RUN: 4DIG001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM047N.rwl.conv LOG FILE PROCESSED: GERM047N.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. DENSITY_MINIMUM 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 0.278 0.036 1.029 4.415 0.096 0.501 2 028023 1844 1995 152 0.297 0.046 1.075 4.332 0.087 0.666 3 028025 1844 1995 152 0.276 0.048 1.550 7.097 0.102 0.559 4 028027 1844 1995 152 0.288 0.047 0.958 4.930 0.098 0.654 5 028031 1855 1995 141 0.204 0.039 0.981 4.877 0.115 0.651 6 028033 1857 1995 139 0.223 0.031 0.748 3.925 0.091 0.627 7 028035 1857 1995 139 0.186 0.029 0.323 2.752 0.114 0.574 8 028037 1855 1995 141 0.215 0.038 2.484 13.601 0.103 0.545 9 028051 1851 1995 145 0.234 0.046 0.709 4.062 0.099 0.743 10 028053 1851 1995 145 0.242 0.036 0.455 4.038 0.102 0.578 11 028055 1851 1995 145 0.226 0.042 0.597 3.986 0.113 0.625 12 028057 1851 1995 145 0.248 0.049 0.560 2.443 0.096 0.787 13 028071 1850 1995 146 0.236 0.032 1.813 8.099 0.092 0.562 14 028073 1852 1995 144 0.245 0.032 0.149 3.419 0.073 0.712 15 028075 1850 1995 146 0.227 0.030 0.524 3.674 0.084 0.582 16 028077 1850 1995 146 0.262 0.037 0.072 2.947 0.066 0.778 17 028091 1845 1995 151 0.258 0.031 1.337 6.590 0.081 0.507 18 028093 1845 1995 151 0.271 0.038 3.054 19.826 0.084 0.357 19 028095 1845 1995 151 0.267 0.037 2.743 18.344 0.078 0.413 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 028097 1845 1995 151 0.252 0.031 1.429 6.069 0.080 0.602 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 0.247 0.038 1.130 6.471 0.093 0.601 STANDARD DEVIATION 4 0.029 0.006 0.842 4.979 0.014 0.110 MEDIAN (50TH QUANTILE) 146 0.246 0.037 0.970 4.373 0.094 0.592 INTERQUARTILE RANGE 6 0.043 0.012 0.947 3.044 0.020 0.107 MINIMUM VALUE 136 0.186 0.029 0.072 2.443 0.066 0.357 LOWER HINGE (25TH QUANTILE) 144 0.226 0.032 0.542 3.800 0.083 0.552 UPPER HINGE (75TH QUANTILE) 151 0.269 0.044 1.489 6.844 0.102 0.660 MAXIMUM VALUE 152 0.297 0.049 3.054 19.826 0.115 0.787 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.409 0.245 0.018 -0.760 3.524 -0.348 0.856 MINIMUM CORRELATION: -0.348 SERIES 028033 AND 028095 139 YEARS MAXIMUM CORRELATION: 0.856 SERIES 028093 AND 028095 151 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 0.825 0.514 0.425 0.259 SDEV 0.049 0.274 0.239 0.229 SERR 0.020 0.020 0.017 0.017 EPS 0.988 0.955 0.937 0.875 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 0.251 0.032 1.804 8.474 0.061 0.711 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.407 0.133 0.005 35 117 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.18 0.27 1.01 1.06 1.33 31.48 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.05 0.62 0.87 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 0.706 0.633 0.553 0.498 0.430 0.440 0.397 0.382 0.345 0.359 PACF 0.706 0.268 0.080 0.052 -0.011 0.132 0.011 0.034 -0.010 0.084 95% C.L. 0.162 0.229 0.271 0.300 0.321 0.335 0.350 0.362 0.372 0.381 |------------------ 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 0.659 0.503 0.355 |================== 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 1 0.06644541 0.01723865 0.00000000 0.25425744 2 028023 1 0.10841682 0.02084190 0.00000000 0.26479486 3 028025 1 0.10421498 0.01741731 0.00000000 0.23999299 4 028027 1 0.12739058 0.00946991 0.00000000 0.22043407 5 028031 1 0.16386253 0.18104449 0.00000000 0.19832887 6 028033 3 0.00000000 0.00000000 0.00026411 0.20610122 7 028035 3 0.00000000 0.00000000 0.00001778 0.18472631 8 028037 1 0.17913646 0.18149364 0.00000000 0.20907697 9 028051 1 0.10451000 0.01410226 0.00000000 0.18940777 10 028053 1 0.00817011 0.02057227 0.00000000 0.23894379 11 028055 1 0.06352796 0.02401564 0.00000000 0.20880546 12 028057 3 0.00000000 