RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM045E.rwl.conv LOG FILE PROCESSED: GERM045E.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: 026 1 Sulzbach-Tal (D), EU-Pr. WIDTH_EARLY ABAL - 026 2 Germany silver fir, European fir 390 4750-742 1894 1995 - 026 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 7 026025 MISSING VALUES FOUND: 1 IN 1 GAPS / 1931 1931 / -------------------------------------------------------------------- 13 026041 MISSING VALUES FOUND: 1 IN 1 GAPS / 1956 1956 / -------------------------------------------------------------------- 15 026045 MISSING VALUES FOUND: 1 IN 1 GAPS / 1956 1956 / -------------------------------------------------------------------- 16 026047 MISSING VALUES FOUND: 1 IN 1 GAPS / 1970 1970 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 026011 1901 1995 95 2.052 1.215 0.221 2.270 0.375 0.658 2 026013 1901 1995 95 1.812 1.092 0.765 3.278 0.339 0.713 3 026015 1901 1995 95 1.723 1.040 0.655 2.624 0.345 0.759 4 026017 1901 1995 95 2.065 1.055 0.332 2.696 0.351 0.625 5 026021 1910 1995 86 1.947 0.903 0.624 3.006 0.298 0.724 6 026023 1910 1995 86 1.849 1.100 0.760 2.670 0.299 0.820 7 026025 1910 1995 86 2.042 1.084 0.753 3.062 0.300 0.768 8 026027 1911 1995 85 2.131 0.883 0.688 3.462 0.289 0.664 9 026031 1898 1995 98 2.166 1.369 0.558 2.484 0.309 0.833 10 026033 1899 1995 97 2.301 1.457 0.464 2.168 0.287 0.823 11 026035 1900 1995 96 2.016 1.399 0.891 2.485 0.300 0.868 12 026037 1898 1995 98 2.381 1.501 0.645 2.632 0.303 0.830 13 026041 1896 1995 100 1.474 1.126 1.292 3.959 0.288 0.855 14 026043 1894 1995 102 1.741 1.174 0.525 2.576 0.341 0.833 15 026045 1899 1995 97 2.080 1.347 0.549 2.274 0.349 0.806 16 026047 1895 1995 101 1.802 1.397 0.861 2.812 0.336 0.865 17 026051 1918 1995 78 2.962 1.613 0.481 2.800 0.445 0.437 18 026053 1919 1995 77 2.629 1.561 0.696 3.063 0.326 0.710 19 026055 1919 1995 77 3.604 1.648 0.268 2.676 0.378 0.485 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 026057 1921 1995 75 3.273 1.519 0.609 2.454 0.343 0.603 NUMBER OF SERIES READ IN: 20 FROM 1894 TO 1995 102 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 91 2.203 1.274 0.632 2.773 0.330 0.734 STANDARD DEVIATION 8 0.538 0.236 0.238 0.435 0.039 0.124 MEDIAN (50TH QUANTILE) 95 2.059 1.281 0.635 2.673 0.331 0.764 INTERQUARTILE RANGE 12 0.510 0.391 0.254 0.550 0.047 0.171 MINIMUM VALUE 75 1.474 0.883 0.221 2.168 0.287 0.437 LOWER HINGE (25TH QUANTILE) 85 1.831 1.088 0.503 2.484 0.300 0.661 UPPER HINGE (75TH QUANTILE) 97 2.341 1.479 0.757 3.034 0.347 0.831 MAXIMUM VALUE 102 3.604 1.648 1.292 3.959 0.445 0.868 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.553 0.268 0.019 -0.979 2.964 -0.168 0.879 MINIMUM CORRELATION: -0.168 SERIES 026033 AND 026055 77 YEARS MAXIMUM CORRELATION: 0.879 SERIES 026031 AND 026037 98 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 84.28 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 105. 171. 190. 190. 190. 190. 190. RBAR 0.478 0.523 0.645 0.464 0.446 0.373 0.301 SDEV 0.224 0.242 0.174 0.235 0.273 0.310 0.410 SERR 0.022 0.019 0.013 0.017 0.020 0.022 0.030 EPS 0.943 0.956 0.973 0.945 0.942 0.922 0.896 NSS 18.1 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 1894 1995 102 2.020 1.052 0.559 2.628 0.282 0.810 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.465 0.173 0.425 39 63 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.34 3.17 1.00 1.15 4.32 305.97 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.00 0.86 0.92 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 95. 