RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN026P.rwl.conv LOG FILE PROCESSED: FRAN026P.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 LATEWOOD_PERCENT 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 4.232 1.152 0.499 2.541 0.230 0.402 2 490012 1855 1976 122 3.357 0.861 0.648 3.294 0.278 0.007 3 490021 1904 1977 74 2.672 0.629 0.853 3.911 0.247 0.123 4 490022 1900 1977 78 2.710 0.669 0.220 2.895 0.267 0.128 5 490031 1837 1972 136 2.849 0.878 0.487 3.109 0.261 0.480 6 490032 1795 1966 172 3.106 1.227 1.246 4.801 0.295 0.408 7 490041 1763 1967 205 2.363 0.726 0.833 3.552 0.256 0.391 8 490042 1743 1971 229 2.166 0.567 0.885 4.826 0.253 0.217 9 490051 1855 1977 123 2.309 0.668 0.845 4.662 0.288 0.233 10 490052 1793 1977 185 2.388 0.693 0.859 4.549 0.251 0.388 11 490061 1843 1977 135 2.576 0.932 -0.140 3.396 0.304 0.452 12 490062 1832 1977 146 2.560 0.807 0.188 2.953 0.286 0.344 13 490071 1800 1976 177 3.011 0.949 0.220 3.970 0.289 0.301 14 490072 1799 1974 176 2.732 0.835 0.389 3.090 0.286 0.323 15 490081 1798 1961 164 3.511 0.975 0.478 2.797 0.207 0.526 16 490082 1771 1977 207 2.455 0.805 0.695 4.627 0.287 0.273 17 490091 1828 1977 150 1.916 0.728 0.015 2.992 0.347 0.286 18 490092 1833 1977 145 2.149 0.787 0.538 2.836 0.260 0.601 19 490101 1834 1977 144 2.314 1.171 0.875 2.971 0.271 0.781 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 490102 1825 1965 141 2.018 0.987 0.579 4.159 0.357 0.608 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 2.670 0.852 0.561 3.597 0.276 0.364 STANDARD DEVIATION 39 0.561 0.184 0.343 0.769 0.035 0.184 MEDIAN (50TH QUANTILE) 145 2.568 0.821 0.558 3.345 0.275 0.366 INTERQUARTILE RANGE 47 0.619 0.253 0.544 1.392 0.034 0.213 MINIMUM VALUE 74 1.916 0.567 -0.140 2.541 0.207 0.007 LOWER HINGE (25TH QUANTILE) 129 2.311 0.709 0.304 2.962 0.254 0.253 UPPER HINGE (75TH QUANTILE) 176 2.930 0.962 0.849 4.354 0.289 0.466 MAXIMUM VALUE 229 4.232 1.227 1.246 4.826 0.357 0.781 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.221 0.160 0.012 -0.196 2.794 -0.261 0.581 MINIMUM CORRELATION: -0.261 SERIES 490032 AND 490101 133 YEARS MAXIMUM CORRELATION: 0.581 SERIES 490062 AND 490101 144 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 0.582 0.321 0.309 0.344 0.302 0.273 0.245 SDEV 0.048 0.179 0.183 0.186 0.183 0.195 0.204 SERR 0.028 0.034 0.031 0.018 0.015 0.015 0.021 EPS 0.890 0.830 0.871 0.903 0.891 0.882 0.862 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 2.570 0.488 0.494 3.768 0.197 0.139 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.309 0.242 0.108 67 168 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.34 0.73 1.00 1.06 1.80 29.24 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.14 0.00 0.83 0.97 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 0.138 0.196 0.085 0.092 0.002 0.039 0.048 0.057 0.087 -0.006 PACF 0.138 0.181 0.040 0.045 -0.037 0.016 0.044 0.039 0.066 -0.050 95% C.L. 0.130 0.133 0.138 0.139 0.140 0.140 0.140 0.140 0.141 0.141 |------------------ 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 0.055 0.114 0.185 |================== 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 3 0.00000000 0.00000000 -0.01110466 4.92019606 2 490012 3 0.00000000 0.00000000 -0.00574504 3.71012330 3 490021 3 0.00000000 0.00000000 0.00720800 2.40186214 4 490022 3 0.00000000 0.00000000 0.00272550 2.60247087 5 490031 3 0.00000000 0.00000000 0.00055682 2.81090188 6 490032 1 3.14762950 0.09011525 0.00000000 2.91198635 7 490041 1 1.35323739 