RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM044E.rwl.conv LOG FILE PROCESSED: GERM044E.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: 025 1 Sulzbach-Tal (D), EU-Pr. WIDTH_EARLY PCAB - 025 2 Germany Norway spruce 390 4750-742 1890 1995 - 025 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 17 025101 MISSING VALUES FOUND: 5 IN 1 GAPS / 1899 1903 / -------------------------------------------------------------------- 18 025103 MISSING VALUES FOUND: 4 IN 1 GAPS / 1899 1902 / -------------------------------------------------------------------- 19 025105 MISSING VALUES FOUND: 2 IN 1 GAPS / 1908 1909 / -------------------------------------------------------------------- 20 025107 MISSING VALUES FOUND: 10 IN 1 GAPS / 1904 1913 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 025021 1917 1995 79 3.786 1.439 0.221 2.096 0.204 0.794 2 025023 1917 1995 79 2.995 1.464 0.819 2.801 0.251 0.803 3 025025 1917 1995 79 2.999 1.492 1.045 3.338 0.228 0.809 4 025027 1917 1995 79 3.092 1.335 0.410 2.191 0.204 0.824 5 025031 1917 1995 79 2.089 1.023 1.437 5.101 0.301 0.681 6 025033 1917 1995 79 1.717 1.002 0.987 3.228 0.380 0.722 7 025035 1917 1995 79 1.985 0.884 0.766 3.377 0.305 0.590 8 025037 1917 1995 79 2.594 0.962 0.424 3.164 0.309 0.519 9 025061 1890 1995 106 2.495 1.424 1.016 3.359 0.344 0.723 10 025063 1890 1995 106 2.194 1.331 1.081 3.686 0.308 0.810 11 025065 1890 1995 106 2.716 1.646 1.443 4.717 0.348 0.744 12 025067 1890 1995 106 2.779 1.286 1.075 3.850 0.319 0.663 13 025091 1893 1995 103 1.727 1.008 1.605 4.886 0.260 0.847 14 025093 1893 1995 103 1.537 1.013 1.596 4.407 0.258 0.876 15 025095 1893 1995 103 1.965 0.851 1.143 4.909 0.270 0.675 16 025097 1893 1995 103 1.822 0.990 1.647 7.275 0.273 0.739 17 025101 1891 1995 105 1.709 0.998 1.049 3.796 0.398 0.683 18 025103 1891 1995 105 1.906 1.071 0.684 2.883 0.395 0.680 19 025105 1892 1995 104 1.967 1.092 0.944 4.036 0.355 0.648 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 025107 1891 1995 105 1.732 1.018 1.238 4.860 0.415 0.714 NUMBER OF SERIES READ IN: 20 FROM 1890 TO 1995 106 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 93 2.290 1.167 1.031 3.898 0.306 0.727 STANDARD DEVIATION 12 0.608 0.235 0.403 1.193 0.063 0.089 MEDIAN (50TH QUANTILE) 100 2.037 1.047 1.047 3.741 0.307 0.722 INTERQUARTILE RANGE 24 0.971 0.380 0.545 1.593 0.092 0.128 MINIMUM VALUE 79 1.537 0.851 0.221 2.096 0.204 0.519 LOWER HINGE (25TH QUANTILE) 79 1.777 1.000 0.793 3.196 0.259 0.678 UPPER HINGE (75TH QUANTILE) 103 2.748 1.380 1.337 4.789 0.352 0.806 MAXIMUM VALUE 106 3.786 1.646 1.647 7.275 0.415 0.876 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.448 0.233 0.017 -0.118 2.309 -0.117 0.897 MINIMUM CORRELATION: -0.117 SERIES 025031 AND 025095 79 YEARS MAXIMUM CORRELATION: 0.897 SERIES 025023 AND 025025 79 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 82.67 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 6. 66. 190. 190. 190. 190. 190. 190. RBAR 0.796 0.675 0.480 0.518 0.519 0.568 0.353 0.206 SDEV 0.081 0.170 0.279 0.332 0.247 0.208 0.268 0.316 SERR 0.033 0.021 0.020 0.024 0.018 0.015 0.019 0.023 EPS 0.978 0.973 0.949 0.956 0.956 0.963 0.916 0.838 NSS 11.1 17.2 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 1890 1995 106 2.291 0.850 0.535 2.479 0.228 0.719 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.593 0.317 0.300 29 77 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.14 0.40 1.01 1.09 1.49 3.33 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.42 0.85 0.92 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 103. 