RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN026E.rwl.conv LOG FILE PROCESSED: FRAN026E.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: 490 1 Arette, Col St. Martin WIDTH_EARLY ABAL - 490 2 France silver fir, European fir 1500 4259-45 1743 1977 - 490 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 12 490062 MISSING VALUES FOUND: 1 IN 1 GAPS / 1892 1892 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 490011 1855 1977 123 0.642 0.353 1.049 4.182 0.258 0.808 2 490012 1855 1976 122 0.608 0.249 0.252 2.762 0.305 0.529 3 490021 1904 1977 74 1.406 0.720 0.868 3.197 0.212 0.835 4 490022 1900 1977 78 1.227 0.483 0.641 2.973 0.228 0.757 5 490031 1837 1972 136 0.694 0.272 -0.293 3.154 0.219 0.782 6 490032 1795 1966 172 0.561 0.335 1.089 4.037 0.281 0.814 7 490041 1763 1967 205 0.436 0.146 0.173 2.968 0.245 0.562 8 490042 1743 1971 229 0.388 0.135 0.435 3.057 0.235 0.625 9 490051 1855 1977 123 0.494 0.262 0.710 2.741 0.223 0.887 10 490052 1793 1977 185 0.602 0.269 1.473 5.171 0.214 0.829 11 490061 1843 1977 135 0.663 0.474 1.212 3.828 0.255 0.869 12 490062 1832 1977 146 0.755 0.451 0.329 2.289 0.215 0.888 13 490071 1800 1976 177 0.698 0.399 0.390 2.628 0.271 0.803 14 490072 1799 1974 176 0.564 0.310 0.688 2.907 0.237 0.827 15 490081 1798 1961 164 0.561 0.230 0.992 4.129 0.255 0.635 16 490082 1771 1977 207 0.582 0.259 0.806 4.275 0.202 0.801 17 490091 1828 1977 150 0.930 0.570 0.410 2.119 0.195 0.898 18 490092 1833 1977 145 0.498 0.217 -0.022 2.445 0.193 0.837 19 490101 1834 1977 144 1.051 0.711 1.321 4.099 0.212 0.904 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 490102 1825 1965 141 1.281 0.604 0.113 2.383 0.201 0.798 NUMBER OF SERIES READ IN: 20 FROM 1743 TO 1977 235 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 152 0.732 0.372 0.632 3.267 0.233 0.784 STANDARD DEVIATION 39 0.292 0.174 0.474 0.823 0.030 0.110 MEDIAN (50TH QUANTILE) 145 0.625 0.323 0.665 3.015 0.226 0.811 INTERQUARTILE RANGE 47 0.282 0.225 0.730 1.384 0.043 0.083 MINIMUM VALUE 74 0.388 0.135 -0.293 2.119 0.193 0.529 LOWER HINGE (25TH QUANTILE) 129 0.561 0.254 0.290 2.685 0.212 0.769 UPPER HINGE (75TH QUANTILE) 176 0.843 0.479 1.020 4.068 0.255 0.853 MAXIMUM VALUE 229 1.406 0.720 1.473 5.171 0.305 0.904 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.344 0.271 0.020 -0.577 3.316 -0.488 0.839 MINIMUM CORRELATION: -0.488 SERIES 490051 AND 490081 107 YEARS MAXIMUM CORRELATION: 0.839 SERIES 490091 AND 490102 138 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.40 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1825. 1850. 1875. 1900. 1925. 1950. CORR 3. 28. 36. 105. 153. 171. 91. RBAR 0.218 0.483 0.416 0.276 0.275 0.270 0.625 SDEV 0.206 0.262 0.213 0.343 0.348 0.364 0.250 SERR 0.119 0.050 0.036 0.033 0.028 0.028 0.026 EPS 0.618 0.906 0.915 0.871 0.878 0.881 0.970 NSS 5.8 10.4 15.1 17.7 18.9 19.9 19.2 |======================== 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 1743 1977 235 0.552 0.209 0.261 2.482 0.208 0.759 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.778 0.602 -0.090 111 124 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 2.06 3.45 1.03 1.48 4.93 77.86 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.21 0.00 0.79 1.00 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 146. 48. 74. 129. 176. 