0.00000000 -0.00071260 0.29995114 13 028071 3 0.00000000 0.00000000 0.00010163 0.22862636 14 028073 1 0.06685746 0.02113134 0.00000000 0.22401893 15 028075 1 0.09415616 0.00737753 0.00000000 0.16907912 16 028077 1 0.08167925 0.01799419 0.00000000 0.23326495 17 028091 1 0.06778646 0.02641996 0.00000000 0.24168853 18 028093 1 0.09571679 0.03847513 0.00000000 0.25501439 19 028095 1 0.07792940 0.02182544 0.00000000 0.24489544 SERIES IDENT OPTION A B C D 20 028097 1 0.07024288 0.03507613 0.00000000 0.23948506 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 028021 1844 1995 152 1.000 0.116 1.051 4.425 0.095 0.402 2 028023 1844 1995 152 1.000 0.121 0.801 3.674 0.087 0.521 3 028025 1844 1995 152 1.000 0.141 1.498 7.049 0.101 0.441 4 028027 1844 1995 152 1.000 0.130 1.024 5.952 0.097 0.496 5 028031 1855 1995 141 1.000 0.167 0.495 3.367 0.113 0.620 6 028033 1857 1995 139 1.000 0.136 0.891 4.065 0.090 0.598 7 028035 1857 1995 139 1.000 0.155 0.323 2.764 0.113 0.569 8 028037 1855 1995 141 1.000 0.139 1.309 5.583 0.102 0.458 9 028051 1851 1995 145 1.000 0.161 0.392 3.081 0.099 0.674 10 028053 1851 1995 145 1.000 0.148 0.458 4.041 0.102 0.576 11 028055 1851 1995 145 1.000 0.173 0.717 4.051 0.112 0.597 12 028057 1851 1995 145 1.000 0.152 0.438 2.667 0.096 0.678 13 028071 1850 1995 146 1.000 0.134 1.560 7.012 0.091 0.536 14 028073 1852 1995 144 1.000 0.109 -0.154 4.337 0.073 0.603 15 028075 1850 1995 146 1.000 0.105 0.304 3.380 0.084 0.430 16 028077 1850 1995 146 1.000 0.119 0.162 3.248 0.066 0.728 17 028091 1845 1995 151 1.000 0.098 1.000 4.855 0.081 0.383 18 028093 1845 1995 151 1.000 0.106 1.429 10.243 0.084 0.162 19 028095 1845 1995 151 1.000 0.111 1.653 10.626 0.077 0.283 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 028097 1845 1995 151 1.000 0.103 1.431 6.013 0.079 0.482 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 147 1.000 0.131 0.839 5.022 0.092 0.512 STANDARD DEVIATION 4 0.000 0.023 0.527 2.264 0.013 0.138 MEDIAN (50TH QUANTILE) 146 1.000 0.132 0.846 4.201 0.093 0.529 INTERQUARTILE RANGE 6 0.000 0.040 0.954 2.609 0.019 0.164 MINIMUM VALUE 139 1.000 0.098 -0.154 2.667 0.066 0.162 LOWER HINGE (25TH QUANTILE) 144 1.000 0.110 0.415 3.374 0.082 0.436 UPPER HINGE (75TH QUANTILE) 151 1.000 0.150 1.369 5.983 0.101 0.600 MAXIMUM VALUE 152 1.000 0.173 1.653 10.626 0.113 0.728 |------------------------ 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 1.000 0.109 0.985 4.198 0.095 0.328 2 028023 1844 1995 152 0.999 0.107 0.761 3.890 0.087 0.385 3 028025 1844 1995 152 0.999 0.127 1.559 7.776 0.101 0.322 4 028027 1844 1995 152 0.999 0.119 0.955 5.829 0.097 0.407 5 028031 1855 1995 141 0.999 0.156 0.427 3.193 0.114 0.555 6 028033 1857 1995 139 0.999 0.118 0.769 3.663 0.090 0.474 7 028035 1857 1995 139 0.999 0.139 0.259 2.960 0.113 0.472 8 028037 1855 1995 141 0.999 0.132 1.373 6.534 0.102 0.388 9 028051 1851 1995 145 0.998 0.128 0.580 4.370 0.099 0.471 10 028053 1851 1995 145 0.999 0.135 0.788 4.905 0.102 0.475 11 028055 1851 1995 145 0.998 0.146 0.717 3.932 0.112 0.443 12 028057 1851 1995 145 0.997 0.114 0.481 3.165 0.096 0.400 13 028071 1850 1995 146 0.999 0.104 0.889 5.400 0.091 0.300 14 028073 1852 1995 144 0.999 0.103 0.286 5.184 0.073 0.543 15 028075 1850 1995 146 1.000 0.100 0.371 3.511 0.084 0.352 16 028077 1850 1995 146 0.999 0.096 -0.141 2.821 0.066 0.587 17 028091 1845 1995 151 1.000 0.096 0.935 4.786 0.081 0.369 18 028093 1845 1995 151 1.000 0.103 1.601 11.442 0.084 0.119 19 028095 1845 1995 151 1.000 0.109 1.802 11.659 0.078 0.251 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 028097 1845 1995 151 1.000 0.094 1.107 5.344 0.079 0.385 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 147 0.999 