0.03200880 0.00000000 2.16023088 8 490042 1 0.45917740 0.01157907 0.00000000 2.00626373 9 490051 3 0.00000000 0.00000000 -0.00190098 2.42647862 10 490052 3 0.00000000 0.00000000 0.00109630 2.28566575 11 490061 3 0.00000000 0.00000000 -0.00874978 3.17113328 12 490062 1 1.10397744 0.02576552 0.00000000 2.26997948 13 490071 3 0.00000000 0.00000000 -0.00694894 3.62902021 14 490072 3 0.00000000 0.00000000 0.00023193 2.71123576 15 490081 3 0.00000000 0.00000000 0.00174341 3.36744952 16 490082 3 0.00000000 0.00000000 0.00048494 2.40468740 17 490091 1 1.22399569 0.06293479 0.00000000 1.79032290 18 490092 1 1.94024849 0.03605510 0.00000000 1.78685760 19 490101 1 3.43179393 0.02598566 0.00000000 1.42992008 SERIES IDENT OPTION A B C D 20 490102 1 2.59862542 0.04345171 0.00000000 1.60377860 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 490011 1855 1977 123 1.000 0.252 0.385 3.011 0.228 0.305 2 490012 1855 1976 122 1.000 0.250 0.784 4.006 0.276 -0.037 3 490021 1904 1977 74 1.000 0.227 0.783 3.595 0.244 0.063 4 490022 1900 1977 78 1.000 0.245 0.191 3.059 0.264 0.112 5 490031 1837 1972 136 1.000 0.308 0.491 3.137 0.259 0.477 6 490032 1795 1966 172 1.000 0.353 0.853 3.960 0.293 0.335 7 490041 1763 1967 205 1.000 0.279 0.774 3.696 0.255 0.250 8 490042 1743 1971 229 1.000 0.258 0.931 4.992 0.252 0.177 9 490051 1855 1977 123 1.000 0.287 0.808 4.508 0.286 0.222 10 490052 1793 1977 185 1.000 0.288 0.823 4.462 0.250 0.375 11 490061 1843 1977 135 0.999 0.364 0.304 4.125 0.301 0.403 12 490062 1832 1977 146 1.000 0.300 0.165 3.232 0.282 0.302 13 490071 1800 1976 177 0.999 0.301 0.210 3.575 0.288 0.239 14 490072 1799 1974 176 1.000 0.306 0.385 3.087 0.284 0.321 15 490081 1798 1961 164 1.000 0.275 0.424 2.691 0.205 0.524 16 490082 1771 1977 207 1.000 0.326 0.641 4.500 0.285 0.270 17 490091 1828 1977 150 1.000 0.366 -0.147 2.728 0.344 0.220 18 490092 1833 1977 145 1.000 0.317 0.886 4.305 0.259 0.428 19 490101 1834 1977 144 1.000 0.359 0.376 2.840 0.269 0.551 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 490102 1825 1965 141 1.001 0.428 -0.020 2.956 0.354 0.493 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 152 1.000 0.304 0.502 3.623 0.274 0.301 STANDARD DEVIATION 39 0.000 0.050 0.323 0.696 0.035 0.155 MEDIAN (50TH QUANTILE) 145 1.000 0.300 0.457 3.585 0.273 0.303 INTERQUARTILE RANGE 47 0.000 0.073 0.539 1.180 0.033 0.194 MINIMUM VALUE 74 0.999 0.227 -0.147 2.691 0.205 -0.037 LOWER HINGE (25TH QUANTILE) 129 1.000 0.267 0.257 3.035 0.253 0.221 UPPER HINGE (75TH QUANTILE) 176 1.000 0.340 0.796 4.215 0.287 0.415 MAXIMUM VALUE 229 1.001 0.428 0.931 4.992 0.354 0.551 |------------------------ 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 0.997 0.234 0.334 3.295 0.228 0.209 2 490012 1855 1976 122 0.999 0.243 0.741 3.833 0.276 -0.079 3 490021 1904 1977 74 0.999 0.217 0.652 3.352 0.243 0.010 4 490022 1900 1977 78 0.999 0.232 0.202 3.020 0.264 -0.023 5 490031 1837 1972 136 0.998 0.259 0.139 2.709 0.258 0.276 6 490032 1795 1966 172 0.997 0.320 0.889 4.863 0.293 0.226 7 490041 1763 1967 205 0.999 0.251 0.481 2.803 0.254 0.135 8 490042 1743 1971 229 0.999 0.248 0.883 5.065 0.252 0.109 9 490051 1855 1977 123 0.998 0.279 0.830 4.583 0.286 0.178 10 490052 1793 1977 185 0.998 0.274 0.699 4.022 0.250 0.320 11 490061 1843 1977 135 0.998 0.365 0.560 4.474 0.301 0.371 12 490062 1832 1977 146 0.998 0.291 0.116 3.164 0.282 0.256 13 490071 1800 1976 177 0.998 0.296 0.290 3.499 0.288 0.209 14 490072 1799 1974 176 0.997 0.290 0.633 3.662 0.284 0.219 15 490081 