RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM056L.rwl.conv LOG FILE PROCESSED: GERM056L.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 20 10 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: 055 1 Sirnitz NE (D), EU-Pr. WIDTH_LATE ABAL - 055 2 Germany silver fir, European fir 940 4747-745 1841 1995 - 055 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 3 055025 MISSING VALUES FOUND: 2 IN 1 GAPS / 1979 1980 / -------------------------------------------------------------------- 6 055033 MISSING VALUES FOUND: 2 IN 1 GAPS / 1920 1921 / -------------------------------------------------------------------- 9 055161 MISSING VALUES FOUND: 7 IN 1 GAPS / 1857 1863 / -------------------------------------------------------------------- 12 055167 MISSING VALUES FOUND: 2 IN 1 GAPS / 1936 1937 / -------------------------------------------------------------------- 13 055171 MISSING VALUES FOUND: 2 IN 1 GAPS / 1937 1938 / -------------------------------------------------------------------- 15 055175 MISSING VALUES FOUND: 2 IN 1 GAPS / 1913 1914 / -------------------------------------------------------------------- 19 055215 MISSING VALUES FOUND: 4 IN 1 GAPS / 1941 1944 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 055021 1889 1995 107 0.532 0.304 2.047 8.061 0.309 0.599 2 055023 1865 1995 131 0.507 0.333 1.872 8.070 0.321 0.667 3 055025 1867 1995 129 0.705 0.673 3.095 13.512 0.325 0.830 4 055027 1881 1995 115 0.537 0.322 1.874 7.074 0.366 0.572 5 055031 1869 1995 127 0.674 0.295 -0.020 2.544 0.340 0.452 6 055033 1869 1995 127 0.629 0.337 0.993 4.513 0.396 0.574 7 055035 1869 1995 127 0.639 0.383 0.631 3.059 0.365 0.646 8 055037 1869 1991 123 0.953 0.428 0.799 3.491 0.347 0.496 9 055161 1848 1995 148 0.930 0.557 1.351 5.041 0.301 0.813 10 055163 1848 1995 148 0.521 0.349 1.681 6.096 0.311 0.823 11 055165 1855 1995 141 0.675 0.458 1.872 7.818 0.308 0.770 12 055167 1848 1995 148 0.852 0.525 1.214 4.327 0.316 0.797 13 055171 1842 1995 154 0.516 0.283 1.773 9.488 0.402 0.416 14 055173 1848 1995 148 0.442 0.330 3.221 18.822 0.387 0.586 15 055175 1841 1995 155 0.452 0.274 1.314 4.328 0.413 0.465 16 055177 1841 1995 155 0.418 0.249 2.242 10.137 0.341 0.592 17 055211 1875 1995 121 0.889 0.769 2.401 10.160 0.406 0.709 18 055213 1875 1995 121 0.895 1.108 3.159 12.198 0.368 0.889 19 055215 1875 1995 121 0.699 0.391 1.588 6.787 0.336 0.642 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 055217 1875 1995 121 0.687 0.497 2.667 10.230 0.345 0.763 NUMBER OF SERIES READ IN: 20 FROM 1841 TO 1995 155 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 132 0.658 0.443 1.789 7.788 0.350 0.655 STANDARD DEVIATION 14 0.171 0.208 0.861 4.033 0.036 0.140 MEDIAN (50TH QUANTILE) 127 0.657 0.366 1.823 7.446 0.343 0.644 INTERQUARTILE RANGE 26 0.261 0.198 1.058 5.728 0.059 0.211 MINIMUM VALUE 107 0.418 0.249 -0.020 2.544 0.301 0.416 LOWER HINGE (25TH QUANTILE) 121 0.518 0.313 1.264 4.421 0.319 0.573 UPPER HINGE (75TH QUANTILE) 147 0.779 0.511 2.322 10.148 0.378 0.784 MAXIMUM VALUE 155 0.953 1.108 3.221 18.822 0.413 0.889 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.194 0.219 0.016 0.093 2.697 -0.373 0.752 MINIMUM CORRELATION: -0.373 SERIES 055023 AND 055161 131 YEARS MAXIMUM CORRELATION: 0.752 SERIES 055033 AND 055035 127 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 80.46 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1851. 