12. 75. 86. 98. 102. |----------- 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 0.802 0.749 0.683 0.641 0.578 0.581 0.497 0.436 0.411 0.397 PACF 0.802 0.298 0.067 0.066 -0.029 0.151 -0.138 -0.095 0.071 0.068 95% C.L. 0.198 0.299 0.366 0.413 0.450 0.478 0.505 0.524 0.538 0.550 |------------------ 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 0.696 0.556 0.317 |================== 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 026011 3 0.00000000 0.00000000 -0.02888368 3.43883777 2 026013 1 2.90082431 0.01915691 0.00000000 0.48928902 3 026015 3 0.00000000 0.00000000 -0.02853751 3.09306383 4 026017 3 0.00000000 0.00000000 -0.02517735 3.27335501 5 026021 1 2.36708450 0.05047413 0.00000000 1.42213833 6 026023 1 3.87695384 0.01971348 0.00000000 0.00071997 7 026025 1 3.15373993 0.03960667 0.00000000 1.17696357 8 026027 1 2.59790373 0.06262409 0.00000000 1.66080010 9 026031 3 0.00000000 0.00000000 -0.03525040 3.91132331 10 026033 3 0.00000000 0.00000000 -0.02881641 3.71313787 11 026035 3 0.00000000 0.00000000 -0.03499518 3.71320391 12 026037 3 0.00000000 0.00000000 -0.03376770 4.05282784 13 026041 1 2.59490395 0.01717043 0.00000000 0.23849604 14 026043 3 0.00000000 0.00000000 -0.02039909 2.79172969 15 026045 3 0.00000000 0.00000000 -0.02903336 3.49147892 16 026047 3 0.00000000 0.00000000 -0.02731209 3.18295908 17 026051 3 0.00000000 0.00000000 -0.00953679 3.33849812 18 026053 3 0.00000000 0.00000000 -0.03160629 3.86212587 19 026055 3 0.00000000 0.00000000 0.00939718 3.23740602 SERIES IDENT OPTION A B C D 20 026057 3 0.00000000 0.00000000 -0.02683016 4.29207945 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 026011 1901 1995 95 1.021 0.640 1.965 9.596 0.373 0.502 2 026013 1901 1995 95 1.003 0.553 1.095 4.196 0.337 0.670 3 026015 1901 1995 95 0.998 0.391 0.487 2.735 0.342 0.401 4 026017 1901 1995 95 0.989 0.411 0.566 4.037 0.346 0.373 5 026021 1910 1995 86 1.000 0.386 0.503 3.327 0.294 0.546 6 026023 1910 1995 86 1.013 0.434 1.253 4.902 0.295 0.391 7 026025 1910 1995 86 1.001 0.411 0.507 3.722 0.294 0.558 8 026027 1911 1995 85 1.000 0.327 0.435 3.378 0.283 0.422 9 026031 1898 1995 98 1.007 0.475 0.987 5.418 0.306 0.594 10 026033 1899 1995 97 1.024 0.668 1.333 4.900 0.286 0.810 11 026035 1900 1995 96 1.085 0.749 2.660 11.528 0.298 0.659 12 026037 1898 1995 98 0.993 0.477 0.306 2.592 0.302 0.686 13 026041 1896 1995 100 1.012 0.760 2.095 8.267 0.290 0.785 14 026043 1894 1995 102 1.017 0.685 0.996 4.071 0.338 0.797 15 026045 1899 1995 97 1.025 0.617 1.037 3.980 0.351 0.641 16 026047 1895 1995 101 1.083 0.987 2.513 9.664 0.331 0.804 17 026051 1918 1995 78 0.999 0.555 0.683 3.327 0.439 0.430 18 026053 1919 1995 77 0.984 0.531 0.772 2.683 0.320 0.620 19 026055 1919 1995 77 1.000 0.453 0.235 2.586 0.373 0.491 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 026057 1921 1995 75 0.997 0.426 0.810 3.506 0.338 0.488 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 91 1.013 0.547 1.062 4.921 0.327 0.583 STANDARD DEVIATION 8 0.027 0.164 0.718 2.655 0.039 0.146 MEDIAN (50TH QUANTILE) 95 1.002 0.504 0.898 4.008 0.326 0.576 INTERQUARTILE RANGE 12 0.021 0.235 0.788 1.833 0.050 0.219 MINIMUM VALUE 75 0.984 0.327 0.235 2.586 0.283 0.373 LOWER HINGE (25TH QUANTILE) 85 0.998 0.419 0.505 3.327 0.295 0.459 UPPER HINGE (75TH QUANTILE) 97 1.019 0.654 1.293 5.160 0.344 