26. 79. 79. 105. 106. |----------- 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 0.712 0.554 0.583 0.486 0.368 0.380 0.373 0.321 0.285 0.361 PACF 0.712 0.096 0.323 -0.089 -0.041 0.101 0.046 0.033 -0.034 0.213 95% C.L. 0.194 0.276 0.315 0.353 0.378 0.391 0.405 0.417 0.427 0.434 |------------------ 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 1 0.524 0.719 |================== 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 025021 3 0.00000000 0.00000000 -0.04982522 5.77908468 2 025023 1 5.11871099 0.02320906 0.00000000 0.67637700 3 025025 1 5.16295242 0.02655299 0.00000000 0.86885405 4 025027 3 0.00000000 0.00000000 -0.04930063 5.06379747 5 025031 1 1.74278033 0.04720696 0.00000000 1.64358139 6 025033 3 0.00000000 0.00000000 -0.02419791 2.68500495 7 025035 3 0.00000000 0.00000000 -0.01586782 2.61939621 8 025037 3 0.00000000 0.00000000 -0.01198759 3.07368064 9 025061 1 4.10635376 0.03469326 0.00000000 1.42560244 10 025063 3 0.00000000 0.00000000 -0.03055526 3.82885718 11 025065 3 0.00000000 0.00000000 -0.03075049 4.36128283 12 025067 1 2.90090370 0.02378068 0.00000000 1.73324478 13 025091 1 3.60070205 0.05657611 0.00000000 1.12828326 14 025093 1 3.72757673 0.05857246 0.00000000 0.93818808 15 025095 1 2.46199203 0.07785241 0.00000000 1.67001545 16 025097 1 3.20292616 0.07688031 0.00000000 1.43305683 17 025101 3 0.00000000 0.00000000 -0.01798743 2.67143822 18 025103 1 1.29655492 0.02803165 0.00000000 1.48500025 19 025105 1 1.19368792 0.02249422 0.00000000 1.53405130 SERIES IDENT OPTION A B C D 20 025107 3 0.00000000 0.00000000 -0.01747819 2.78727889 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 025021 1917 1995 79 0.997 0.216 -0.286 3.280 0.200 0.425 2 025023 1917 1995 79 0.998 0.275 0.236 2.855 0.246 0.396 3 025025 1917 1995 79 1.000 0.255 0.229 2.354 0.225 0.415 4 025027 1917 1995 79 1.014 0.282 0.918 5.122 0.200 0.559 5 025031 1917 1995 79 1.000 0.424 1.176 5.479 0.298 0.584 6 025033 1917 1995 79 1.004 0.470 0.945 4.519 0.373 0.447 7 025035 1917 1995 79 0.995 0.394 0.841 3.867 0.301 0.504 8 025037 1917 1995 79 1.000 0.349 0.144 2.767 0.304 0.436 9 025061 1890 1995 106 1.001 0.408 0.498 3.185 0.342 0.317 10 025063 1890 1995 106 1.035 0.466 0.689 3.178 0.307 0.557 11 025065 1890 1995 106 1.012 0.477 0.960 3.719 0.346 0.492 12 025067 1890 1995 106 1.000 0.376 0.701 3.025 0.316 0.413 13 025091 1893 1995 103 1.001 0.318 0.285 2.526 0.258 0.470 14 025093 1893 1995 103 1.003 0.349 0.628 3.991 0.254 0.522 15 025095 1893 1995 103 1.000 0.351 0.524 3.294 0.266 0.484 16 025097 1893 1995 103 1.000 0.416 0.787 3.077 0.269 0.582 17 025101 1891 1995 105 1.009 0.457 0.331 3.050 0.395 0.478 18 025103 1891 1995 105 1.000 0.541 0.884 3.835 0.396 0.659 19 025105 1892 1995 104 1.000 0.531 0.811 3.771 0.349 0.653 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 025107 1891 1995 105 1.005 0.512 0.803 3.523 0.392 0.586 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 1.004 0.393 0.605 3.521 0.302 0.499 STANDARD DEVIATION 12 0.009 0.094 0.356 0.805 0.062 0.089 MEDIAN (50TH QUANTILE) 103 1.000 0.401 0.695 3.287 0.303 0.488 INTERQUARTILE RANGE 26 0.005 0.135 0.555 0.813 0.091 0.140 MINIMUM VALUE 79 0.995 0.216 -0.286 2.354 0.200 0.317 LOWER HINGE (25TH QUANTILE) 79 1.000 0.333 0.308 3.038 0.256 0.431 UPPER