RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM053L.rwl.conv LOG FILE PROCESSED: GERM053L.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: 050 1 Mźnstertal (D), EU-Pr. WIDTH_LATE PCAB - 050 2 Germany Norway spruce 490 4751-747 1881 1995 - 050 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 7 050075 MISSING VALUES FOUND: 5 IN 1 GAPS / 1890 1894 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 050061 1882 1995 114 0.476 0.297 3.099 16.269 0.407 0.488 2 050063 1883 1995 113 0.439 0.242 2.102 8.373 0.298 0.568 3 050065 1882 1995 114 0.336 0.127 1.052 5.045 0.305 0.382 4 050067 1883 1995 113 0.342 0.130 0.594 3.501 0.331 0.383 5 050071 1881 1995 115 0.504 0.216 0.689 2.823 0.404 0.313 6 050073 1881 1958 78 0.494 0.238 1.371 5.374 0.380 0.412 7 050075 1881 1926 46 0.497 0.143 0.482 3.035 0.333 0.002 8 050077 1881 1995 115 0.365 0.179 1.676 8.108 0.374 0.360 9 050081 1883 1995 113 0.326 0.169 1.236 4.857 0.382 0.577 10 050083 1881 1995 115 0.563 0.461 2.148 7.949 0.522 0.516 11 050085 1881 1995 115 0.371 0.228 2.599 12.129 0.405 0.460 12 050087 1893 1995 103 0.316 0.142 1.549 7.394 0.397 0.383 13 050091 1882 1995 114 0.513 0.532 3.506 16.691 0.447 0.506 14 050093 1885 1995 111 0.603 0.665 5.240 37.548 0.471 0.320 15 050095 1896 1995 100 0.468 0.302 1.664 6.123 0.454 0.384 16 050097 1881 1995 115 0.399 0.266 1.936 6.820 0.426 0.405 17 050101 1884 1995 112 0.589 0.625 2.610 10.322 0.446 0.730 18 050103 1884 1995 112 0.389 0.470 3.905 16.816 0.425 0.783 19 050105 1887 1995 109 0.251 0.124 0.878 3.463 0.347 0.557 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 050107 1884 1995 112 0.227 0.095 1.013 4.122 0.351 0.349 NUMBER OF SERIES READ IN: 20 FROM 1881 TO 1995 115 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 107 0.424 0.283 1.967 9.338 0.395 0.444 STANDARD DEVIATION 17 0.108 0.174 1.233 8.012 0.058 0.165 MEDIAN (50TH QUANTILE) 113 0.419 0.233 1.670 7.107 0.400 0.409 INTERQUARTILE RANGE 4 0.161 0.239 1.572 6.736 0.087 0.166 MINIMUM VALUE 41 0.227 0.095 0.482 2.823 0.298 0.002 LOWER HINGE (25TH QUANTILE) 110 0.339 0.143 1.033 4.489 0.349 0.371 UPPER HINGE (75TH QUANTILE) 114 0.501 0.381 2.605 11.226 0.436 0.537 MAXIMUM VALUE 115 0.603 0.665 5.240 37.548 0.522 0.783 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.466 0.127 0.009 -0.244 3.442 0.066 0.846 MINIMUM CORRELATION: 0.066 SERIES 050077 AND 050101 112 YEARS MAXIMUM CORRELATION: 0.846 SERIES 050071 AND 050073 78 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 86.91 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1891. 1910. 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 21. 190. 171. 171. 171. 153. 153. 153. 153. RBAR 0.396 0.429 0.529 0.593 0.622 0.615 0.486 0.304 0.435 SDEV 0.229 0.230 0.195 0.168 0.189 0.161 0.205 0.208 0.229 SERR 0.050 0.017 0.015 0.013 0.014 0.013 0.017 0.017 0.018 EPS 0.919 0.938 0.957 0.966 0.969 0.968 0.946 0.887 0.933 NSS 17.2 20.0 19.9 19.4 19.0 19.0 18.5 18.0 18.0 |======================== 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 1881 1995 115 0.373 0.156 1.314 5.053 0.298 0.543 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.860 0.561 -0.049 72 43 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.97 2.99 1.00 1.23 4.22 34.94 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.08 0.78 0.86 0.94 0.98 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 113. 4. 46. 110. 114. 