RUN: 4DIG001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM047T.rwl.conv LOG FILE PROCESSED: GERM047T.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_LATE 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 7.608 0.774 -0.095 2.615 0.088 0.412 2 028023 1844 1995 152 7.725 0.747 -0.072 2.776 0.087 0.410 3 028025 1844 1995 152 7.619 0.797 -0.156 2.273 0.085 0.455 4 028027 1844 1995 152 7.633 0.811 -0.230 2.603 0.082 0.516 5 028031 1855 1995 141 6.614 0.743 -0.347 3.577 0.097 0.352 6 028033 1857 1995 139 6.521 0.717 0.055 2.520 0.113 0.198 7 028035 1857 1995 139 6.778 0.706 -0.194 2.827 0.110 0.168 8 028037 1855 1995 141 6.722 0.729 -0.356 4.108 0.105 0.245 9 028051 1851 1995 145 6.890 0.941 -0.157 2.309 0.090 0.639 10 028053 1851 1995 145 6.846 0.725 0.074 2.790 0.092 0.401 11 028055 1851 1995 145 6.969 0.631 -0.079 3.318 0.079 0.397 12 028057 1851 1995 145 7.271 0.733 -0.015 2.660 0.074 0.566 13 028071 1850 1995 146 6.946 0.682 0.184 2.472 0.086 0.404 14 028073 1852 1995 144 7.196 0.678 0.145 2.759 0.080 0.420 15 028075 1850 1995 146 7.105 0.757 0.058 2.582 0.096 0.378 16 028077 1850 1995 146 7.238 0.758 -0.162 2.801 0.082 0.494 17 028091 1845 1995 151 6.998 0.664 0.047 3.219 0.079 0.440 18 028093 1845 1995 151 7.092 0.662 0.103 3.516 0.080 0.419 19 028095 1845 1995 151 7.086 0.674 -0.041 2.977 0.075 0.483 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 028097 1845 1995 151 6.922 0.630 0.123 3.099 0.080 0.361 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 7.089 0.728 -0.056 2.890 0.088 0.408 STANDARD DEVIATION 4 0.345 0.071 0.157 0.463 0.011 0.113 MEDIAN (50TH QUANTILE) 146 7.042 0.727 -0.057 2.783 0.086 0.411 INTERQUARTILE RANGE 6 0.386 0.081 0.225 0.567 0.014 0.100 MINIMUM VALUE 136 6.521 0.630 -0.356 2.273 0.074 0.168 LOWER HINGE (25TH QUANTILE) 144 6.868 0.676 -0.159 2.592 0.080 0.369 UPPER HINGE (75TH QUANTILE) 151 7.254 0.757 0.066 3.159 0.094 0.469 MAXIMUM VALUE 152 7.725 0.941 0.184 4.108 0.113 0.639 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.610 0.145 0.011 -0.206 2.180 0.242 0.884 MINIMUM CORRELATION: 0.242 SERIES 028033 AND 028051 139 YEARS MAXIMUM CORRELATION: 0.884 SERIES 028021 AND 028025 152 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 0.909 0.553 0.621 0.630 SDEV 0.011 0.175 0.161 0.158 SERR 0.005 0.013 0.012 0.011 EPS 0.994 0.961 0.970 0.971 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 7.107 0.573 0.042 2.728 0.069 0.415 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.174 0.054 0.185 34 118 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.24 0.86 1.01 1.04 1.91 8.44 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.04 0.74 0.87 0.91 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 0.412 0.434 0.288 0.310 0.222 0.231 0.205 0.087 0.194 0.130 PACF 0.412 0.318 0.047 0.110 0.014 0.045 0.048 -0.122 0.126 0.024 95% C.L. 0.162 0.188 0.213 0.223 0.234 0.239 0.245 0.249 0.250 0.254 |------------------ 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 0.264 0.287 0.322 |================== 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 -0.00472377 7.96932888 2 028023 3 0.00000000 0.00000000 -0.00777961 8.32027149 3 028025 3 0.00000000 0.00000000 -0.00456108 7.96754122 4 028027 3 0.00000000 0.00000000 -0.00653767 8.13289452 5 028031 3 0.00000000 0.00000000 -0.00678496 7.09598780 6 028033 3 0.00000000 0.00000000 -0.00361943 6.78987026 7 028035 1 0.44925505 0.02441548 0.00000000 6.65124989 8 028037 3 0.00000000 0.00000000 -0.00601661 7.14909410 9 028051 1 3.76728725 0.00470704 0.00000000 4.16610575 10 028053 3 0.00000000 0.00000000 -0.00352063 7.10348845 11 028055 3 0.00000000 