HINGE (75TH QUANTILE) 105 1.005 0.468 0.863 3.851 0.347 0.570 MAXIMUM VALUE 106 1.035 0.541 1.176 5.479 0.396 0.659 |------------------------ 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 025021 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 025023 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 025025 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 025027 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 025031 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 025033 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 025035 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 025037 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 025061 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 025063 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 025065 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 025067 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 025091 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 025093 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 025095 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 025097 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 025101 -67 70 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 025103 -67 70 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 025105 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 025107 -67 70 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 025021 1917 1995 79 0.999 0.207 -0.413 3.368 0.199 0.372 2 025023 1917 1995 79 0.997 0.253 0.001 2.491 0.246 0.294 3 025025 1917 1995 79 0.998 0.242 0.085 2.383 0.224 0.371 4 025027 1917 1995 79 0.994 0.214 0.215 4.056 0.201 0.354 5 025031 1917 1995 79 0.995 0.408 1.223 5.540 0.298 0.534 6 025033 1917 1995 79 0.994 0.451 0.839 3.862 0.372 0.439 7 025035 1917 1995 79 0.995 0.334 0.436 3.497 0.303 0.315 8 025037 1917 1995 79 0.997 0.336 0.071 2.783 0.305 0.401 9 025061 1890 1995 106 0.991 0.375 0.664 3.978 0.341 0.185 10 025063 1890 1995 106 0.989 0.376 0.537 2.945 0.306 0.485 11 025065 1890 1995 106 0.989 0.411 0.662 2.848 0.345 0.414 12 025067 1890 1995 106 0.992 0.342 0.621 2.916 0.315 0.311 13 025091 1893 1995 103 0.997 0.301 0.392 2.878 0.258 0.378 14 025093 1893 1995 103 0.993 0.314 0.694 3.795 0.254 0.383 15 025095 1893 1995 103 0.997 0.341 0.723 4.161 0.266 0.436 16 025097 1893 1995 103 0.997 0.409 0.809 3.147 0.269 0.569 17 025101 1891 1995 105 0.995 0.435 0.246 2.924 0.395 0.470 18 025103 1891 1995 105 0.979 0.478 0.647 3.300 0.396 0.558 19 025105 1892 1995 104 0.992 0.533 1.221 5.276 0.350 0.646 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 025107 1891 1995 105 0.984 0.434 0.342 2.875 0.393 0.502 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 0.993 0.360 0.501 3.451 0.302 0.421 STANDARD DEVIATION 12 0.005 0.088 0.401 0.846 0.062 0.109 MEDIAN (50TH QUANTILE) 103 0.995 0.359 0.579 3.224 0.304 0.407 INTERQUARTILE RANGE 26 0.006 0.115 0.478 1.044 0.091 0.131 MINIMUM VALUE 79 0.979 0.207 -0.413 2.383 0.199 0.185 LOWER HINGE (25TH QUANTILE) 79 0.991 0.308 0.231 2.876 0.256 0.362 UPPER HINGE (75TH QUANTILE) 105 0.997 0.423 0.709 3.920 0.347 0.493 MAXIMUM VALUE 106 0.999 0.533 1.223 5.540 0.396 0.646 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.414 0.175 0.013 -0.342 2.904 -0.110 0.755 MINIMUM CORRELATION: -0.110 SERIES 025031 AND 025095 79 YEARS MAXIMUM CORRELATION: 0.755 SERIES 025061 AND 025067 106 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 82.67 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 6. 