RUN: 4DIG001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM052N.rwl.conv LOG FILE PROCESSED: GERM052N.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: 049 1 Seehalde (D), EU-Pr. DENSITY_MINIMUM PCAB - 049 2 Germany Norway spruce 1250 4751-802 1756 1995 - 049 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 9 049031 MISSING VALUES FOUND: 5 IN 1 GAPS / 1985 1989 / -------------------------------------------------------------------- 10 049033 MISSING VALUES FOUND: 5 IN 1 GAPS / 1917 1921 / -------------------------------------------------------------------- 11 049035 MISSING VALUES FOUND: 7 IN 1 GAPS / 1798 1804 / -------------------------------------------------------------------- 12 049037 MISSING VALUES FOUND: 5 IN 1 GAPS / 1928 1932 / -------------------------------------------------------------------- 14 049043 MISSING VALUES FOUND: 8 IN 1 GAPS / 1798 1805 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 049011 1791 1995 205 0.259 0.047 3.159 16.266 0.085 0.606 2 049013 1791 1995 205 0.255 0.033 3.450 25.554 0.075 0.517 3 049015 1791 1995 205 0.239 0.030 2.134 10.499 0.068 0.622 4 049017 1790 1995 206 0.261 0.042 3.882 26.153 0.068 0.679 5 049021 1782 1995 214 0.237 0.028 2.110 14.399 0.082 0.488 6 049023 1782 1995 214 0.241 0.031 1.111 5.244 0.083 0.609 7 049025 1782 1995 214 0.248 0.030 1.088 6.295 0.071 0.690 8 049027 1807 1995 189 0.252 0.023 0.072 3.105 0.073 0.423 9 049031 1777 1995 219 0.241 0.042 3.495 20.020 0.074 0.763 10 049033 1777 1995 219 0.228 0.037 3.045 15.203 0.078 0.760 11 049035 1777 1995 219 0.230 0.043 3.083 16.537 0.080 0.744 12 049037 1780 1995 216 0.236 0.038 2.172 10.296 0.093 0.571 13 049041 1756 1995 240 0.269 0.034 3.810 28.012 0.061 0.517 14 049043 1758 1995 238 0.260 0.028 3.626 31.533 0.067 0.502 15 049045 1756 1995 240 0.249 0.037 4.544 36.664 0.077 0.612 16 049047 1757 1995 239 0.265 0.031 2.832 23.006 0.071 0.521 17 049051 1756 1995 240 0.243 0.040 4.059 28.739 0.076 0.545 18 049053 1756 1995 240 0.221 0.033 1.975 13.152 0.083 0.642 19 049055 1763 1995 233 0.222 0.025 1.383 7.224 0.075 0.621 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 049057 1756 1995 240 0.210 0.033 2.928 15.752 0.082 0.601 NUMBER OF SERIES READ IN: 20 FROM 1756 TO 1995 240 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 220 0.243 0.034 2.698 17.682 0.076 0.602 STANDARD DEVIATION 15 0.016 0.006 1.163 9.474 0.008 0.094 MEDIAN (50TH QUANTILE) 214 0.242 0.033 2.986 16.009 0.075 0.608 INTERQUARTILE RANGE 31 0.024 0.009 1.518 15.456 0.011 0.141 MINIMUM VALUE 189 0.210 0.023 0.072 3.105 0.061 0.423 LOWER HINGE (25TH QUANTILE) 208 0.233 0.030 2.043 10.397 0.071 0.519 UPPER HINGE (75TH QUANTILE) 239 0.257 0.039 3.561 25.853 0.082 0.661 MAXIMUM VALUE 240 0.269 0.047 4.544 36.664 0.093 0.763 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.387 0.201 0.015 -0.086 2.218 -0.045 0.819 MINIMUM CORRELATION: -0.045 SERIES 049035 AND 049053 219 YEARS MAXIMUM CORRELATION: 0.819 SERIES 049031 AND 049035 219 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 88.65 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1781. 1810. 1835. 1860. 1885. 1910. 1935. 1960. CORR 10. 105. 190. 190. 190. 190. 190. 190. RBAR 0.746 0.314 0.349 0.375 0.184 0.332 0.454 0.409 SDEV 0.093 0.241 0.233 0.174 0.183 0.190 0.157 0.162 SERR 0.029 0.024 0.017 0.013 0.013 0.014 0.011 0.012 EPS 0.974 0.897 0.915 0.923 0.818 0.909 0.943 0.933 NSS 12.7 19.1 20.0 20.0 20.0 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 1756 1995 240 0.246 0.029 3.911 27.962 0.053 0.649 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.534 0.240 -0.031 51 189 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.24 1.17 1.00 1.06 2.23 25.44 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.07 0.60 0.86 0.92 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 219. 