0.678 MAXIMUM VALUE 102 1.085 0.987 2.660 11.528 0.439 0.810 |------------------------ 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 026011 -67 63 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 026013 -67 63 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 026015 -67 63 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 026017 -67 63 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 026021 -67 57 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 026023 -67 57 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 026025 -67 57 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 026027 -67 56 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 026031 -67 65 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 026033 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 026035 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 026037 -67 65 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 026041 -67 67 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 026043 -67 68 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 026045 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 026047 -67 67 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 026051 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 026053 -67 51 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 026055 -67 51 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 026057 -67 50 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 026011 1901 1995 95 0.980 0.529 1.247 5.680 0.369 0.382 2 026013 1901 1995 95 0.984 0.470 0.609 3.242 0.335 0.560 3 026015 1901 1995 95 0.996 0.380 0.482 2.751 0.342 0.381 4 026017 1901 1995 95 0.994 0.394 0.441 3.081 0.346 0.349 5 026021 1910 1995 86 0.990 0.343 0.387 2.843 0.292 0.448 6 026023 1910 1995 86 0.988 0.309 0.493 3.785 0.295 0.152 7 026025 1910 1995 86 0.983 0.360 0.499 4.037 0.293 0.460 8 026027 1911 1995 85 0.997 0.310 0.306 2.915 0.283 0.362 9 026031 1898 1995 98 0.975 0.354 0.144 3.529 0.304 0.451 10 026033 1899 1995 97 0.955 0.381 -0.095 2.558 0.286 0.632 11 026035 1900 1995 96 0.978 0.378 0.109 2.496 0.296 0.541 12 026037 1898 1995 98 0.978 0.409 0.388 2.925 0.300 0.579 13 026041 1896 1995 100 0.962 0.521 1.218 4.276 0.286 0.685 14 026043 1894 1995 102 0.923 0.423 0.459 2.727 0.335 0.587 15 026045 1899 1995 97 0.978 0.526 1.528 6.970 0.349 0.546 16 026047 1895 1995 101 0.949 0.466 0.852 3.842 0.329 0.436 17 026051 1918 1995 78 0.965 0.492 0.961 4.205 0.438 0.376 18 026053 1919 1995 77 0.977 0.420 0.894 3.182 0.316 0.518 19 026055 1919 1995 77 0.982 0.409 0.537 3.035 0.373 0.434 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 026057 1921 1995 75 0.993 0.396 0.710 3.249 0.338 0.436 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 91 0.976 0.413 0.609 3.566 0.325 0.466 STANDARD DEVIATION 8 0.018 0.068 0.407 1.102 0.039 0.120 MEDIAN (50TH QUANTILE) 95 0.979 0.403 0.496 3.212 0.322 0.449 INTERQUARTILE RANGE 12 0.019 0.099 0.485 1.061 0.049 0.171 MINIMUM VALUE 75 0.923 0.309 -0.095 2.496 0.283 0.152 LOWER HINGE (25TH QUANTILE) 85 0.970 0.369 0.388 2.879 0.294 0.382 UPPER HINGE (75TH QUANTILE) 97 0.989 0.468 0.873 3.940 0.344 0.553 MAXIMUM VALUE 102 0.997 0.529 1.528 6.970 0.438 0.685 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.364 0.201 0.015 -0.195 2.582 -0.217 0.768 MINIMUM CORRELATION: -0.217 SERIES 026033 AND 026051 78 YEARS MAXIMUM CORRELATION: 0.768 SERIES 026051 AND 026055 77 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 84.28 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 105. 