66. 190. 190. 190. 190. 190. 190. RBAR 0.847 0.568 0.453 0.503 0.560 0.602 0.378 0.232 SDEV 0.069 0.198 0.296 0.269 0.234 0.179 0.236 0.264 SERR 0.028 0.024 0.021 0.020 0.017 0.013 0.017 0.019 EPS 0.984 0.958 0.943 0.953 0.962 0.968 0.924 0.858 NSS 11.1 17.2 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 1890 1995 106 0.988 0.247 0.038 2.546 0.221 0.403 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.488 0.166 0.105 24 82 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.27 0.58 1.00 1.08 1.65 3.11 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.05 0.73 0.86 0.92 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 0.400 0.183 0.198 -0.013 -0.221 -0.154 -0.249 -0.253 -0.242 -0.069 PACF 0.400 0.028 0.138 -0.169 -0.225 -0.009 -0.167 -0.033 -0.148 0.110 95% C.L. 0.194 0.223 0.229 0.235 0.235 0.243 0.247 0.256 0.265 0.273 |------------------ 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 1 0.162 0.402 |======================= 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 0.426 0.192 0.180 -0.044 -0.237 -0.229 -0.339 -0.342 -0.298 -0.108 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 0.426 2 0.420 0.013 3 0.418 -0.035 0.115 4 0.441 -0.042 0.198 -0.200 5 0.399 0.000 0.190 -0.108 -0.210 6 0.383 -0.009 0.205 -0.108 -0.178 -0.079 7 0.366 -0.047 0.182 -0.064 -0.180 0.003 -0.213 8 0.346 -0.046 0.165 -0.070 -0.163 -0.002 -0.178 -0.094 9 0.332 -0.074 0.165 -0.095 -0.174 0.024 -0.186 -0.040 -0.154 10 0.347 -0.070 0.183 -0.098 -0.157 0.033 -0.202 -0.033 -0.186 0.098 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) 815.49 796.29 798.27 798.87 796.53 793.77 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 795.11 792.20 793.26 792.72 793.71 SELECTED AUTOREGRESSION ORDER: 1 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 0.426 R-SQUARED DUE TO POOLED AUTOREGRESSION: 18.12 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 122.13 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.426 0.181 0.077 0.033 0.014 0.006 0.003 0.001 0.000 0.0002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 025021 1 0.140 0.374 2 025023 1 0.092 0.298 3 025025 1 0.139 0.373 4 025027 1 0.129 0.354 5 025031 1 0.291 0.535 6 025033 1 0.195 0.440 7 025035 1 0.102 0.315 8 025037 1 0.167 0.401 9 025061 1 0.081 0.186 10 025063 1 0.248 0.485 11 025065 1 0.190 0.415 12 025067 1 0.103 0.312 13 025091 1 0.149 0.384 14 025093 1 0.177 0.388 15 025095 1 0.199 0.441 16 025097 1 0.343 0.576 17 025101 1 0.225 0.474 18 025103 1 0.323 0.559 19 025105 1 0.420 0.648 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 025107 1 0.255 0.504 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.198 0.423 STANDARD DEVIATION 0 0.092 0.109 MEDIAN 1 0.183 0.408 INTERQUARTILE RANGE 0 0.117 0.131 MINIMUM VALUE 1 0.081 0.186 LOWER HINGE 1 0.134 0.363 UPPER HINGE 1 0.251 0.495 MAXIMUM VALUE 1 0.420 0.648 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 025021 1917 1995 79 1.000 0.192 -0.303 3.232 0.234 -0.003 2 025023 1917 1995 79 1.000 0.241 0.134 2.738 0.279 -0.019 3 025025 1917 1995 79 1.000 0.225 -0.087 2.721 0.275 0.000 4 025027 1917 1995 79 1.000 0.200 0.448 4.660 0.238 -0.023 5 025031 1917 1995 79 1.000 0.344 1.300 5.807 0.348 0.043 6 025033 1917 1995 79 1.000 0.405 1.137 5.148 0.425 0.014 7 025035 1917 1995 79 1.000 0.317 0.510 3.973 0.352 -0.018 8 025037 1917 1995 79 1.000 