0.117 0.825 5.228 0.092 0.401 STANDARD DEVIATION 4 0.001 0.018 0.494 2.501 0.013 0.110 MEDIAN (50TH QUANTILE) 146 0.999 0.111 0.779 4.578 0.093 0.394 INTERQUARTILE RANGE 6 0.001 0.027 0.592 2.027 0.019 0.133 MINIMUM VALUE 139 0.997 0.094 -0.141 2.821 0.066 0.119 LOWER HINGE (25TH QUANTILE) 144 0.999 0.103 0.454 3.587 0.082 0.340 UPPER HINGE (75TH QUANTILE) 151 1.000 0.130 1.046 5.614 0.102 0.473 MAXIMUM VALUE 152 1.000 0.156 1.802 11.659 0.114 0.587 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.337 0.165 0.012 0.222 2.982 -0.098 0.779 MINIMUM CORRELATION: -0.098 SERIES 028033 AND 028095 139 YEARS MAXIMUM CORRELATION: 0.779 SERIES 028093 AND 028095 151 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 0.840 0.525 0.330 0.272 SDEV 0.039 0.188 0.219 0.212 SERR 0.016 0.014 0.016 0.015 EPS 0.989 0.957 0.908 0.882 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 0.997 0.072 1.019 5.101 0.062 0.330 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.226 0.096 -0.008 58 94 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.19 0.68 1.01 1.06 1.74 102.27 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.06 0.82 0.88 0.95 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 0.328 0.238 0.134 0.038 -0.056 0.056 0.015 -0.004 -0.069 -0.043 PACF 0.328 0.146 0.023 -0.046 -0.091 0.109 0.005 -0.028 -0.093 -0.006 95% C.L. 0.162 0.179 0.187 0.189 0.190 0.190 0.191 0.191 0.191 0.191 |------------------ 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 0.137 0.285 0.157 |======================= 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 0.329 0.236 0.132 -0.014 -0.035 0.052 0.006 0.012 -0.022 -0.037 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 0.329 2 0.282 0.143 3 0.279 0.137 0.021 4 0.281 0.152 0.050 -0.103 5 0.277 0.153 0.055 -0.094 -0.033 6 0.281 0.163 0.049 -0.110 -0.062 0.104 7 0.282 0.162 0.048 -0.109 -0.061 0.106 -0.008 8 0.282 0.164 0.047 -0.111 -0.060 0.109 -0.004 -0.014 9 0.281 0.164 0.053 -0.114 -0.066 0.111 0.004 0.000 -0.050 10 0.280 0.164 0.053 -0.112 -0.066 0.109 0.005 0.002 -0.046 -0.014 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) 858.88 843.50 842.35 844.28 844.66 846.49 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 846.84 848.83 850.80 852.42 854.39 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 0.282 0.143 R-SQUARED DUE TO POOLED AUTOREGRESSION: 12.63 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 114.46 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.282 0.223 0.103 0.061 0.032 0.018 0.010 0.005 0.003 0.0015 0.001 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 028021 2 0.161 0.254 0.237 2 028023 2 0.191 0.316 0.195 3 028025 2 0.138 0.298 0.108 4 028027 2 0.184 0.368 0.105 5 028031 2 0.343 0.450 0.196 6 028033 2 0.304 0.337 0.291 7 028035 2 0.257 0.393 0.178 8 028037 2 0.159 0.361 0.079 9 028051 2 0.277 0.417 0.166 10 028053 2 0.242 0.453 0.070 11 028055 2 0.279 0.342 0.249 12 028057 2 0.224 0.338 0.187 13 028071 2 0.174 0.229 0.280 14 028073 2 0.324 0.450 0.180 15 028075 2 0.178 0.296 0.198 16 028077 2 0.374 0.503 0.159 17 028091 2 0.193 0.301 0.218 18 028093 2 0.082 0.091 0.257 19 028095 2 0.092 0.233 0.105 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 028097 2 0.157 0.355 0.086 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.217 0.339 0.177 STANDARD DEVIATION 0 0.081 0.095 0.067 MEDIAN 2 0.192 0.340 0.183 INTERQUARTILE RANGE 0 0.118 0.108 0.121 MINIMUM VALUE 2 0.082 0.091 0.070 LOWER HINGE 2 0.160 0.297 0.107 UPPER HINGE 2 0.278 0.405 0.227 MAXIMUM VALUE 2 0.374 0.503 0.291 |------------------- 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 0.100 1.030 4.511 0.107 -0.001 2 028023 1844 1995 152 1.000 0.096 1.037 