115. |----------- 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 0.538 0.360 0.230 0.106 0.066 0.097 0.081 0.048 0.135 0.123 PACF 0.538 0.099 0.003 -0.060 0.017 0.089 0.005 -0.033 0.140 0.015 95% C.L. 0.187 0.234 0.253 0.260 0.262 0.262 0.263 0.264 0.265 0.267 |------------------ 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 0.300 0.540 |================== 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 050061 3 0.00000000 0.00000000 0.00255187 0.32896909 2 050063 3 0.00000000 0.00000000 0.00264023 0.28871050 3 050065 3 0.00000000 0.00000000 -0.00005889 0.33970192 4 050067 3 0.00000000 0.00000000 -0.00010638 0.34836441 5 050071 3 0.00000000 0.00000000 0.00190294 0.39362928 6 050073 3 0.00000000 0.00000000 0.00326294 0.36560106 7 050075 3 0.00000000 0.00000000 -0.00062584 0.52841079 8 050077 1 0.14575016 0.01674557 0.00000000 0.30058521 9 050081 3 0.00000000 0.00000000 0.00141718 0.24550411 10 050083 3 0.00000000 0.00000000 0.00227705 0.43132266 11 050085 3 0.00000000 0.00000000 0.00098603 0.31341878 12 050087 3 0.00000000 0.00000000 0.00118251 0.25433466 13 050091 3 0.00000000 0.00000000 0.00658472 0.13471200 14 050093 3 0.00000000 0.00000000 0.00674649 0.22471908 15 050095 3 0.00000000 0.00000000 0.00361686 0.28564849 16 050097 3 0.00000000 0.00000000 0.00243234 0.25814188 17 050101 3 0.00000000 0.00000000 0.01051919 -0.00522684 18 050103 3 0.00000000 0.00000000 0.00487392 0.11337356 19 050105 3 0.00000000 0.00000000 -0.00013141 0.25869521 SERIES IDENT OPTION A B C D 20 050107 3 0.00000000 0.00000000 -0.00011062 0.23375000 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 050061 1882 1995 114 0.996 0.579 3.567 20.570 0.403 0.438 2 050063 1883 1995 113 1.000 0.490 2.267 10.936 0.295 0.458 3 050065 1882 1995 114 1.000 0.377 1.064 5.072 0.303 0.380 4 050067 1883 1995 113 1.000 0.381 0.631 3.545 0.328 0.382 5 050071 1881 1995 115 0.999 0.407 0.682 2.944 0.401 0.213 6 050073 1881 1958 78 0.999 0.420 0.609 3.563 0.374 0.306 7 050075 1881 1926 46 1.000 0.285 0.241 2.657 0.305 0.143 8 050077 1881 1995 115 1.000 0.482 1.463 6.162 0.371 0.364 9 050081 1883 1995 113 1.003 0.478 0.700 3.190 0.378 0.519 10 050083 1881 1995 115 0.997 0.774 2.042 7.308 0.517 0.458 11 050085 1881 1995 115 1.000 0.597 2.486 12.019 0.402 0.434 12 050087 1893 1995 103 1.000 0.428 1.199 5.440 0.393 0.316 13 050091 1882 1995 114 1.021 0.795 3.100 15.237 0.443 0.410 14 050093 1885 1995 111 0.986 0.890 5.546 42.097 0.468 0.237 15 050095 1896 1995 100 0.991 0.580 1.840 7.136 0.450 0.302 16 050097 1881 1995 115 0.996 0.591 1.702 6.226 0.423 0.324 17 050101 1884 1995 112 1.888 4.697 6.609 44.420 0.439 0.637 18 050103 1884 1995 112 1.012 0.877 3.156 12.976 0.422 0.732 19 050105 1887 1995 109 1.000 0.494 0.849 3.338 0.344 0.553 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 050107 1884 1995 112 1.000 0.418 1.003 4.119 0.348 0.344 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 107 1.044 0.752 2.038 10.948 0.390 0.397 STANDARD DEVIATION 16 0.199 0.944 1.681 12.034 0.059 0.141 MEDIAN (50TH QUANTILE) 113 1.000 0.492 1.583 6.194 0.397 0.381 INTERQUARTILE RANGE 4 0.002 0.267 2.019 8.944 0.085 0.147 MINIMUM VALUE 46 0.986 0.285 0.241 2.657 0.295 0.143 LOWER HINGE (25TH QUANTILE) 110 0.998 0.419 0.774 3.554 0.346 0.311 UPPER HINGE (75TH QUANTILE) 114 1.000 0.686 2.793 12.498 0.431 0.458 MAXIMUM VALUE 115 1.888 4.697 6.609 44.420 0.517 0.732 |------------------------ 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 050061 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 