0.308 0.502 3.638 0.349 -0.035 9 025061 1890 1995 106 1.000 0.369 0.695 4.705 0.376 -0.041 10 025063 1890 1995 106 1.000 0.328 0.452 2.877 0.364 -0.061 11 025065 1890 1995 106 1.000 0.374 0.619 3.448 0.425 -0.062 12 025067 1890 1995 106 1.000 0.325 0.610 3.327 0.357 -0.025 13 025091 1893 1995 103 1.000 0.277 0.485 3.363 0.306 -0.020 14 025093 1893 1995 103 1.000 0.289 0.838 4.415 0.307 -0.072 15 025095 1893 1995 103 1.000 0.306 0.611 4.173 0.323 -0.036 16 025097 1893 1995 103 1.000 0.333 0.573 3.781 0.357 -0.072 17 025101 1891 1995 105 1.000 0.383 0.116 3.133 0.476 0.004 18 025103 1891 1995 105 1.000 0.396 0.191 3.122 0.494 -0.065 19 025105 1892 1995 104 1.000 0.406 1.171 5.973 0.463 0.011 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 025107 1891 1995 105 1.001 0.371 -0.027 2.988 0.444 0.021 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 1.000 0.319 0.499 3.861 0.360 -0.023 STANDARD DEVIATION 12 0.000 0.066 0.419 0.979 0.076 0.033 MEDIAN (50TH QUANTILE) 103 1.000 0.327 0.506 3.543 0.355 -0.021 INTERQUARTILE RANGE 26 0.000 0.089 0.494 1.410 0.118 0.053 MINIMUM VALUE 79 1.000 0.192 -0.303 2.721 0.234 -0.072 LOWER HINGE (25TH QUANTILE) 79 1.000 0.283 0.162 3.128 0.307 -0.051 UPPER HINGE (75TH QUANTILE) 105 1.000 0.373 0.657 4.538 0.425 0.002 MAXIMUM VALUE 106 1.001 0.406 1.300 5.973 0.494 0.043 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.425 0.148 0.011 0.172 2.497 0.089 0.781 MINIMUM CORRELATION: 0.089 SERIES 025031 AND 025097 79 YEARS MAXIMUM CORRELATION: 0.781 SERIES 025065 AND 025067 106 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 82.67 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 6. 66. 190. 190. 190. 190. 190. 190. RBAR 0.803 0.592 0.478 0.495 0.443 0.517 0.366 0.327 SDEV 0.109 0.161 0.228 0.247 0.220 0.164 0.195 0.217 SERR 0.045 0.020 0.017 0.018 0.016 0.012 0.014 0.016 EPS 0.978 0.961 0.948 0.952 0.941 0.955 0.920 0.907 NSS 11.1 17.2 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 1890 1995 106 0.992 0.223 -0.132 3.496 0.254 -0.048 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.484 0.161 0.072 24 82 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.15 0.62 1.00 1.05 1.67 2.54 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.63 0.85 0.92 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 -0.047 -0.044 0.192 0.002 -0.229 0.045 -0.140 -0.119 -0.147 0.033 PACF -0.047 -0.046 0.188 0.017 -0.222 -0.010 -0.163 -0.054 -0.183 0.017 95% C.L. 0.194 0.195 0.195 0.202 0.202 0.212 0.212 0.215 0.218 0.222 |------------------ 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 -0.037 0.191 0.000 -0.228 0.028 -0.144 -0.134 -0.152 0.026 PACF -0.002 -0.037 0.191 -0.002 -0.222 -0.007 -0.165 -0.055 -0.180 0.027 95% C.L. 0.194 0.194 0.195 0.201 0.201 0.211 0.211 0.215 0.218 0.222 |----------------- 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 1 0.001 -0.002 |========================= 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 1890 1995 106 0.991 0.248 0.045 2.476 0.215 0.437 |------------ 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 0.433 0.205 0.206 -0.003 -0.211 -0.145 -0.245 -0.260 -0.219 -0.066 PACF 0.433 0.022 0.135 -0.176 -0.217 0.014 -0.173 -0.031 -0.108 0.108 95% C.L. 0.194 0.228 0.235 0.241 0.241 0.248 0.251 0.260 0.270 0.277 |------------------- 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 1 0.190 0.435 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.21 MINUTES