4.978 0.101 0.013 3 028025 1844 1995 152 1.000 0.119 1.608 8.480 0.116 0.001 4 028027 1844 1995 152 1.000 0.108 1.093 6.420 0.115 0.003 5 028031 1855 1995 141 1.000 0.127 0.425 3.467 0.136 -0.010 6 028033 1857 1995 139 1.000 0.099 0.685 3.505 0.108 -0.039 7 028035 1857 1995 139 1.000 0.120 0.283 2.913 0.135 -0.017 8 028037 1855 1995 141 1.000 0.121 1.543 8.879 0.121 0.001 9 028051 1851 1995 145 1.000 0.108 0.428 3.783 0.123 -0.044 10 028053 1851 1995 145 1.000 0.117 0.980 4.679 0.127 -0.008 11 028055 1851 1995 145 1.000 0.125 0.913 4.172 0.132 -0.053 12 028057 1851 1995 145 1.000 0.101 0.491 3.244 0.114 -0.044 13 028071 1850 1995 146 1.000 0.094 0.706 4.625 0.099 0.013 14 028073 1852 1995 144 1.000 0.085 0.147 5.046 0.090 0.006 15 028075 1850 1995 146 1.000 0.090 0.360 3.796 0.095 0.010 16 028077 1850 1995 146 1.000 0.076 0.363 3.262 0.083 -0.005 17 028091 1845 1995 151 1.000 0.086 0.740 4.106 0.095 -0.031 18 028093 1845 1995 151 1.000 0.099 1.662 13.474 0.090 -0.013 19 028095 1845 1995 151 1.000 0.104 2.194 16.255 0.088 -0.021 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 028097 1845 1995 151 1.000 0.086 1.164 5.911 0.095 -0.001 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 147 1.000 0.103 0.893 5.775 0.109 -0.012 STANDARD DEVIATION 4 0.000 0.015 0.541 3.527 0.017 0.020 MEDIAN (50TH QUANTILE) 146 1.000 0.100 0.826 4.568 0.107 -0.006 INTERQUARTILE RANGE 6 0.000 0.025 0.702 2.522 0.027 0.028 MINIMUM VALUE 139 1.000 0.076 0.147 2.913 0.083 -0.053 LOWER HINGE (25TH QUANTILE) 144 1.000 0.092 0.427 3.644 0.095 -0.026 UPPER HINGE (75TH QUANTILE) 151 1.000 0.118 1.129 6.166 0.122 0.002 MAXIMUM VALUE 152 1.000 0.127 2.194 16.255 0.136 0.013 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.387 0.125 0.009 0.388 3.212 0.130 0.783 MINIMUM CORRELATION: 0.130 SERIES 028031 AND 028073 141 YEARS MAXIMUM CORRELATION: 0.783 SERIES 028093 AND 028095 151 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 0.828 0.538 0.355 0.356 SDEV 0.037 0.137 0.175 0.171 SERR 0.015 0.010 0.013 0.012 EPS 0.988 0.959 0.917 0.917 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 0.996 0.067 0.914 4.829 0.073 -0.020 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.242 0.095 -0.021 69 83 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.13 0.58 1.00 1.07 1.65 129.61 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 0.57 0.87 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 -0.019 -0.003 0.027 -0.050 -0.080 0.084 -0.010 -0.015 -0.094 -0.041 PACF -0.019 -0.003 0.026 -0.049 -0.082 0.081 -0.005 -0.014 -0.108 -0.043 95% C.L. 0.162 0.162 0.162 0.162 0.163 0.164 0.165 0.165 0.165 0.166 |------------------ RESIDUAL CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 0 0.000 |---------- REWHITENED CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS -----------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.000 0.001 0.025 -0.051 -0.079 0.083 -0.009 -0.017 -0.095 -0.042 PACF 0.000 0.001 0.025 -0.051 -0.079 0.083 -0.007 -0.017 -0.108 -0.039 95% C.L. 0.162 0.162 0.162 0.162 0.163 0.164 0.165 0.165 0.165 0.166 |----------------- 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 0.001 |========================= 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 0.997 0.072 0.862 4.891 0.063 0.328 |------------ 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 0.325 0.223 0.109 0.012 -0.040 0.048 -0.025 -0.044 -0.102 -0.063 PACF 0.325 0.131 0.004 -0.056 -0.051 0.092 -0.046 -0.050 -0.090 0.009 95% C.L. 0.162 0.179 0.186 0.187 0.187 0.188 0.188 0.188 0.188 0.190 |------------------- 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 0.131 0.288 0.142 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.24 MINUTES