229. |----------- 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 0.756 0.738 0.661 0.617 0.572 0.571 0.533 0.489 0.450 0.451 PACF 0.756 0.390 0.072 0.036 0.030 0.123 0.022 -0.064 -0.035 0.097 95% C.L. 0.130 0.191 0.235 0.264 0.288 0.307 0.324 0.339 0.351 0.360 |------------------ 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 0.650 0.456 0.401 |================== 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 490011 1 0.89107096 0.02219404 0.00000000 0.33997843 2 490012 3 0.00000000 0.00000000 -0.00429009 0.87195504 3 490021 1 2.50901651 0.04394817 0.00000000 0.68090129 4 490022 1 0.91946304 0.03779692 0.00000000 0.93734056 5 490031 3 0.00000000 0.00000000 -0.00236618 0.85583335 6 490032 3 0.00000000 0.00000000 -0.00076558 0.62721133 7 490041 3 0.00000000 0.00000000 0.00051009 0.38311908 8 490042 3 0.00000000 0.00000000 -0.00010776 0.40003449 9 490051 1 0.64482123 0.10827356 0.00000000 0.44830224 10 490052 3 0.00000000 0.00000000 0.00079207 0.52860808 11 490061 1 1.66926169 0.08977333 0.00000000 0.53095007 12 490062 1 0.48746479 0.07074606 0.00000000 0.70600277 13 490071 3 0.00000000 0.00000000 0.00102396 0.60649461 14 490072 3 0.00000000 0.00000000 -0.00145046 0.69217271 15 490081 3 0.00000000 0.00000000 -0.00208167 0.73320138 16 490082 3 0.00000000 0.00000000 -0.00162169 0.75078183 17 490091 3 0.00000000 0.00000000 -0.01179028 1.82056642 18 490092 3 0.00000000 0.00000000 -0.00292588 0.71200287 19 490101 3 0.00000000 0.00000000 -0.01205763 1.92501163 SERIES IDENT OPTION A B C D 20 490102 3 0.00000000 0.00000000 -0.01146984 2.09584808 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 490011 1855 1977 123 0.999 0.453 0.920 3.758 0.256 0.684 2 490012 1855 1976 122 0.999 0.377 1.731 9.439 0.303 0.339 3 490021 1904 1977 74 1.001 0.299 0.526 3.799 0.208 0.615 4 490022 1900 1977 78 1.000 0.369 1.193 4.971 0.224 0.700 5 490031 1837 1972 136 0.996 0.390 -0.115 3.034 0.217 0.773 6 490032 1795 1966 172 0.998 0.597 1.153 4.254 0.279 0.813 7 490041 1763 1967 205 0.999 0.332 0.348 3.372 0.243 0.538 8 490042 1743 1971 229 1.000 0.347 0.412 2.997 0.234 0.621 9 490051 1855 1977 123 0.999 0.520 1.155 4.176 0.221 0.875 10 490052 1793 1977 185 1.000 0.426 1.204 4.415 0.213 0.806 11 490061 1843 1977 135 0.999 0.661 1.745 6.337 0.252 0.879 12 490062 1832 1977 146 1.000 0.618 0.591 2.659 0.221 0.899 13 490071 1800 1976 177 0.998 0.566 0.412 2.671 0.270 0.791 14 490072 1799 1974 176 0.995 0.515 0.457 2.563 0.235 0.806 15 490081 1798 1961 164 0.998 0.381 1.549 6.087 0.253 0.595 16 490082 1771 1977 207 0.997 0.459 1.695 6.838 0.201 0.821 17 490091 1828 1977 150 1.088 0.545 3.262 14.774 0.193 0.768 18 490092 1833 1977 145 0.987 0.381 0.579 3.305 0.192 0.812 19 490101 1834 1977 144 1.027 0.421 0.388 2.350 0.210 0.765 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 490102 1825 1965 141 0.981 0.306 0.311 2.553 0.199 0.697 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 152 1.003 0.448 0.976 4.718 0.231 0.730 STANDARD DEVIATION 39 0.022 0.108 0.767 2.972 0.030 0.136 MEDIAN (50TH QUANTILE) 145 0.999 0.423 0.755 3.779 0.223 0.771 INTERQUARTILE RANGE 47 0.002 0.160 0.965 2.695 0.044 0.160 MINIMUM VALUE 74 0.981 0.299 -0.115 2.350 0.192 0.339 LOWER HINGE (25TH QUANTILE) 129 0.997 0.373 0.412 2.834 0.209 0.653 UPPER HINGE (75TH QUANTILE) 176 1.000 0.533 1.377 5.529 0.252 0.812 MAXIMUM VALUE 229 1.088 0.661 3.262 14.774 0.303 0.899 |------------------------ 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 490011 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 490012 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 490021 -67 49 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 490022 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 490031 