0.00000000 -0.00259676 7.15852880 12 028057 3 0.00000000 0.00000000 -0.00876823 7.91076994 13 028071 3 0.00000000 0.00000000 -0.00622078 7.40311766 14 028073 3 0.00000000 0.00000000 -0.00543905 7.59037304 15 028075 3 0.00000000 0.00000000 -0.00561567 7.51802540 16 028077 3 0.00000000 0.00000000 -0.00793616 7.82159567 17 028091 3 0.00000000 0.00000000 -0.00350300 7.26430750 18 028093 3 0.00000000 0.00000000 -0.00491321 7.46505976 19 028095 3 0.00000000 0.00000000 -0.00325490 7.33353090 SERIES IDENT OPTION A B C D 20 028097 3 0.00000000 0.00000000 -0.00250282 7.11240005 |-------------------- 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 0.097 -0.242 2.988 0.088 0.352 2 028023 1844 1995 152 1.000 0.086 -0.192 2.938 0.087 0.250 3 028025 1844 1995 152 1.000 0.101 -0.147 2.339 0.085 0.415 4 028027 1844 1995 152 1.000 0.099 -0.381 2.879 0.081 0.446 5 028031 1855 1995 141 1.000 0.105 -0.285 3.422 0.096 0.268 6 028033 1857 1995 139 1.000 0.108 0.047 2.703 0.111 0.177 7 028035 1857 1995 139 1.000 0.102 -0.329 2.955 0.109 0.144 8 028037 1855 1995 141 1.000 0.102 -0.381 3.816 0.104 0.165 9 028051 1851 1995 145 1.000 0.116 0.365 3.379 0.089 0.475 10 028053 1851 1995 145 1.000 0.104 0.092 2.718 0.092 0.369 11 028055 1851 1995 145 1.000 0.089 0.010 3.362 0.078 0.376 12 028057 1851 1995 145 1.000 0.087 0.092 2.484 0.074 0.397 13 028071 1850 1995 146 1.000 0.090 0.147 2.422 0.086 0.303 14 028073 1852 1995 144 1.000 0.088 -0.059 2.764 0.079 0.337 15 028075 1850 1995 146 1.000 0.101 0.057 2.442 0.095 0.303 16 028077 1850 1995 146 1.000 0.094 -0.127 2.948 0.082 0.373 17 028091 1845 1995 151 1.000 0.092 0.041 3.589 0.079 0.403 18 028093 1845 1995 151 1.000 0.087 -0.200 4.182 0.079 0.340 19 028095 1845 1995 151 1.000 0.093 -0.136 3.380 0.075 0.455 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 028097 1845 1995 151 1.000 0.089 -0.005 3.219 0.079 0.334 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 147 1.000 0.097 -0.082 3.046 0.087 0.334 STANDARD DEVIATION 4 0.000 0.008 0.195 0.493 0.011 0.095 MEDIAN (50TH QUANTILE) 146 1.000 0.096 -0.093 2.951 0.085 0.346 INTERQUARTILE RANGE 6 0.000 0.013 0.273 0.669 0.014 0.115 MINIMUM VALUE 139 1.000 0.086 -0.381 2.339 0.074 0.144 LOWER HINGE (25TH QUANTILE) 144 1.000 0.089 -0.221 2.710 0.079 0.286 UPPER HINGE (75TH QUANTILE) 151 1.000 0.102 0.052 3.379 0.093 0.400 MAXIMUM VALUE 152 1.000 0.116 0.365 4.182 0.111 0.475 |------------------------ 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 0.088 -0.045 2.910 0.088 0.209 2 028023 1844 1995 152 1.000 0.080 -0.203 3.070 0.087 0.145 3 028025 1844 1995 152 1.000 0.092 -0.083 2.330 0.085 0.291 4 028027 1844 1995 152 1.000 0.092 -0.388 2.950 0.081 0.362 5 028031 1855 1995 141 1.000 0.103 -0.249 3.362 0.096 0.240 6 028033 1857 1995 139 1.000 0.105 0.045 2.685 0.111 0.147 7 028035 1857 1995 139 1.000 0.101 -0.349 3.060 0.109 0.119 8 028037 1855 1995 141 1.000 0.101 -0.430 3.748 0.104 0.148 9 028051 1851 1995 145 0.999 0.096 0.177 2.811 0.089 0.209 10 028053 1851 1995 145 1.000 0.095 -0.035 2.801 0.092 0.245 11 028055 1851 1995 145 1.000 0.084 -0.066 3.216 0.078 0.289 12 028057 1851 1995 145 1.000 0.079 0.102 2.550 0.074 0.263 13 028071 1850 1995 146 1.000 0.086 0.144 2.503 0.086 0.230 14 028073 1852 1995 144 1.000 0.086 -0.006 2.733 0.079 0.307 15 028075 1850 1995 146 1.000 0.098 0.087 2.488 0.095 0.260 16 028077 1850 1995 146 1.000 0.086 -0.135 2.810 0.082 0.258 17 028091 1845 1995 151 1.000 0.082 0.325 3.438 0.079 0.258 18 028093 1845 1995 151 1.000 0.081 0.089 3.736 0.079 0.224 19 028095 1845 1995 151 1.000 0.085 0.161 2.977 0.075 0.344 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 