0.063 -0.037 -0.217 0.065 9 0.470 0.235 -0.013 0.057 0.067 -0.038 -0.196 0.103 -0.082 10 0.478 0.224 0.006 0.061 0.060 -0.044 -0.195 0.080 -0.129 0.099 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) 1213.01 1140.68 1133.61 1135.56 1137.53 1139.33 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1139.49 1136.07 1137.42 1138.40 1138.89 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 0.472 0.241 R-SQUARED DUE TO POOLED AUTOREGRESSION: 42.23 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 173.09 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.472 0.464 0.333 0.269 0.207 0.162 0.126 0.099 0.077 0.0602 0.047 0.037 0.029 0.022 0.017 0.014 0.011 0.008 0.006 0.0051 0.004 0.003 0.002 0.002 0.001 0.001 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 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 028021 2 0.495 0.588 0.153 2 028023 2 0.510 0.607 0.140 3 028025 2 0.500 0.560 0.192 4 028027 2 0.615 0.679 0.129 5 028031 2 0.730 0.850 0.005 6 028033 2 0.619 0.840 -0.069 7 028035 2 0.459 0.609 0.088 8 028037 2 0.474 0.641 0.060 9 028051 2 0.606 0.623 0.187 10 028053 2 0.628 0.767 0.028 11 028055 2 0.516 0.515 0.258 12 028057 2 0.597 0.653 0.148 13 028071 2 0.452 0.452 0.287 14 028073 2 0.339 0.353 0.315 15 028075 2 0.437 0.481 0.239 16 028077 2 0.623 0.527 0.309 17 028091 2 0.511 0.646 0.090 18 028093 2 0.542 0.628 0.140 19 028095 2 0.545 0.591 0.187 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 028097 2 0.444 0.615 0.072 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.532 0.611 0.148 STANDARD DEVIATION 0 0.090 0.119 0.103 MEDIAN 2 0.513 0.612 0.144 INTERQUARTILE RANGE 0 0.144 0.106 0.135 MINIMUM VALUE 2 0.339 0.353 -0.069 LOWER HINGE 2 0.466 0.543 0.080 UPPER HINGE 2 0.610 0.649 0.216 MAXIMUM VALUE 2 0.730 0.850 0.315 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 028021 1844 1995 152 1.000 0.219 0.433 3.256 0.245 -0.020 2 028023 1844 1995 152 1.000 0.245 0.071 3.374 0.281 -0.026 3 028025 1844 1995 152 1.000 0.252 0.105 3.357 0.285 -0.008 4 028027 1844 1995 152 1.000 0.254 0.483 3.464 0.281 0.001 5 028031 1855 1995 141 1.000 0.240 0.358 3.595 0.258 0.000 6 028033 1857 1995 139 1.000 0.258 0.136 3.367 0.282 0.000 7 028035 1857 1995 139 1.000 0.253 0.432 3.894 0.270 0.010 8 028037 1855 1995 141 1.000 0.246 0.277 3.470 0.277 0.006 9 028051 1851 1995 145 1.000 0.229 0.370 3.265 0.256 0.017 10 028053 1851 1995 145 1.000 0.275 0.032 5.216 0.308 0.004 11 028055 1851 1995 145 1.000 0.246 0.407 3.928 0.277 0.002 12 028057 1851 1995 145 1.000 0.259 0.388 3.082 0.285 0.001 13 028071 1850 1995 146 1.000 0.195 0.023 3.551 0.208 0.016 14 028073 1852 1995 144 1.000 0.210 0.604 4.066 0.225 0.003 15 028075 1850 1995 146 1.000 0.218 0.327 3.218 0.247 0.017 16 028077 1850 1995 146 1.000 0.203 0.057 2.839 0.240 0.012 17 028091 1845 1995 151 1.000 0.212 0.792 5.255 0.229 0.000 18 028093 1845 1995 151 1.000 0.212 0.324 3.192 0.238 -0.006 19 028095 1845 1995 151 1.000 0.231 0.633 4.013 0.257 0.007 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 028097 1845 1995 151 1.000 0.216 0.313 3.910 0.241 0.008 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 147 1.000 0.234 0.328 3.666 0.260 0.002 STANDARD DEVIATION 4 0.000 0.022 0.212 0.630 0.025 0.011 MEDIAN (50TH QUANTILE) 146 1.000 0.235 0.343 3.467 0.258 0.003 INTERQUARTILE RANGE 6 0.000 0.038 0.312 0.659 0.040 0.009 MINIMUM VALUE 139 1.000 0.195 0.023 2.839 0.208 -0.026 LOWER HINGE (25TH QUANTILE) 144 1.000 0.214 0.120 3.260 0.241 0.000 UPPER HINGE (75TH QUANTILE) 151 1.000 0.253 0.433 3.919 0.281 0.009 MAXIMUM VALUE 152 1.000 0.275 0.792 5.255 0.308 0.017 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.517 0.109 0.008 0.662 3.484 0.255 0.826 MINIMUM CORRELATION: 0.255 SERIES 028021 AND 028037 141 YEARS MAXIMUM CORRELATION: 0.826 SERIES 028073 AND 028075 144 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 94.81 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1869. 1900. 1925. 1950. CORR 6. 190. 190. 190. RBAR 0.844 0.616 0.539 0.543 SDEV 0.043 0.127 0.134 0.122 SERR 0.018 0.009 0.010 0.009 EPS 0.990 0.970 0.959 0.960 NSS 17.9 20.0 20.0 20.0 |======================== 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 1844 1995 152 0.998 0.173 0.139 3.074 0.213 -0.145 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.247 0.085 0.074 43 109 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.17 0.39 1.04 1.12 1.51 2.70 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.05 0.68 0.88 0.93 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 -0.144 0.054 -0.021 0.006 0.074 0.011 -0.127 0.035 -0.161 0.060 PACF -0.144 0.034 -0.009 0.000 0.077 0.032 -0.132 0.000 -0.151 0.007 95% C.L. 0.162 0.166 0.166 0.166 0.166 0.167 0.167 0.170 0.170 0.174 |------------------ 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 0.023 -0.147 |---------- 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 0.003 -0.002 -0.011 0.011 0.084 0.003 -0.124 -0.005 -0.150 0.031 PACF 0.003 -0.002 -0.011 0.011 0.083 0.002 -0.124 -0.003 -0.154 0.023 95% C.L. 0.162 0.162 0.162 0.162 0.162 0.163 0.163 0.166 0.166 0.169 |----------------- 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 0.000 0.003 -0.002 |========================= 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 1844 1995 152 1.004 0.227 0.530 3.137 0.158 0.625 |------------ 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 0.621 0.525 0.375 0.285 0.212 0.102 -0.017 -0.036 -0.125 -0.083 PACF 0.621 0.227 -0.030 -0.009 0.002 -0.097 -0.140 0.036 -0.091 0.076 95% C.L. 0.162 0.216 0.247 0.262 0.270 0.274 0.275 0.275 0.275 0.277 |------------------- 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 0.434 0.480 0.240 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.20 MINUTES