1870. 1880. 1890. 1900. 1910. 1920. 1930. 1940. 1950. CORR 1. 28. 91. 153. 190. 190. 190. 190. 190. 190. RBAR 0.616 0.730 0.585 0.456 0.228 0.150 0.327 0.288 0.321 0.297 SDEV 0.000 0.236 0.220 0.270 0.419 0.297 0.264 0.284 0.270 0.264 SERR 0.000 0.045 0.023 0.022 0.030 0.022 0.019 0.021 0.020 0.019 EPS 0.904 0.971 0.961 0.942 0.855 0.779 0.907 0.890 0.904 0.894 NSS 5.8 12.6 17.5 19.5 20.0 20.0 20.0 20.0 20.0 20.0 YEAR 1960. 1970. 1980. CORR 190. 190. 190. RBAR 0.149 0.366 0.375 SDEV 0.295 0.305 0.303 SERR 0.021 0.022 0.022 EPS 0.778 0.920 0.923 NSS 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 1841 1995 155 0.546 0.205 0.411 2.942 0.260 0.574 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.797 0.627 -0.058 81 74 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.73 2.25 1.00 1.13 3.39 32.60 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.05 0.49 0.87 0.93 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 128. 27. 107. 121. 148. 155. |----------- 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 0.570 0.473 0.362 0.322 0.285 0.206 0.152 0.137 0.119 0.099 PACF 0.570 0.218 0.041 0.071 0.052 -0.045 -0.030 0.027 0.013 -0.001 95% C.L. 0.161 0.206 0.233 0.247 0.257 0.265 0.269 0.272 0.273 0.275 |------------------ 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 0.384 0.452 0.234 |================== 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 055021 3 0.00000000 0.00000000 0.00063667 0.49739552 2 055023 1 0.41155487 0.04510646 0.00000000 0.43866226 3 055025 3 0.00000000 0.00000000 0.00184055 0.58949631 4 055027 1 1.02820837 0.06379221 0.00000000 0.40113884 5 055031 3 0.00000000 0.00000000 -0.00107471 0.74319082 6 055033 3 0.00000000 0.00000000 -0.00281680 0.80829751 7 055035 3 0.00000000 0.00000000 -0.00480432 0.94692540 8 055037 3 0.00000000 0.00000000 0.00094981 0.89428228 9 055161 3 0.00000000 0.00000000 0.00476760 0.55234867 10 055163 3 0.00000000 0.00000000 -0.00189237 0.66152233 11 055165 3 0.00000000 0.00000000 0.00123734 0.58725530 12 055167 3 0.00000000 0.00000000 0.00448103 0.52330142 13 055171 3 0.00000000 0.00000000 0.00193948 0.36370182 14 055173 3 0.00000000 0.00000000 0.00047463 0.40700495 15 055175 3 0.00000000 0.00000000 -0.00033203 0.48101172 16 055177 3 0.00000000 0.00000000 0.00087954 0.34939590 17 055211 3 0.00000000 0.00000000 0.01114090 0.20966116 18 055213 3 0.00000000 0.00000000 0.01404390 0.03795042 19 055215 3 0.00000000 0.00000000 0.00424637 0.43600494 SERIES IDENT OPTION A B C D 20 055217 3 0.00000000 0.00000000 0.00611929 0.31333470 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 055021 1889 1995 107 1.000 0.565 1.914 7.271 0.306 0.590 2 055023 1865 1995 131 0.998 0.599 1.395 6.112 0.319 0.603 3 055025 1867 1995 129 1.004 0.930 2.887 11.596 0.318 0.821 4 055027 1881 1995 115 1.000 0.446 1.993 11.116 0.362 0.323 5 055031 1869 1995 127 1.000 0.442 0.048 2.577 