30. 189. 210. 240. 240. |----------- 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 0.646 0.556 0.464 0.445 0.394 0.355 0.293 0.246 0.219 0.198 PACF 0.646 0.238 0.066 0.122 0.034 0.019 -0.030 -0.028 0.010 0.009 95% C.L. 0.129 0.175 0.202 0.219 0.234 0.245 0.253 0.259 0.263 0.266 |------------------ 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 0.630 0.503 0.340 |================== 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 049011 1 0.11895734 0.02104946 0.00000000 0.23211183 2 049013 1 0.32349771 0.31833610 0.00000000 0.25057060 3 049015 1 0.15964039 0.12946764 0.00000000 0.23378076 4 049017 1 0.39459652 0.26920086 0.00000000 0.25457600 5 049021 1 0.06297440 0.00812442 0.00000000 0.20746507 6 049023 1 0.06203711 0.02071687 0.00000000 0.22753136 7 049025 1 0.09349396 0.01380924 0.00000000 0.21830247 8 049027 3 0.00000000 0.00000000 -0.00021838 0.27238658 9 049031 1 0.33806103 0.17875044 0.00000000 0.23218875 10 049033 1 0.25747776 0.12660281 0.00000000 0.21909815 11 049035 1 0.28311300 0.12344848 0.00000000 0.22113343 12 049037 1 0.16099654 0.07046217 0.00000000 0.22478324 13 049041 1 0.20480986 0.17688416 0.00000000 0.26471466 14 049043 3 0.00000000 0.00000000 -0.00004751 0.26514563 15 049045 3 0.00000000 0.00000000 -0.00026545 0.28127858 16 049047 1 0.07542235 0.01855728 0.00000000 0.24808043 17 049051 1 0.28444681 0.16897920 0.00000000 0.23697877 18 049053 1 0.21659130 0.16489114 0.00000000 0.21554911 19 049055 3 0.00000000 0.00000000 -0.00015435 0.23986162 SERIES IDENT OPTION A B C D 20 049057 1 0.14744277 0.08260456 0.00000000 0.20269918 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 049011 1791 1995 205 1.000 0.123 2.353 14.373 0.085 0.380 2 049013 1791 1995 205 1.000 0.088 0.141 3.458 0.074 0.415 3 049015 1791 1995 205 1.000 0.094 0.839 3.908 0.068 0.510 4 049017 1790 1995 206 1.000 0.101 1.231 5.427 0.066 0.652 5 049021 1782 1995 214 1.000 0.099 1.527 10.341 0.082 0.298 6 049023 1782 1995 214 1.000 0.108 0.293 3.533 0.083 0.467 7 049025 1782 1995 214 1.000 0.074 0.651 4.638 0.071 0.185 8 049027 1807 1995 189 1.000 0.079 0.211 3.699 0.073 0.209 9 049031 1777 1995 219 1.000 0.102 0.688 3.246 0.072 0.548 10 049033 1777 1995 219 1.000 0.084 -0.047 3.004 0.078 0.301 11 049035 1777 1995 219 1.000 0.105 0.662 3.653 0.078 0.498 12 049037 1780 1995 216 1.000 0.116 0.578 3.458 0.092 0.360 13 049041 1756 1995 240 1.000 0.099 3.622 35.376 0.060 0.418 14 049043 1758 1995 238 1.000 0.105 3.315 29.241 0.065 0.498 15 049045 1756 1995 240 1.000 0.119 4.209 34.528 0.077 0.505 16 049047 1757 1995 239 1.000 0.087 1.675 12.791 0.071 0.316 17 049051 1756 1995 240 1.000 0.107 1.197 7.407 0.075 0.441 18 049053 1756 1995 240 1.000 0.110 -0.178 3.741 0.083 0.548 19 049055 1763 1995 233 1.000 0.100 1.089 5.503 0.075 0.543 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 049057 1756 1995 240 1.000 0.113 1.462 9.807 0.082 0.423 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 222 1.000 0.101 1.276 10.057 0.075 0.426 STANDARD DEVIATION 15 0.000 0.013 1.230 10.507 0.008 0.121 MEDIAN (50TH QUANTILE) 219 1.000 0.102 0.964 5.033 0.075 0.432 INTERQUARTILE RANGE 29 0.000 0.018 1.165 7.973 0.011 0.170 MINIMUM VALUE 189 1.000 0.074 -0.178 3.004 0.060 0.185 LOWER HINGE (25TH QUANTILE) 210 1.000 0.091 0.435 3.593 0.071 0.338 UPPER HINGE (75TH QUANTILE) 