028097 1845 1995 151 1.000 0.081 0.234 3.104 0.079 0.182 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 147 1.000 0.090 -0.031 2.964 0.087 0.237 STANDARD DEVIATION 4 0.000 0.008 0.210 0.392 0.011 0.066 MEDIAN (50TH QUANTILE) 146 1.000 0.087 -0.021 2.930 0.085 0.243 INTERQUARTILE RANGE 6 0.000 0.014 0.293 0.451 0.014 0.081 MINIMUM VALUE 139 0.999 0.079 -0.430 2.330 0.074 0.119 LOWER HINGE (25TH QUANTILE) 144 1.000 0.083 -0.169 2.709 0.079 0.195 UPPER HINGE (75TH QUANTILE) 151 1.000 0.097 0.123 3.160 0.093 0.276 MAXIMUM VALUE 152 1.000 0.105 0.325 3.748 0.111 0.362 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.575 0.145 0.010 -0.041 2.263 0.232 0.861 MINIMUM CORRELATION: 0.232 SERIES 028031 AND 028051 141 YEARS MAXIMUM CORRELATION: 0.861 SERIES 028021 AND 028023 152 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 0.552 0.633 0.641 SDEV 0.016 0.176 0.161 0.138 SERR 0.007 0.013 0.012 0.010 EPS 0.993 0.961 0.972 0.973 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 0.999 0.071 0.055 2.794 0.070 0.233 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.007 -0.002 0.058 45 107 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.28 0.68 1.00 1.07 1.76 14.53 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.71 0.86 0.93 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 0.232 0.270 0.084 0.098 -0.031 -0.021 -0.037 -0.205 -0.046 -0.120 PACF 0.232 0.229 -0.020 0.028 -0.075 -0.034 -0.003 -0.206 0.053 -0.031 95% C.L. 0.162 0.171 0.182 0.183 0.184 0.184 0.184 0.184 0.190 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 0.106 0.181 0.231 |======================= 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 0.154 0.226 0.038 0.029 -0.104 -0.038 -0.054 -0.225 -0.021 -0.097 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 0.154 2 0.122 0.207 3 0.126 0.210 -0.022 4 0.126 0.215 -0.020 -0.022 5 0.123 0.212 0.005 -0.007 -0.116 6 0.122 0.212 0.005 -0.004 -0.114 -0.014 7 0.122 0.212 0.005 -0.004 -0.114 -0.014 0.001 8 0.122 0.209 -0.020 -0.005 -0.113 0.033 0.028 -0.220 9 0.133 0.208 -0.022 0.001 -0.113 0.034 0.017 -0.226 0.053 10 0.135 0.203 -0.021 0.002 -0.115 0.034 0.016 -0.222 0.055 -0.022 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) 854.14 852.51 847.83 849.75 851.68 851.63 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 853.60 855.60 850.06 851.64 853.57 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 0.122 0.207 R-SQUARED DUE TO POOLED AUTOREGRESSION: 6.56 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 107.02 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.122 0.222 0.052 0.052 0.017 0.013 0.005 0.003 0.001 0.0009 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 028021 2 0.101 0.159 0.243 2 028023 2 0.105 0.104 0.292 3 028025 2 0.156 0.213 0.276 4 028027 2 0.178 0.285 0.223 5 028031 2 0.118 0.195 0.214 6 028033 2 0.039 0.130 0.123 7 028035 2 0.031 0.105 0.129 8 028037 2 0.029 0.150 0.033 9 028051 2 0.065 0.181 0.140 10 028053 2 0.076 0.216 0.122 11 028055 2 0.127 0.236 0.192 12 028057 2 0.074 0.254 0.047 13 028071 2 0.091 0.187 0.196 14 028073 2 0.136 0.255 0.192 15 028075 2 0.108 0.213 0.195 16 028077 2 0.088 0.230 0.135 17 028091 2 0.166 0.180 0.309 18 028093 2 0.081 0.189 0.173 19 028095 2 0.192 0.251 0.277 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 028097 2 0.121 0.128 0.300 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.104 0.193 0.191 STANDARD DEVIATION 0 0.047 0.052 0.079 MEDIAN 2 0.103 0.192 0.194 INTERQUARTILE RANGE 0 0.057 0.078 0.127 MINIMUM VALUE 2 0.029 0.104 0.033 LOWER HINGE 2 0.075 0.155 0.132 UPPER HINGE 2 0.132 0.233 0.259 MAXIMUM VALUE 2 0.192 