0.337 0.445 6 055033 1869 1995 127 0.996 0.514 1.076 4.870 0.391 0.526 7 055035 1869 1995 127 0.980 0.542 0.688 3.069 0.362 0.586 8 055037 1869 1991 123 1.000 0.444 0.723 3.295 0.344 0.479 9 055161 1848 1995 148 0.989 0.540 1.688 6.887 0.303 0.763 10 055163 1848 1995 148 0.995 0.661 1.868 6.927 0.309 0.804 11 055165 1855 1995 141 0.999 0.647 1.556 6.345 0.306 0.763 12 055167 1848 1995 148 0.993 0.528 0.800 3.151 0.314 0.733 13 055171 1842 1995 154 0.999 0.499 1.274 6.167 0.397 0.392 14 055173 1848 1995 148 1.000 0.722 2.871 15.940 0.385 0.578 15 055175 1841 1995 155 1.000 0.604 1.304 4.305 0.406 0.473 16 055177 1841 1995 155 1.000 0.562 1.747 7.232 0.339 0.577 17 055211 1875 1995 121 1.017 0.565 0.722 3.862 0.402 0.548 18 055213 1875 1995 121 1.244 1.189 2.381 9.549 0.365 0.770 19 055215 1875 1995 121 0.995 0.504 1.878 9.541 0.331 0.580 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 055217 1875 1995 121 1.008 0.543 1.386 5.215 0.342 0.653 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 133 1.011 0.602 1.510 6.751 0.347 0.600 STANDARD DEVIATION 14 0.055 0.177 0.730 3.404 0.035 0.141 MEDIAN (50TH QUANTILE) 128 1.000 0.553 1.476 6.256 0.340 0.583 INTERQUARTILE RANGE 27 0.005 0.116 0.958 4.323 0.059 0.246 MINIMUM VALUE 107 0.980 0.442 0.048 2.577 0.303 0.323 LOWER HINGE (25TH QUANTILE) 121 0.996 0.509 0.938 4.083 0.316 0.502 UPPER HINGE (75TH QUANTILE) 148 1.000 0.625 1.896 8.406 0.375 0.748 MAXIMUM VALUE 155 1.244 1.189 2.887 15.940 0.406 0.821 |------------------------ 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 055021 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 055023 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 055025 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 055027 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 055031 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 055033 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 055035 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 055037 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 055161 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 055163 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 055165 -67 94 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 055167 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 055171 -67 103 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 055173 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 055175 -67 103 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 055177 -67 103 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 055211 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 055213 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 055215 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 055217 -67 81 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 055021 1889 1995 107 0.991 0.364 0.887 4.333 0.305 0.306 2 055023 1865 1995 131 0.971 0.463 1.138 4.811 0.319 0.545 3 055025 1867 1995 129 0.976 0.516 2.231 9.151 0.319 0.640 4 055027 1881 1995 115 0.993 0.377 1.043 4.482 0.362 0.269 5 055031 1869 1995 127 0.994 0.428 0.150 2.741 0.337 0.439 6 055033 1869 1995 127 0.993 0.467 