239 1.000 0.109 1.601 11.566 0.082 0.508 MAXIMUM VALUE 240 1.000 0.123 4.209 35.376 0.092 0.652 |------------------------ 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 049011 -67 137 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 049013 -67 137 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 049015 -67 137 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 049017 -67 138 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 049021 -67 143 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 049023 -67 143 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 049025 -67 143 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 049027 -67 126 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 049031 -67 146 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 049033 -67 146 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 049035 -67 146 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 049037 -67 144 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 049041 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 049043 -67 159 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 049045 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 049047 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 049051 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 049053 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 049055 -67 156 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 049057 -67 160 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 049011 1791 1995 205 1.000 0.121 2.552 15.336 0.085 0.359 2 049013 1791 1995 205 1.000 0.082 0.129 3.833 0.074 0.313 3 049015 1791 1995 205 1.000 0.081 0.708 4.135 0.068 0.340 4 049017 1790 1995 206 1.000 0.084 0.699 4.778 0.066 0.489 5 049021 1782 1995 214 1.000 0.096 1.826 12.417 0.082 0.252 6 049023 1782 1995 214 1.000 0.107 0.310 3.641 0.083 0.456 7 049025 1782 1995 214 1.000 0.073 0.735 4.930 0.071 0.153 8 049027 1807 1995 189 1.000 0.076 0.206 3.592 0.073 0.153 9 049031 1777 1995 219 0.999 0.090 0.584 3.513 0.073 0.420 10 049033 1777 1995 219 1.000 0.081 0.002 3.038 0.078 0.258 11 049035 1777 1995 219 1.000 0.096 0.962 4.954 0.078 0.392 12 049037 1780 1995 216 1.000 0.105 0.884 4.317 0.092 0.210 13 049041 1756 1995 240 1.000 0.089 4.916 51.348 0.060 0.287 14 049043 1758 1995 238 1.000 0.097 2.525 21.456 0.065 0.474 15 049045 1756 1995 240 1.000 0.108 3.189 24.989 0.077 0.467 16 049047 1757 1995 239 1.000 0.085 1.776 14.121 0.071 0.290 17 049051 1756 1995 240 0.999 0.100 1.534 9.755 0.075 0.360 18 049053 1756 1995 240 1.000 0.097 -0.201 3.310 0.083 0.422 19 049055 1763 1995 233 1.000 0.094 0.664 4.359 0.075 0.492 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 049057 1756 1995 240 1.000 0.105 1.598 11.541 0.082 0.342 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 222 1.000 0.093 1.280 10.468 0.075 0.347 STANDARD DEVIATION 15 0.000 0.012 1.258 11.577 0.008 0.107 MEDIAN (50TH QUANTILE) 219 1.000 0.095 0.810 4.854 0.075 0.350 INTERQUARTILE RANGE 29 0.000 0.019 1.354 9.532 0.011 0.166 MINIMUM VALUE 189 0.999 0.073 -0.201 3.038 0.060 0.153 LOWER HINGE (25TH QUANTILE) 210 1.000 0.083 0.447 3.737 0.071 0.273 UPPER HINGE (75TH QUANTILE) 239 1.000 0.102 1.801 13.269 0.082 0.439 MAXIMUM VALUE 240 1.000 0.121 4.916 51.348 0.092 0.492 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.296 0.118 0.009 0.341 2.747 -0.023 0.651 MINIMUM CORRELATION: -0.023 SERIES 049011 AND 049023 205 YEARS MAXIMUM CORRELATION: 0.651 SERIES 049045 AND 049047 239 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 88.65 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1781. 