171. 190. 190. 190. 190. 190. RBAR 0.448 0.562 0.478 0.426 0.448 0.412 0.371 SDEV 0.257 0.200 0.241 0.256 0.250 0.305 0.352 SERR 0.025 0.015 0.017 0.019 0.018 0.022 0.026 EPS 0.936 0.962 0.948 0.937 0.942 0.933 0.922 NSS 18.1 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 1894 1995 102 0.932 0.285 0.035 2.410 0.251 0.477 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.383 0.171 0.116 37 65 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.34 0.55 1.02 1.16 1.71 5.29 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.00 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 0.472 0.386 0.237 0.162 0.043 0.056 -0.151 -0.228 -0.218 -0.161 PACF 0.472 0.210 -0.008 -0.007 -0.085 0.045 -0.229 -0.163 0.004 0.060 95% C.L. 0.198 0.238 0.261 0.270 0.274 0.274 0.274 0.277 0.285 0.291 |------------------ 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 0.264 0.373 0.217 |======================= 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 0.353 0.302 0.172 0.092 -0.054 -0.024 -0.278 -0.289 -0.264 -0.173 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 0.353 2 0.282 0.203 3 0.278 0.198 0.018 4 0.278 0.203 0.026 -0.027 5 0.275 0.207 0.053 0.011 -0.135 6 0.276 0.206 0.053 0.009 -0.137 0.009 7 0.278 0.168 0.055 0.024 -0.080 0.086 -0.277 8 0.234 0.182 0.042 0.027 -0.071 0.112 -0.233 -0.159 9 0.228 0.173 0.047 0.025 -0.070 0.114 -0.226 -0.150 -0.040 10 0.230 0.180 0.058 0.019 -0.067 0.113 -0.228 -0.158 -0.051 0.048 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) 793.42 781.82 779.53 781.50 783.43 783.56 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 785.55 779.38 778.77 780.61 782.38 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 0.282 0.203 R-SQUARED DUE TO POOLED AUTOREGRESSION: 16.08 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 119.17 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.282 0.282 0.137 0.096 0.055 0.035 0.021 0.013 0.008 0.0049 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 026011 2 0.215 0.293 0.259 2 026013 2 0.405 0.406 0.286 3 026015 2 0.221 0.293 0.248 4 026017 2 0.178 0.275 0.224 5 026021 2 0.218 0.400 0.118 6 026023 2 0.044 0.151 0.030 7 026025 2 0.243 0.388 0.171 8 026027 2 0.197 0.302 0.168 9 026031 2 0.255 0.348 0.238 10 026033 2 0.440 0.495 0.219 11 026035 2 0.335 0.480 0.138 12 026037 2 0.354 0.551 0.056 13 026041 2 0.479 0.619 0.100 14 026043 2 0.420 0.419 0.293 15 026045 2 0.328 0.454 0.171 16 026047 2 0.262 0.335 0.241 17 026051 2 0.201 0.320 0.166 18 026053 2 0.285 0.465 0.109 19 026055 2 0.208 0.422 0.040 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 026057 2 0.202 0.427 0.032 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.274 0.392 0.165 STANDARD DEVIATION 0 0.106 0.107 0.085 MEDIAN 2 0.249 0.403 0.169 INTERQUARTILE RANGE 0 0.139 0.149 0.135 MINIMUM VALUE 2 0.044 0.151 0.030 LOWER HINGE 2 0.205 0.311 0.105 UPPER HINGE 2 0.344 0.460 0.240 MAXIMUM VALUE 2 0.479 0.619 0.293 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 026011 1901 1995 95 1.000 0.468 1.948 9.137 0.420 -0.007 2 026013 1901 1995 95 1.000 0.369 1.228 5.590 0.384 0.057 3 026015 1901 1995 95 1.000 0.338 0.399 2.618 0.381 0.033 4 026017 1901 1995 95 1.000 0.358 0.762 3.243 0.389 0.022 5 026021 1910 1995 86 1.000 0.304 0.509 3.063 0.343 0.000 6 026023 1910 1995 86 1.000 0.305 0.547 3.776 0.307 -0.005 7 