0.650 3.195 0.391 0.439 7 055035 1869 1995 127 0.989 0.513 2.061 11.272 0.361 0.451 8 055037 1869 1991 123 0.994 0.398 0.683 3.279 0.343 0.397 9 055161 1848 1995 148 0.989 0.436 1.104 4.579 0.303 0.618 10 055163 1848 1995 148 0.988 0.538 1.487 5.286 0.308 0.678 11 055165 1855 1995 141 0.986 0.602 1.783 8.184 0.305 0.723 12 055167 1848 1995 148 0.991 0.492 1.062 4.597 0.314 0.669 13 055171 1842 1995 154 0.996 0.488 1.313 6.503 0.397 0.361 14 055173 1848 1995 148 0.977 0.616 2.682 15.101 0.385 0.511 15 055175 1841 1995 155 0.967 0.445 1.053 4.200 0.404 0.264 16 055177 1841 1995 155 0.980 0.417 0.922 4.595 0.339 0.422 17 055211 1875 1995 121 0.978 0.487 0.239 2.640 0.402 0.474 18 055213 1875 1995 121 0.977 0.616 1.092 4.789 0.367 0.686 19 055215 1875 1995 121 0.996 0.469 1.686 9.125 0.332 0.535 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 055217 1875 1995 121 0.986 0.449 0.877 4.798 0.341 0.570 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 133 0.986 0.479 1.207 5.883 0.347 0.500 STANDARD DEVIATION 14 0.009 0.073 0.634 3.174 0.035 0.141 MEDIAN (50TH QUANTILE) 128 0.988 0.468 1.077 4.693 0.340 0.492 INTERQUARTILE RANGE 27 0.015 0.082 0.704 3.077 0.059 0.220 MINIMUM VALUE 107 0.967 0.364 0.150 2.640 0.303 0.264 LOWER HINGE (25TH QUANTILE) 121 0.978 0.432 0.882 4.266 0.317 0.410 UPPER HINGE (75TH QUANTILE) 148 0.993 0.514 1.586 7.344 0.376 0.629 MAXIMUM VALUE 155 0.996 0.616 2.682 15.101 0.404 0.723 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.283 0.158 0.011 -0.094 2.981 -0.197 0.634 MINIMUM CORRELATION: -0.197 SERIES 055023 AND 055161 131 YEARS MAXIMUM CORRELATION: 0.634 SERIES 055031 AND 055033 127 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 80.46 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1851. 1870. 1880. 1890. 1900. 1910. 1920. 1930. 1940. 1950. CORR 1. 28. 91. 153. 190. 190. 190. 190. 190. 190. RBAR 0.484 0.661 0.572 0.505 0.254 0.146 0.346 0.296 0.323 0.308 SDEV 0.000 0.277 0.235 0.209 0.368 0.296 0.263 0.278 0.264 0.258 SERR 0.000 0.052 0.025 0.017 0.027 0.022 0.019 0.020 0.019 0.019 EPS 0.846 0.961 0.959 0.952 0.872 0.774 0.914 0.894 0.905 0.899 NSS 5.8 12.6 17.5 19.5 20.0 20.0 20.0 20.0 20.0 20.0 YEAR 1960. 1970. 1980. CORR 190. 190. 190. RBAR 0.145 0.440 0.394 SDEV 0.300 0.261 0.291 SERR 0.022 0.019 0.021 EPS 0.772 0.940 0.929 NSS 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 1841 1995 155 0.943 0.271 0.463 3.854 0.239 0.407 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.587 0.302 0.058 49 106 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.23 0.87 1.00 1.11 1.98 23.34 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.07 0.57 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 0.404 0.275 0.170 0.078 0.091 -0.056 -0.122 -0.075 -0.108 -0.125 PACF 0.404 0.133 0.024 -0.031 0.054 -0.135 -0.103 0.029 -0.043 -0.069 95% C.L. 0.161 0.185 0.195 0.199 0.200 0.201 0.201 0.203 0.204 0.205 |------------------ 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 0.184 0.355 0.135 |======================= 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 0.471 0.317 0.165 0.096 0.017 -0.077 -0.168 -0.123 -0.142 -0.165 