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 490032 -67 115 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 490041 -67 137 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 490042 -67 153 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 490051 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 490052 -67 123 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 490061 -67 90 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 490062 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 490071 -67 118 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 490072 -67 117 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 490081 -67 109 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 490082 -67 138 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 490091 -67 100 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 490092 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 490101 -67 96 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 490102 -67 94 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 490011 1855 1977 123 0.988 0.387 0.723 3.180 0.256 0.608 2 490012 1855 1976 122 0.996 0.358 1.651 9.253 0.303 0.300 3 490021 1904 1977 74 0.995 0.254 -0.172 2.799 0.206 0.500 4 490022 1900 1977 78 0.994 0.312 0.741 3.780 0.224 0.607 5 490031 1837 1972 136 0.983 0.302 0.046 3.283 0.216 0.654 6 490032 1795 1966 172 0.989 0.455 2.109 11.131 0.280 0.607 7 490041 1763 1967 205 0.997 0.299 0.306 3.475 0.243 0.398 8 490042 1743 1971 229 0.998 0.339 0.389 3.012 0.234 0.607 9 490051 1855 1977 123 0.971 0.338 0.320 3.009 0.219 0.738 10 490052 1793 1977 185 0.984 0.355 0.919 3.743 0.212 0.740 11 490061 1843 1977 135 0.958 0.448 0.950 3.771 0.251 0.782 12 490062 1832 1977 146 0.940 0.412 -0.133 2.303 0.221 0.814 13 490071 1800 1976 177 0.974 0.349 0.712 3.806 0.267 0.483 14 490072 1799 1974 176 0.970 0.346 0.746 2.830 0.233 0.595 15 490081 1798 1961 164 0.991 0.307 1.038 4.617 0.252 0.388 16 490082 1771 1977 207 0.982 0.336 1.063 4.845 0.201 0.677 17 490091 1828 1977 150 0.991 0.280 0.824 3.462 0.192 0.605 18 490092 1833 1977 145 0.995 0.282 0.433 3.362 0.192 0.622 19 490101 1834 1977 144 0.982 0.335 0.410 2.492 0.210 0.678 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 490102 1825 1965 141 0.994 0.248 0.342 2.743 0.199 0.497 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 152 0.984 0.337 0.671 4.045 0.231 0.595 STANDARD DEVIATION 39 0.015 0.057 0.553 2.217 0.030 0.134 MEDIAN (50TH QUANTILE) 145 0.988 0.337 0.717 3.412 0.223 0.607 INTERQUARTILE RANGE 47 0.017 0.056 0.604 0.874 0.044 0.180 MINIMUM VALUE 74 0.940 0.248 -0.172 2.303 0.192 0.300 LOWER HINGE (25TH QUANTILE) 129 0.978 0.300 0.331 2.920 0.208 0.498 UPPER HINGE (75TH QUANTILE) 176 0.995 0.357 0.935 3.793 0.252 0.678 MAXIMUM VALUE 229 0.998 0.455 2.109 11.131 0.303 0.814 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.336 0.197 0.014 -0.430 3.311 -0.263 0.761 MINIMUM CORRELATION: -0.263 SERIES 490051 AND 490081 107 YEARS MAXIMUM CORRELATION: 0.761 SERIES 490051 AND 490052 123 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.40 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1825. 1850. 1875. 1900. 1925. 1950. CORR 3. 28. 36. 105. 153. 171. 