026025 1910 1995 86 1.000 0.312 0.616 3.883 0.339 0.006 8 026027 1911 1995 85 1.000 0.285 0.324 2.940 0.335 -0.036 9 026031 1898 1995 98 1.000 0.305 0.709 4.598 0.332 -0.012 10 026033 1899 1995 97 1.000 0.287 0.124 4.098 0.322 -0.033 11 026035 1900 1995 96 1.000 0.309 0.374 3.224 0.345 -0.016 12 026037 1898 1995 98 1.000 0.331 0.455 3.526 0.389 -0.008 13 026041 1896 1995 100 1.000 0.376 0.902 4.873 0.380 -0.001 14 026043 1894 1995 102 1.000 0.325 0.660 3.862 0.358 -0.049 15 026045 1899 1995 97 1.000 0.433 1.159 6.855 0.454 0.015 16 026047 1895 1995 101 1.002 0.398 0.806 5.244 0.391 -0.027 17 026051 1918 1995 78 1.000 0.448 0.875 3.510 0.489 -0.022 18 026053 1919 1995 77 1.000 0.355 0.589 3.456 0.395 0.004 19 026055 1919 1995 77 1.000 0.367 0.480 2.575 0.430 -0.001 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 026057 1921 1995 75 1.000 0.355 0.475 3.027 0.407 -0.001 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 91 1.000 0.351 0.697 4.155 0.380 -0.004 STANDARD DEVIATION 8 0.001 0.053 0.400 1.592 0.046 0.024 MEDIAN (50TH QUANTILE) 95 1.000 0.346 0.603 3.651 0.383 -0.003 INTERQUARTILE RANGE 12 0.000 0.065 0.376 1.592 0.060 0.024 MINIMUM VALUE 75 1.000 0.285 0.124 2.575 0.307 -0.049 LOWER HINGE (25TH QUANTILE) 85 1.000 0.307 0.465 3.143 0.341 -0.019 UPPER HINGE (75TH QUANTILE) 97 1.000 0.372 0.841 4.735 0.401 0.005 MAXIMUM VALUE 102 1.002 0.468 1.948 9.137 0.489 0.057 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.425 0.142 0.010 0.179 2.557 0.113 0.790 MINIMUM CORRELATION: 0.113 SERIES 026033 AND 026051 78 YEARS MAXIMUM CORRELATION: 0.790 SERIES 026051 AND 026055 77 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 84.28 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 105. 171. 190. 190. 190. 190. 190. RBAR 0.460 0.570 0.545 0.518 0.501 0.431 0.404 SDEV 0.239 0.160 0.170 0.181 0.188 0.214 0.260 SERR 0.023 0.012 0.012 0.013 0.014 0.016 0.019 EPS 0.939 0.964 0.960 0.956 0.953 0.938 0.931 NSS 18.1 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 1894 1995 102 0.974 0.231 0.123 2.781 0.275 -0.004 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.489 0.197 0.025 44 58 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.46 0.72 1.02 1.17 1.89 17.59 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 0.00 0.87 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 -0.004 0.049 0.032 0.025 -0.054 0.136 -0.122 -0.172 -0.107 -0.064 PACF -0.004 0.049 0.033 0.023 -0.058 0.133 -0.121 -0.186 -0.108 -0.054 95% C.L. 0.198 0.198 0.199 0.199 0.199 0.199 0.203 0.206 0.211 0.214 |------------------ 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 -0.002 -0.001 0.035 0.016 -0.050 0.143 -0.115 -0.177 -0.102 -0.059 PACF -0.002 -0.001 0.035 0.016 -0.050 0.142 -0.119 -0.177 -0.114 -0.064 95% C.L. 0.198 0.198 0.198 0.198 0.198 0.199 0.203 0.205 0.211 0.213 |----------------- 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 -0.002 -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 1894 1995 102 0.974 0.253 0.109 2.434 0.234 0.364 |------------ 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 0.360 0.310 0.178 0.118 0.007 0.064 -0.145 -0.209 -0.182 -0.130 PACF 0.360 0.207 0.018 -0.002 -0.081 0.066 -0.198 -0.171 -0.017 0.037 95% C.L. 0.198 0.222 0.239 0.244 0.246 0.246 0.247 0.250 0.257 0.262 |------------------- 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 0.170 0.286 0.211 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.22 MINUTES