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 0.471 2 0.413 0.123 3 0.417 0.136 -0.032 4 0.417 0.136 -0.031 -0.002 5 0.416 0.135 -0.025 0.017 -0.045 6 0.412 0.137 -0.027 0.031 -0.003 -0.100 7 0.400 0.136 -0.024 0.027 0.014 -0.050 -0.123 8 0.403 0.138 -0.024 0.026 0.014 -0.054 -0.135 0.031 9 0.405 0.131 -0.027 0.027 0.016 -0.055 -0.129 0.051 -0.048 10 0.401 0.136 -0.037 0.023 0.017 -0.053 -0.131 0.061 -0.014 -0.082 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) 1276.64 1239.83 1239.47 1241.31 1243.31 1245.00 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1245.43 1245.08 1246.93 1248.58 1249.53 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 0.413 0.123 R-SQUARED DUE TO POOLED AUTOREGRESSION: 23.33 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 130.42 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.413 0.293 0.172 0.107 0.065 0.040 0.025 0.015 0.009 0.0057 0.003 0.002 0.001 0.001 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 055021 2 0.120 0.293 0.060 2 055023 2 0.347 0.448 0.202 3 055025 2 0.426 0.716 -0.110 4 055027 2 0.084 0.277 0.026 5 055031 2 0.245 0.335 0.243 6 055033 2 0.218 0.374 0.159 7 055035 2 0.270 0.493 0.047 8 055037 2 0.177 0.357 0.108 9 055161 2 0.385 0.599 0.033 10 055163 2 0.488 0.659 0.046 11 055165 2 0.530 0.730 -0.003 12 055167 2 0.453 0.635 0.055 13 055171 2 0.146 0.319 0.119 14 055173 2 0.266 0.481 0.061 15 055175 2 0.170 0.221 0.186 16 055177 2 0.196 0.397 0.079 17 055211 2 0.259 0.394 0.179 18 055213 2 0.484 0.640 0.077 19 055215 2 0.296 0.584 -0.091 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 055217 2 0.352 0.503 0.127 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.295 0.473 0.080 STANDARD DEVIATION 0 0.132 0.155 0.090 MEDIAN 2 0.268 0.465 0.069 INTERQUARTILE RANGE 0 0.219 0.271 0.103 MINIMUM VALUE 2 0.084 0.221 -0.110 LOWER HINGE 2 0.186 0.346 0.040 UPPER HINGE 2 0.406 0.617 0.143 MAXIMUM VALUE 2 0.530 0.730 0.243 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 055021 1889 1995 107 1.000 0.345 1.067 4.683 0.347 0.003 2 055023 1865 1995 131 1.000 0.374 1.317 5.450 0.370 -0.012 3 055025 1867 1995 129 1.000 0.390 1.379 7.635 0.412 -0.011 4 055027 1881 1995 115 1.000 0.361 1.032 4.581 0.404 0.013 5 055031 1869 1995 127 1.000 0.372 0.424 3.347 0.384 0.011 6 055033 1869 1995 127 1.000 0.412 0.656 3.377 0.467 0.003 7 055035 1869 1995 127 1.000 0.438 1.354 6.417 0.442 0.066 8 055037 1869 1991 123 1.000 0.363 0.972 4.723 0.393 0.008 9 055161 1848 1995 148 1.000 0.342 0.813 4.885 0.367 -0.003 10 055163 1848 1995 148 1.000 0.388 1.582 9.141 0.391 0.018 11 055165 1855 1995 141 1.000 0.413 1.726 10.217 0.402 0.005 12 055167 1848 1995 148 1.000 0.364 1.426 8.958 0.383 0.002 13 055171 1842 1995 154 1.001 0.450 1.155 6.055 0.475 -0.008 14 055173 1848 1995 148 1.003 0.521 1.952 9.471 0.483 0.036 15 055175 1841 1995 155 1.000 0.421 1.010 4.252 0.446 -0.039 16 055177 1841 1995 155 1.000 0.375 1.135 5.579 0.385 0.000 17 055211 1875 1995 121 1.000 0.420 0.606 3.075 0.453 0.016 18 055213 1875 1995 121 1.000 0.441 0.976 4.395 0.461 -0.006 19 055215 1875 1995 121 1.000 0.395 1.240 6.767 0.421 0.007 