1798 1961 164 0.995 0.227 1.078 6.000 0.206 0.196 16 490082 1771 1977 207 0.996 0.296 0.503 4.755 0.285 0.141 17 490091 1828 1977 150 0.998 0.369 0.042 2.862 0.344 0.183 18 490092 1833 1977 145 0.995 0.263 0.740 5.452 0.259 0.223 19 490101 1834 1977 144 0.991 0.326 0.475 3.016 0.269 0.473 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 490102 1825 1965 141 0.986 0.373 0.243 3.407 0.355 0.185 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 152 0.997 0.283 0.526 3.892 0.274 0.191 STANDARD DEVIATION 39 0.003 0.048 0.294 0.962 0.035 0.127 MEDIAN (50TH QUANTILE) 145 0.998 0.277 0.531 3.581 0.272 0.202 INTERQUARTILE RANGE 47 0.002 0.062 0.474 1.577 0.033 0.103 MINIMUM VALUE 74 0.986 0.217 0.042 2.709 0.206 -0.079 LOWER HINGE (25TH QUANTILE) 129 0.996 0.246 0.266 3.092 0.253 0.138 UPPER HINGE (75TH QUANTILE) 176 0.998 0.308 0.740 4.669 0.287 0.241 MAXIMUM VALUE 229 0.999 0.373 1.078 6.000 0.355 0.473 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.277 0.114 0.008 0.115 2.842 0.005 0.551 MINIMUM CORRELATION: 0.005 SERIES 490022 AND 490071 77 YEARS MAXIMUM CORRELATION: 0.551 SERIES 490041 AND 490081 164 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 0.501 0.279 0.362 0.390 0.339 0.304 0.242 SDEV 0.103 0.189 0.141 0.142 0.152 0.171 0.175 SERR 0.059 0.036 0.024 0.014 0.012 0.013 0.018 EPS 0.854 0.800 0.895 0.919 0.907 0.897 0.860 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 0.984 0.172 0.399 3.441 0.197 0.009 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.208 0.126 0.067 71 164 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.29 0.58 1.00 1.07 1.66 15.19 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.13 0.00 0.84 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 0.009 0.089 0.014 0.008 -0.082 -0.050 -0.035 -0.058 0.047 -0.079 PACF 0.009 0.089 0.012 0.000 -0.085 -0.051 -0.020 -0.047 0.056 -0.077 95% C.L. 0.130 0.130 0.132 0.132 0.132 0.132 0.133 0.133 0.133 0.134 |------------------ 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 0 0.000 |======================= 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 0.001 -0.019 0.010 -0.032 -0.041 -0.038 -0.019 -0.067 0.072 0.000 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 0.001 2 0.001 -0.019 3 0.001 -0.019 0.010 4 0.001 -0.019 0.010 -0.032 5 0.000 -0.019 0.010 -0.032 -0.041 6 -0.001 -0.020 0.010 -0.033 -0.041 -0.039 7 -0.002 -0.021 0.009 -0.033 -0.041 -0.039 -0.021 8 -0.004 -0.024 0.006 -0.035 -0.040 -0.041 -0.021 -0.069 9 0.001 -0.022 0.009 -0.032 -0.038 -0.041 -0.019 -0.069 0.069 10 0.002 -0.023 0.009 -0.033 -0.038 -0.041 -0.019 -0.069 0.069 -0.007 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) 1693.69 1695.69 1697.60 1699.58 1701.33 1702.94 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1704.58 1706.48 1707.36 1708.24 1710.23 SELECTED AUTOREGRESSION ORDER: 0 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 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 490011 0 0.044 2 490012 0 0.006 3 490021 0 0.000 4 490022 0 0.001 5 490031 0 0.076 6 490032 0 0.053 7 490041 0 0.019 8 490042 0 0.012 9 490051 0 0.033 10 490052 0 0.102 11 490061 0 0.141 12 490062 0 0.069 13 490071 0 0.045 14 490072 0 0.048 15 490081 0 0.045 16 490082 0 0.020 17 490091 0 0.034 18 490092 0 0.051 19 490101 0 0.230 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 490102 0 0.034 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 0 0.053 STANDARD DEVIATION 0 0.054 MEDIAN 0 0.045 INTERQUARTILE RANGE 0 0.041 MINIMUM VALUE 0 