91. RBAR 0.253 0.523 0.481 0.318 0.319 0.353 0.447 SDEV 0.252 0.173 0.173 0.280 0.311 0.233 0.195 SERR 0.145 0.033 0.029 0.027 0.025 0.018 0.020 EPS 0.663 0.919 0.933 0.892 0.899 0.916 0.939 NSS 5.8 10.4 15.1 17.7 18.9 19.9 19.2 |======================== 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 1743 1977 235 0.974 0.223 0.223 3.170 0.204 0.383 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.223 0.114 0.116 61 174 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.18 0.39 1.00 1.05 1.43 3.88 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.11 0.00 0.86 0.97 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 0.382 0.357 0.168 0.121 0.011 0.051 -0.049 -0.175 -0.219 -0.201 PACF 0.382 0.247 -0.036 -0.008 -0.067 0.051 -0.069 -0.203 -0.113 -0.014 95% C.L. 0.130 0.148 0.162 0.165 0.167 0.167 0.167 0.167 0.170 0.175 |------------------ 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 0.200 0.287 0.249 |======================= 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 0.444 0.399 0.169 0.125 0.061 0.034 -0.048 -0.141 -0.177 -0.116 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 0.444 2 0.332 0.252 3 0.357 0.284 -0.099 4 0.356 0.286 -0.097 -0.007 5 0.356 0.288 -0.100 -0.012 0.013 6 0.356 0.288 -0.101 -0.009 0.017 -0.010 7 0.356 0.289 -0.102 -0.018 0.042 0.021 -0.089 8 0.343 0.292 -0.096 -0.021 0.028 0.061 -0.040 -0.137 9 0.334 0.290 -0.092 -0.019 0.027 0.055 -0.021 -0.115 -0.065 10 0.339 0.297 -0.091 -0.022 0.025 0.056 -0.014 -0.135 -0.088 0.069 LAST TERM IN EACH ROW ABOVE EQUALS THE PARTIAL AUTOCORRELATION COEFFICIENT AKAIKE INFORMATION CRITERION: AR( 0) AR( 1) AR( 2) AR( 3) AR( 4) AR( 5) 1806.33 1756.83 1743.48 1743.16 1745.14 1747.10 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1749.08 1749.22 1746.76 1747.76 1748.65 SELECTED AUTOREGRESSION ORDER: 3 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 0.357 0.284 -0.099 R-SQUARED DUE TO POOLED AUTOREGRESSION: 25.50 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 134.23 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.357 0.412 0.149 0.135 0.050 0.041 0.016 0.012 0.005 0.0037 0.001 0.001 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 490011 3 0.427 0.560 0.268 -0.245 2 490012 3 0.178 0.235 0.315 -0.080 3 490021 3 0.280 0.465 0.183 -0.170 4 490022 3 0.415 0.584 0.198 -0.226 5 490031 3 0.466 0.540 0.252 -0.083 6 490032 3 0.425 0.469 0.322 -0.103 7 490041 3 0.232 0.286 0.282 0.011 8 490042 3 0.410 0.461 0.197 0.059 9 490051 3 0.577 0.596 0.285 -0.104 10 490052 3 0.612 0.534 0.369 -0.095 11 490061 3 0.658 0.649 0.346 -0.195 12 490062 3 0.696 0.578 0.315 -0.026 13 490071 3 0.270 0.413 0.221 -0.095 14 490072 3 0.425 0.400 0.316 0.017 15 490081 3 0.220 0.272 0.249 0.064 16 490082 3 0.517 0.438 0.229 0.137 17 490091 3 0.443 0.445 0.317 -0.047 18 490092 3 0.401 0.530 0.138 0.015 19 490101 3 0.476 0.600 0.136 -0.023 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 490102 3 0.292 0.383 0.176 0.074 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.421 0.472 0.256 -0.056 STANDARD DEVIATION 0 0.145 0.116 0.069 0.104 MEDIAN 3 0.425 0.467 0.260 -0.064 INTERQUARTILE RANGE 0 0.210 0.163 0.118 0.120 MINIMUM VALUE 3 0.178 0.235 0.136 -0.245 LOWER HINGE 3 0.286 0.407 0.197 -0.104 UPPER HINGE 3 0.496 0.569 0.315 0.016 MAXIMUM VALUE 3 0.696 0.649 0.369 0.137 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 490011 1855 1977 123 1.000 0.294 0.677 3.899 0.315 0.020 2 490012 1855 1976 122 1.000 0.325 2.133 15.467 0.326 0.004 3 490021 1904 1977 74 1.000 0.215 0.031 3.142 0.250 0.001 4 490022 1900 1977 78 1.000 0.240 1.112 4.421 0.262 0.024 5 490031 1837 1972 136 1.000 0.220 0.363 3.591 0.244 -0.008 6 490032 1795 1966 172 1.000 0.345 2.589 19.534 0.339 0.001 7 490041 1763 1967 205 1.000 0.262 0.535 4.714 0.275 0.008 8 490042 1743 1971 229 1.000 0.261 0.716 4.756 0.279 0.008 9 490051 1855 