0.285 0.309 |------------------- 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 0.084 -0.261 3.581 0.092 -0.010 2 028023 1844 1995 152 1.000 0.076 -0.205 3.056 0.087 -0.006 3 028025 1844 1995 152 1.000 0.085 -0.360 2.792 0.093 -0.003 4 028027 1844 1995 152 1.000 0.083 -0.359 2.942 0.094 0.001 5 028031 1855 1995 141 1.000 0.097 -0.300 3.470 0.103 0.033 6 028033 1857 1995 139 1.000 0.103 0.039 2.818 0.118 0.007 7 028035 1857 1995 139 1.000 0.099 -0.282 2.875 0.113 0.002 8 028037 1855 1995 141 1.000 0.100 -0.503 3.888 0.112 0.010 9 028051 1851 1995 145 1.000 0.093 0.081 3.580 0.097 -0.007 10 028053 1851 1995 145 1.000 0.091 -0.160 2.732 0.102 0.004 11 028055 1851 1995 145 1.000 0.079 -0.340 3.444 0.086 0.018 12 028057 1851 1995 145 1.000 0.076 -0.137 2.685 0.084 0.001 13 028071 1850 1995 146 1.000 0.082 0.086 2.566 0.093 -0.004 14 028073 1852 1995 144 1.000 0.080 -0.067 2.701 0.090 -0.013 15 028075 1850 1995 146 1.000 0.093 -0.035 2.532 0.105 0.012 16 028077 1850 1995 146 1.000 0.082 -0.241 2.816 0.092 0.007 17 028091 1845 1995 151 1.000 0.076 0.211 3.239 0.084 -0.034 18 028093 1845 1995 151 1.000 0.077 0.195 3.640 0.086 -0.005 19 028095 1845 1995 151 1.000 0.076 0.434 3.655 0.083 -0.021 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 028097 1845 1995 151 1.000 0.076 0.328 3.413 0.083 -0.013 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 147 1.000 0.085 -0.094 3.121 0.095 -0.001 STANDARD DEVIATION 4 0.000 0.009 0.255 0.426 0.011 0.014 MEDIAN (50TH QUANTILE) 146 1.000 0.082 -0.148 2.999 0.093 -0.001 INTERQUARTILE RANGE 6 0.000 0.016 0.375 0.763 0.016 0.016 MINIMUM VALUE 139 1.000 0.076 -0.503 2.532 0.083 -0.034 LOWER HINGE (25TH QUANTILE) 144 1.000 0.077 -0.291 2.762 0.086 -0.009 UPPER HINGE (75TH QUANTILE) 151 1.000 0.093 0.084 3.525 0.102 0.007 MAXIMUM VALUE 152 1.000 0.103 0.434 3.888 0.118 0.033 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.593 0.125 0.009 0.174 2.325 0.355 0.868 MINIMUM CORRELATION: 0.355 SERIES 028031 AND 028051 141 YEARS MAXIMUM CORRELATION: 0.868 SERIES 028075 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 0.843 0.537 0.624 0.677 SDEV 0.028 0.183 0.156 0.103 SERR 0.011 0.013 0.011 0.008 EPS 0.990 0.959 0.971 0.977 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 0.999 0.067 -0.093 3.020 0.075 -0.006 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.039 0.010 0.042 53 99 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.24 0.77 1.00 1.13 1.90 10.21 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.75 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 -0.006 0.047 0.003 0.044 -0.078 0.019 0.010 -0.202 0.022 -0.068 PACF -0.006 0.047 0.003 0.042 -0.078 0.014 0.017 -0.207 0.028 -0.059 95% C.L. 0.162 0.162 0.163 0.163 0.163 0.164 0.164 0.164 0.170 0.170 |------------------ 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 0.008 0.041 -0.080 0.025 0.010 -0.201 0.021 -0.058 PACF 0.000 -0.001 0.008 0.041 -0.080 0.026 0.010 -0.203 0.031 -0.070 95% C.L. 0.162 0.162 0.162 0.162 0.163 0.164 0.164 0.164 0.170 0.170 |----------------- 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 0.000 -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 1.000 0.069 0.021 2.814 0.071 0.149 |------------ 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 0.148 0.222 0.052 0.081 -0.052 -0.004 -0.022 -0.203 -0.023 -0.106 PACF 0.148 0.205 -0.004 0.031 -0.080 -0.012 0.006 -0.212 0.043 -0.033 95% C.L. 0.162 0.166 0.173 0.174 0.175 0.175 0.175 0.175 0.181 0.181 |------------------- 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 0.065 0.119 0.207 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.32 MINUTES