1810. 1835. 1860. 1885. 1910. 1935. 1960. CORR 10. 105. 190. 190. 190. 190. 190. 190. RBAR 0.285 0.358 0.352 0.337 0.185 0.356 0.457 0.417 SDEV 0.219 0.177 0.234 0.162 0.172 0.173 0.152 0.152 SERR 0.069 0.017 0.017 0.012 0.012 0.013 0.011 0.011 EPS 0.836 0.914 0.916 0.910 0.820 0.917 0.944 0.935 NSS 12.7 19.1 20.0 20.0 20.0 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 1756 1995 240 0.995 0.053 0.495 3.915 0.052 0.181 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.200 0.085 -0.014 88 152 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.26 0.87 1.00 1.07 1.94 18.43 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.69 0.87 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 0.180 0.218 0.071 0.157 0.072 0.087 0.105 0.042 -0.032 -0.038 PACF 0.180 0.192 0.005 0.111 0.021 0.026 0.072 -0.020 -0.083 -0.045 95% C.L. 0.129 0.133 0.139 0.140 0.143 0.143 0.144 0.145 0.145 0.146 |------------------ 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 0.069 0.147 0.192 |======================= 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 0.140 0.186 0.075 0.159 0.058 0.020 0.067 0.012 -0.083 -0.090 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 0.140 2 0.117 0.169 3 0.111 0.166 0.031 4 0.108 0.146 0.017 0.121 5 0.106 0.146 0.016 0.120 0.010 6 0.107 0.150 0.016 0.126 0.014 -0.036 7 0.109 0.149 0.010 0.125 0.006 -0.042 0.050 8 0.110 0.148 0.010 0.127 0.007 -0.039 0.052 -0.020 9 0.107 0.154 0.006 0.128 0.021 -0.037 0.070 -0.007 -0.115 10 0.099 0.154 0.011 0.125 0.023 -0.028 0.070 0.004 -0.107 -0.075 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) 1299.12 1296.35 1291.36 1293.13 1291.57 1293.54 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1295.23 1296.62 1298.52 1297.32 1297.97 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 0.117 0.169 R-SQUARED DUE TO POOLED AUTOREGRESSION: 4.78 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 105.02 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.117 0.183 0.041 0.036 0.011 0.007 0.003 0.002 0.001 0.0003 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 049011 2 0.132 0.364 -0.004 2 049013 2 0.110 0.282 0.104 3 049015 2 0.152 0.295 0.136 4 049017 2 0.297 0.358 0.268 5 049021 2 0.111 0.198 0.217 6 049023 2 0.236 0.376 0.176 7 049025 2 0.029 0.144 0.061 8 049027 2 0.034 0.141 0.097 9 049031 2 0.231 0.332 0.213 10 049033 2 0.120 0.198 0.235 11 049035 2 0.229 0.283 0.279 12 049037 2 0.085 0.183 0.129 13 049041 2 0.093 0.315 -0.094 14 049043 2 0.318 0.479 0.131 15 049045 2 0.325 0.437 0.198 16 049047 2 0.132 0.274 0.163 17 049051 2 0.189 0.269 0.257 18 049053 2 0.189 0.388 0.085 19 049055 2 0.312 0.396 0.220 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 049057 2 0.129 0.343 0.002 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.172 0.303 0.144 STANDARD DEVIATION 0 0.092 0.095 0.100 MEDIAN 2 0.142 0.305 0.150 INTERQUARTILE RANGE 0 0.123 0.136 0.127 MINIMUM VALUE 2 0.029 0.141 -0.094 LOWER HINGE 2 0.110 0.234 0.091 UPPER HINGE 2 0.233 0.370 0.218 MAXIMUM VALUE 2 0.325 0.479 0.279 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 049011 1791 1995 205 1.000 0.113 1.932 11.673 0.105 -0.003 2 049013 1791 1995 205 1.000 0.077 0.370 3.847 0.085 -0.005 3 049015 1791 1995 205 1.000 0.075 0.781 5.473 0.081 -0.021 4 049017 1790 1995 206 1.000 0.071 0.118 3.380 0.077 0.017 5 049021 1782 1995 214 1.000 0.090 1.800 11.678 0.091 -0.019 6 049023 1782 1995 214 1.000 0.094 0.618 6.038 0.099 0.011 7 049025 1782 1995 214 1.000 0.072 0.743 4.925 0.077 -0.002 8 049027 1807 1995 