050063 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 050065 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 050067 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 050071 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 050073 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 050075 -67 30 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 050077 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 050081 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 050083 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 050085 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 050087 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 050091 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 050093 -67 74 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 050095 -67 67 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 050097 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 050101 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 050103 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 050105 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 050107 -67 75 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 050061 1882 1995 114 0.993 0.483 2.770 15.330 0.404 0.304 2 050063 1883 1995 113 0.994 0.466 2.478 13.159 0.294 0.427 3 050065 1882 1995 114 0.997 0.361 0.958 4.694 0.303 0.344 4 050067 1883 1995 113 0.993 0.346 0.499 3.569 0.327 0.297 5 050071 1881 1995 115 0.998 0.393 0.614 2.971 0.401 0.166 6 050073 1881 1958 78 0.996 0.413 0.725 3.953 0.374 0.290 7 050075 1881 1926 46 0.995 0.253 0.119 3.257 0.305 -0.086 8 050077 1881 1995 115 0.994 0.461 1.502 6.498 0.371 0.325 9 050081 1883 1995 113 0.988 0.405 0.539 3.417 0.378 0.327 10 050083 1881 1995 115 0.977 0.673 1.895 6.932 0.517 0.380 11 050085 1881 1995 115 0.990 0.563 3.053 17.930 0.401 0.360 12 050087 1893 1995 103 0.993 0.390 0.962 4.654 0.392 0.223 13 050091 1882 1995 114 0.981 0.705 3.327 16.435 0.443 0.341 14 050093 1885 1995 111 0.977 0.678 4.316 30.083 0.467 0.169 15 050095 1896 1995 100 0.988 0.479 1.407 5.528 0.449 0.175 16 050097 1881 1995 115 0.980 0.483 1.381 4.861 0.423 0.201 17 050101 1884 1995 112 2.365 4.089 3.477 14.087 0.441 0.810 18 050103 1884 1995 112 0.962 0.637 2.558 10.011 0.421 0.602 19 050105 1887 1995 109 0.988 0.453 0.971 4.118 0.343 0.472 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 050107 1884 1995 112 0.994 0.388 0.873 3.758 0.348 0.286 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 107 1.057 0.656 1.721 8.762 0.390 0.321 STANDARD DEVIATION 16 0.308 0.817 1.191 7.058 0.059 0.181 MEDIAN (50TH QUANTILE) 113 0.993 0.463 1.394 5.194 0.396 0.315 INTERQUARTILE RANGE 4 0.010 0.209 1.865 9.767 0.087 0.158 MINIMUM VALUE 46 0.962 0.253 0.119 2.971 0.294 -0.086 LOWER HINGE (25TH QUANTILE) 110 0.985 0.391 0.799 3.855 0.346 0.212 UPPER HINGE (75TH QUANTILE) 114 0.995 0.600 2.664 13.623 0.432 0.370 MAXIMUM VALUE 115 2.365 4.089 4.316 30.083 0.517 0.810 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.447 0.149 0.011 -0.731 3.735 -0.006 0.808 MINIMUM CORRELATION: -0.006 SERIES 050083 AND 050101 112 YEARS MAXIMUM CORRELATION: 0.808 SERIES 050071 AND 050073 78 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 86.91 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1891. 1910. 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 21. 190. 171. 171. 171. 153. 153. 153. 