0.000 LOWER HINGE 0 0.020 UPPER HINGE 0 0.061 MAXIMUM VALUE 0 0.230 |------------------- 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 0.234 0.334 3.295 0.227 0.209 2 490012 1855 1976 122 1.000 0.243 0.741 3.833 0.276 -0.079 3 490021 1904 1977 74 1.000 0.217 0.652 3.352 0.243 0.010 4 490022 1900 1977 78 1.000 0.232 0.202 3.020 0.264 -0.023 5 490031 1837 1972 136 1.000 0.259 0.139 2.709 0.257 0.276 6 490032 1795 1966 172 1.000 0.320 0.889 4.863 0.292 0.226 7 490041 1763 1967 205 1.000 0.251 0.481 2.803 0.254 0.135 8 490042 1743 1971 229 1.000 0.248 0.883 5.065 0.252 0.109 9 490051 1855 1977 123 1.000 0.279 0.830 4.583 0.285 0.178 10 490052 1793 1977 185 1.000 0.274 0.699 4.022 0.249 0.320 11 490061 1843 1977 135 1.000 0.365 0.560 4.474 0.300 0.371 12 490062 1832 1977 146 1.000 0.291 0.116 3.164 0.281 0.256 13 490071 1800 1976 177 1.000 0.296 0.290 3.499 0.287 0.209 14 490072 1799 1974 176 1.000 0.290 0.633 3.662 0.283 0.219 15 490081 1798 1961 164 1.000 0.227 1.078 6.000 0.204 0.196 16 490082 1771 1977 207 1.000 0.296 0.503 4.755 0.284 0.141 17 490091 1828 1977 150 1.000 0.369 0.042 2.862 0.343 0.183 18 490092 1833 1977 145 1.000 0.263 0.740 5.452 0.258 0.223 19 490101 1834 1977 144 1.000 0.326 0.475 3.016 0.266 0.473 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 490102 1825 1965 141 1.000 0.373 0.243 3.407 0.350 0.185 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 152 1.000 0.283 0.526 3.892 0.273 0.191 STANDARD DEVIATION 39 0.000 0.048 0.294 0.962 0.034 0.127 MEDIAN (50TH QUANTILE) 145 1.000 0.277 0.531 3.581 0.271 0.202 INTERQUARTILE RANGE 47 0.000 0.062 0.474 1.577 0.033 0.103 MINIMUM VALUE 74 1.000 0.217 0.042 2.709 0.204 -0.079 LOWER HINGE (25TH QUANTILE) 129 1.000 0.246 0.266 3.092 0.253 0.138 UPPER HINGE (75TH QUANTILE) 176 1.000 0.308 0.740 4.669 0.286 0.241 MAXIMUM VALUE 229 1.000 0.373 1.078 6.000 0.350 0.473 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.277 0.114 0.008 0.115 2.842 0.005 0.551 MINIMUM CORRELATION: 0.005 SERIES 490022 AND 490071 77 YEARS MAXIMUM CORRELATION: 0.551 SERIES 490041 AND 490081 164 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 0.501 0.279 0.362 0.390 0.339 0.304 0.242 SDEV 0.103 0.189 0.141 0.142 0.152 0.171 0.175 SERR 0.059 0.036 0.024 0.014 0.012 0.013 0.018 EPS 0.854 0.800 0.895 0.919 0.907 0.897 0.860 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 0.987 0.172 0.404 3.443 0.197 0.008 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.210 0.127 0.066 71 164 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.28 0.62 1.00 1.08 1.69 15.12 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 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 0.008 0.089 0.013 0.007 -0.081 -0.050 -0.035 -0.060 0.047 -0.079 PACF 0.008 0.089 0.012 -0.001 -0.084 -0.050 -0.020 -0.049 0.055 -0.077 95% C.L. 0.130 0.130 0.132 0.132 0.132 0.132 0.133 0.133 0.133 0.134 |------------------ 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 |========================= 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 0.987 0.172 0.404 3.443 0.197 0.008 |------------ 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 0.008 0.089 0.013 0.007 -0.081 -0.050 -0.035 -0.060 0.047 -0.079 PACF 0.008 0.089 0.012 -0.001 -0.084 -0.050 -0.020 -0.049 0.055 -0.077 95% C.L. 0.130 0.130 0.132 0.132 0.132 0.132 0.133 0.133 0.133 0.134 |------------------- 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 0 0.000 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.24 MINUTES