189 1.000 0.075 0.279 3.729 0.079 0.001 9 049031 1777 1995 219 1.000 0.079 0.804 3.854 0.086 -0.032 10 049033 1777 1995 219 1.000 0.076 0.107 2.878 0.088 -0.010 11 049035 1777 1995 219 1.000 0.085 1.090 5.528 0.091 -0.031 12 049037 1780 1995 216 1.000 0.102 1.037 4.944 0.102 -0.021 13 049041 1756 1995 240 1.000 0.084 5.358 57.795 0.072 0.003 14 049043 1758 1995 238 1.000 0.077 1.282 12.828 0.082 -0.092 15 049045 1756 1995 240 1.000 0.084 1.578 12.458 0.096 -0.083 16 049047 1757 1995 239 1.000 0.078 1.478 11.988 0.083 -0.042 17 049051 1756 1995 240 1.000 0.090 1.821 11.929 0.085 0.004 18 049053 1756 1995 240 1.000 0.087 -0.081 3.212 0.100 -0.007 19 049055 1763 1995 233 1.000 0.078 0.290 2.931 0.091 -0.052 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 049057 1756 1995 240 1.000 0.098 1.915 16.871 0.101 0.000 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 222 1.000 0.084 1.166 9.898 0.088 -0.019 STANDARD DEVIATION 15 0.000 0.011 1.183 12.078 0.010 0.029 MEDIAN (50TH QUANTILE) 219 1.000 0.082 0.921 5.500 0.087 -0.009 INTERQUARTILE RANGE 29 0.000 0.013 1.359 8.170 0.016 0.032 MINIMUM VALUE 189 1.000 0.071 -0.081 2.878 0.072 -0.092 LOWER HINGE (25TH QUANTILE) 210 1.000 0.077 0.330 3.788 0.081 -0.032 UPPER HINGE (75TH QUANTILE) 239 1.000 0.090 1.689 11.958 0.097 0.000 MAXIMUM VALUE 240 1.000 0.113 5.358 57.795 0.105 0.017 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.349 0.089 0.006 0.189 3.098 0.132 0.607 MINIMUM CORRELATION: 0.132 SERIES 049043 AND 049051 238 YEARS MAXIMUM CORRELATION: 0.607 SERIES 049021 AND 049027 189 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 88.65 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1781. 1810. 1835. 1860. 1885. 1910. 1935. 1960. CORR 10. 105. 190. 190. 190. 190. 190. 190. RBAR 0.317 0.448 0.427 0.379 0.249 0.401 0.494 0.438 SDEV 0.196 0.121 0.178 0.125 0.125 0.124 0.117 0.130 SERR 0.062 0.012 0.013 0.009 0.009 0.009 0.009 0.009 EPS 0.855 0.939 0.937 0.924 0.869 0.930 0.951 0.940 NSS 12.7 19.1 20.0 20.0 20.0 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 1756 1995 240 0.995 0.050 0.411 4.038 0.059 -0.148 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.118 0.038 0.023 95 145 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.19 0.64 1.00 1.08 1.73 83.97 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.07 0.42 0.86 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 -0.147 -0.001 -0.048 0.118 0.032 0.033 0.085 0.019 -0.041 -0.025 PACF -0.147 -0.023 -0.053 0.106 0.066 0.051 0.113 0.044 -0.038 -0.044 95% C.L. 0.129 0.132 0.132 0.132 0.134 0.134 0.134 0.135 0.135 0.135 |------------------ 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 -0.149 |---------- 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 -0.007 -0.034 0.122 0.059 0.056 0.097 0.027 -0.041 -0.029 PACF 0.000 -0.007 -0.034 0.122 0.059 0.058 0.109 0.020 -0.050 -0.040 95% C.L. 0.129 0.129 0.129 0.129 0.131 0.132 0.132 0.133 0.133 0.133 |----------------- 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 -0.007 |========================= 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 1756 1995 240 0.995 0.051 0.533 3.945 0.052 0.142 |------------ 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 0.141 0.202 0.044 0.176 0.106 0.109 0.118 0.050 -0.014 -0.013 PACF 0.141 0.185 -0.005 0.141 0.068 0.037 0.078 -0.018 -0.077 -0.035 95% C.L. 0.129 0.132 0.137 0.137 0.141 0.142 0.143 0.145 0.145 0.145 |------------------- 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 0.054 0.116 0.186 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.28 MINUTES