153. RBAR 0.385 0.403 0.498 0.601 0.635 0.630 0.483 0.317 0.407 SDEV 0.204 0.244 0.215 0.163 0.178 0.166 0.200 0.203 0.233 SERR 0.044 0.018 0.016 0.012 0.014 0.013 0.016 0.016 0.019 EPS 0.915 0.931 0.952 0.967 0.971 0.970 0.945 0.893 0.925 NSS 17.2 20.0 19.9 19.4 19.0 19.0 18.5 18.0 18.0 |======================== 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 1881 1995 115 0.946 0.320 0.854 5.216 0.282 0.425 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.767 0.374 -0.064 75 40 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 2.48 4.58 1.00 1.32 5.90 447.47 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.08 0.80 0.87 0.96 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 0.422 0.182 0.030 -0.069 -0.179 -0.119 -0.128 -0.214 -0.092 -0.046 PACF 0.422 0.005 -0.059 -0.076 -0.140 0.023 -0.073 -0.176 0.063 -0.031 95% C.L. 0.187 0.217 0.222 0.223 0.223 0.228 0.230 0.233 0.240 0.241 |------------------ 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 0.179 0.423 |======================= 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 0.488 0.294 0.169 0.055 -0.014 -0.008 -0.075 -0.135 -0.016 -0.002 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 0.488 2 0.453 0.073 3 0.453 0.072 0.001 4 0.453 0.076 0.027 -0.057 5 0.450 0.077 0.030 -0.037 -0.043 6 0.451 0.078 0.030 -0.040 -0.055 0.028 7 0.454 0.074 0.026 -0.037 -0.049 0.065 -0.083 8 0.446 0.080 0.022 -0.041 -0.046 0.072 -0.041 -0.092 9 0.458 0.085 0.012 -0.034 -0.041 0.069 -0.052 -0.150 0.131 10 0.458 0.085 0.013 -0.035 -0.041 0.069 -0.052 -0.150 0.130 0.003 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) 1022.67 993.37 994.76 996.76 998.39 1000.18 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1002.09 1003.30 1004.33 1004.34 1006.34 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 0.488 R-SQUARED DUE TO POOLED AUTOREGRESSION: 23.83 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 131.28 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.488 0.238 0.116 0.057 0.028 0.014 0.007 0.003 0.002 0.0008 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 050061 1 0.100 0.305 2 050063 1 0.215 0.434 3 050065 1 0.124 0.345 4 050067 1 0.106 0.298 5 050071 1 0.040 0.167 6 050073 1 0.093 0.290 7 050075 1 0.008 -0.087 8 050077 1 0.114 0.325 9 050081 1 0.111 0.332 10 050083 1 0.146 0.380 11 050085 1 0.133 0.363 12 050087 1 0.065 0.229 13 050091 1 0.118 0.342 14 050093 1 0.044 0.169 15 050095 1 0.060 0.178 16 050097 1 0.045 0.202 17 050101 1 0.669 0.811 18 050103 1 0.365 0.604 19 050105 1 0.227 0.476 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 050107 1 0.089 0.286 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.144 0.322 STANDARD DEVIATION 0 0.147 0.181 MEDIAN 1 0.108 0.315 INTERQUARTILE RANGE 0 0.077 0.156 MINIMUM VALUE 1 0.008 -0.087 LOWER HINGE 1 0.062 0.215 UPPER HINGE 1 0.139 0.372 MAXIMUM VALUE 1 0.669 0.811 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 050061 1882 1995 114 1.000 0.460 2.545 15.808 0.485 -0.026 2 050063 1883 1995 113 1.000 0.418 2.832 16.982 0.382 -0.083 3 050065 1882 1995 114 1.000 0.339 1.010 5.366 0.356 0.024 4 050067 1883 1995 113 1.000 0.331 0.576 3.257 0.374 -0.041 5 050071 1881 1995 115 1.000 0.388 0.595 3.165 0.436 -0.018 6 050073 1881 1958 78 1.000 0.396 0.799 4.379 0.421 -0.029 7 050075 1881 1926 46 1.000 0.252 0.278 3.346 0.289 0.002 8 050077 1881 1995 115 1.000 0.436 1.735 7.400 0.422 -0.031 9 050081 1883 1995 113 1.000 0.382 0.271 3.109 0.435 0.000 10 050083 1881 1995 115 1.001 0.622 1.984 8.631 0.619 -0.010 11 050085 1881 1995 115 1.000 0.525 3.251 19.586 0.447 -0.012 12 050087 1893 1995 103 1.000 0.379 0.740 3.863 0.435 -0.028 13 050091 1882 1995 114 1.001 0.661 3.407 17.288 0.502 0.023 14 050093 1885 1995 111 1.000 0.668 4.326 30.037 0.499 -0.021 15 050095 1896 1995 100 1.000 0.471 1.364 5.760 0.486 0.028 16 050097 1881 1995 115 1.000 0.473 1.533 5.339 0.444 -0.014 17 050101 1884 1995 112 1.205 2.071 4.508 22.771 0.927 0.099 18 050103 1884 1995 112 1.002 0.503 2.077 10.297 0.529 -0.025 19 050105 1887 1995 109 1.000 0.398 1.236 4.757 0.417 0.005 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 050107 1884 1995 112 1.000 0.372 1.021 4.119 0.397 -0.024 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 107 1.010 0.527 1.804 9.763 0.465 -0.009 STANDARD DEVIATION 16 0.046 0.379 1.291 7.868 0.129 0.036 MEDIAN (50TH QUANTILE) 113 1.000 0.427 1.448 5.563 0.436 -0.016 INTERQUARTILE RANGE 4 0.000 0.133 1.919 12.404 0.086 0.031 MINIMUM VALUE 46 1.000 0.252 0.271 3.109 0.289 -0.083 LOWER HINGE (25TH QUANTILE) 110 1.000 0.380 0.770 3.991 0.407 -0.027 UPPER HINGE (75TH QUANTILE) 114 1.000 0.514 2.689 16.395 0.493 0.004 MAXIMUM VALUE 115 1.205 2.071 4.508 30.037 0.927 0.099 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.424 0.139 0.010 -0.496 3.211 0.027 0.791 MINIMUM CORRELATION: 0.027 SERIES 050075 AND 050101 43 YEARS MAXIMUM CORRELATION: 0.791 SERIES 050071 AND 050073 78 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 86.91 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1891. 1910. 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 21. 190. 171. 171. 171. 153. 153. 153. 153. RBAR 0.311 0.411 0.491 0.575 0.573 0.547 0.446 0.326 0.390 SDEV 0.218 0.238 0.208 0.173 0.186 0.195 0.219 0.202 0.208 SERR 0.048 0.017 0.016 0.013 0.014 0.016 0.018 0.016 0.017 EPS 0.886 0.933 0.950 0.963 0.962 0.958 0.937 0.897 0.920 NSS 17.2 20.0 19.9 19.4 19.0 19.0 18.5 18.0 18.0 |======================== 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 1881 1995 115 0.956 0.279 0.770 4.590 0.319 0.062 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.658 0.305 -0.011 69 46 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.71 1.78 1.02 1.21 2.99 246.19 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 0.76 0.88 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 0.062 0.047 -0.005 -0.035 -0.129 -0.026 -0.038 -0.202 -0.002 -0.028 PACF 0.062 0.043 -0.011 -0.036 -0.125 -0.008 -0.025 -0.204 0.014 -0.031 95% C.L. 0.187 0.187 0.188 0.188 0.188 0.191 0.191 0.191 0.199 0.199 |------------------ 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 -0.003 0.044 -0.006 -0.027 -0.126 -0.016 -0.024 -0.201 0.012 -0.028 PACF -0.003 0.044 -0.005 -0.029 -0.126 -0.015 -0.013 -0.206 0.003 -0.030 95% C.L. 0.187 0.187 0.187 0.187 0.187 0.190 0.190 0.190 0.197 0.197 |----------------- 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 0.002 -0.003 |========================= 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 1881 1995 115 0.958 0.319 0.601 4.380 0.266 0.492 |------------ 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 0.488 0.245 0.071 -0.048 -0.151 -0.130 -0.159 -0.231 -0.116 -0.082 PACF 0.488 0.009 -0.068 -0.079 -0.113 0.008 -0.089 -0.160 0.078 -0.045 95% C.L. 0.187 0.227 0.236 0.236 0.237 0.240 0.242 0.246 0.253 0.255 |------------------- 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 0.240 0.490 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.29 MINUTES