1977 123 1.000 0.220 0.447 2.738 0.245 0.003 10 490052 1793 1977 185 1.000 0.224 0.471 3.436 0.253 0.016 11 490061 1843 1977 135 1.000 0.266 0.249 3.905 0.296 -0.045 12 490062 1832 1977 146 1.000 0.228 0.398 3.327 0.246 -0.002 13 490071 1800 1976 177 1.000 0.298 1.013 5.889 0.306 -0.005 14 490072 1799 1974 176 1.000 0.262 0.929 4.357 0.272 0.004 15 490081 1798 1961 164 1.000 0.272 0.849 5.356 0.278 -0.002 16 490082 1771 1977 207 1.000 0.234 0.934 6.184 0.239 -0.003 17 490091 1828 1977 150 1.000 0.211 0.878 4.759 0.230 0.003 18 490092 1833 1977 145 1.000 0.218 -0.009 3.356 0.237 -0.001 19 490101 1834 1977 144 1.000 0.243 0.336 3.745 0.267 0.000 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 490102 1825 1965 141 1.000 0.209 -0.081 4.184 0.239 -0.004 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 152 1.000 0.252 0.729 5.538 0.270 0.001 STANDARD DEVIATION 39 0.000 0.039 0.660 4.239 0.032 0.014 MEDIAN (50TH QUANTILE) 145 1.000 0.242 0.606 4.271 0.265 0.001 INTERQUARTILE RANGE 47 0.000 0.049 0.582 1.544 0.043 0.009 MINIMUM VALUE 74 1.000 0.209 -0.081 2.738 0.230 -0.045 LOWER HINGE (25TH QUANTILE) 129 1.000 0.220 0.350 3.514 0.244 -0.003 UPPER HINGE (75TH QUANTILE) 176 1.000 0.269 0.931 5.058 0.288 0.006 MAXIMUM VALUE 229 1.000 0.345 2.589 19.534 0.339 0.024 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.455 0.100 0.007 0.237 2.842 0.209 0.771 MINIMUM CORRELATION: 0.209 SERIES 490051 AND 490071 122 YEARS MAXIMUM CORRELATION: 0.771 SERIES 490021 AND 490031 69 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.40 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1825. 1850. 1875. 1900. 1925. 1950. CORR 3. 28. 36. 105. 153. 171. 91. RBAR 0.553 0.633 0.617 0.429 0.441 0.484 0.506 SDEV 0.051 0.132 0.105 0.142 0.146 0.123 0.115 SERR 0.029 0.025 0.017 0.014 0.012 0.009 0.012 EPS 0.877 0.947 0.960 0.930 0.937 0.949 0.952 NSS 5.8 10.4 15.1 17.7 18.9 19.9 19.2 |======================== 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 1743 1977 235 0.992 0.191 0.378 4.387 0.226 -0.135 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.285 0.120 0.031 72 163 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.37 0.90 1.00 1.10 2.00 5.72 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.13 0.00 0.84 0.97 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 -0.134 -0.015 -0.063 -0.067 -0.064 0.143 0.043 -0.089 -0.155 -0.125 PACF -0.134 -0.033 -0.071 -0.088 -0.093 0.115 0.067 -0.087 -0.182 -0.171 95% C.L. 0.130 0.133 0.133 0.133 0.134 0.134 0.137 0.137 0.138 0.141 |------------------ 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 0.019 -0.134 |---------- 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 -0.007 -0.009 -0.007 -0.089 -0.065 0.123 0.028 -0.112 -0.177 -0.147 PACF -0.007 -0.009 -0.007 -0.089 -0.066 0.121 0.028 -0.123 -0.197 -0.144 95% C.L. 0.130 0.130 0.130 0.130 0.132 0.132 0.134 0.134 0.136 0.140 |----------------- 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 3 0.008 -0.007 -0.009 -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 1743 1977 235 0.992 0.215 0.224 2.978 0.186 0.419 |------------ 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 0.417 0.355 0.103 0.029 -0.039 0.017 -0.088 -0.200 -0.269 -0.246 PACF 0.417 0.219 -0.131 -0.059 -0.018 0.078 -0.116 -0.222 -0.126 -0.002 95% C.L. 0.130 0.151 0.165 0.166 0.166 0.166 0.166 0.167 0.171 0.178 |------------------- 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 3 0.230 0.354 0.264 -0.133 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.24 MINUTES