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 055217 1875 1995 121 1.000 0.364 0.664 4.417 0.420 0.021 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 133 1.000 0.397 1.124 5.871 0.415 0.006 STANDARD DEVIATION 14 0.001 0.043 0.389 2.168 0.039 0.021 MEDIAN (50TH QUANTILE) 128 1.000 0.389 1.101 5.168 0.408 0.004 INTERQUARTILE RANGE 27 0.000 0.056 0.474 2.795 0.065 0.019 MINIMUM VALUE 107 1.000 0.342 0.424 3.075 0.347 -0.039 LOWER HINGE (25TH QUANTILE) 121 1.000 0.364 0.892 4.406 0.385 -0.004 UPPER HINGE (75TH QUANTILE) 148 1.000 0.420 1.366 7.201 0.449 0.014 MAXIMUM VALUE 155 1.003 0.521 1.952 10.217 0.483 0.066 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.301 0.137 0.010 0.125 2.668 -0.019 0.601 MINIMUM CORRELATION: -0.019 SERIES 055025 AND 055165 129 YEARS MAXIMUM CORRELATION: 0.601 SERIES 055035 AND 055037 123 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 80.46 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1851. 1870. 1880. 1890. 1900. 1910. 1920. 1930. 1940. 1950. CORR 1. 28. 91. 153. 190. 190. 190. 190. 190. 190. RBAR 0.467 0.598 0.523 0.390 0.263 0.225 0.407 0.338 0.303 0.355 SDEV 0.000 0.210 0.238 0.272 0.277 0.247 0.206 0.236 0.251 0.229 SERR 0.000 0.040 0.025 0.022 0.020 0.018 0.015 0.017 0.018 0.017 EPS 0.837 0.949 0.951 0.926 0.877 0.853 0.932 0.911 0.897 0.917 NSS 5.8 12.6 17.5 19.5 20.0 20.0 20.0 20.0 20.0 20.0 YEAR 1960. 1970. 1980. CORR 190. 190. 190. RBAR 0.225 0.346 0.354 SDEV 0.238 0.237 0.254 SERR 0.017 0.017 0.018 EPS 0.853 0.914 0.916 NSS 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 1841 1995 155 0.973 0.238 0.381 3.475 0.276 -0.066 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.509 0.243 0.043 57 98 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.19 1.08 1.01 1.06 2.14 8.53 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.63 0.86 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 -0.065 0.008 0.012 -0.015 0.098 -0.076 -0.088 0.048 -0.052 0.000 PACF -0.065 0.004 0.013 -0.013 0.096 -0.065 -0.100 0.036 -0.043 -0.016 95% C.L. 0.161 0.161 0.161 0.161 0.161 0.163 0.164 0.165 0.165 0.166 |------------------ RESIDUAL CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 0 0.000 |---------- REWHITENED CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS -----------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF -0.001 0.001 0.012 -0.007 0.094 -0.076 -0.091 0.038 -0.047 -0.008 PACF -0.001 0.001 0.012 -0.007 0.094 -0.077 -0.092 0.037 -0.045 -0.016 95% C.L. 0.161 0.161 0.161 0.161 0.161 0.162 0.163 0.164 0.165 0.165 |----------------- 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 -0.001 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 1841 1995 155 0.969 0.272 0.379 3.797 0.226 0.468 |------------ 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 0.465 0.315 0.200 0.116 0.096 -0.041 -0.088 -0.056 -0.100 -0.108 PACF 0.465 0.126 0.016 -0.013 0.032 -0.135 -0.063 0.038 -0.062 -0.044 95% C.L. 0.161 0.192 0.205 0.210 0.212 0.213 0.213 0.214 0.214 0.216 |------------------- 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 0.233 0.410 0.127 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.31 MINUTES