RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM054E.rwl.conv LOG FILE PROCESSED: GERM054E.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: 051 1 Mźnstertal (D), EU-Pr. WIDTH_EARLY ABAL - 051 2 Germany silver fir, European fir 460 4751-746 1864 1995 - 051 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 6 051023 MISSING VALUES FOUND: 3 IN 1 GAPS / 1948 1950 / -------------------------------------------------------------------- 19 051055 MISSING VALUES FOUND: 2 IN 2 GAPS / 1875 1875 / 1961 1961 / -------------------------------------------------------------------- 20 051057 MISSING VALUES FOUND: 2 IN 1 GAPS / 1961 1962 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 051011 1873 1995 123 1.542 1.062 1.018 3.896 0.296 0.812 2 051013 1873 1995 123 1.522 0.947 1.768 8.463 0.326 0.807 3 051015 1871 1995 125 1.402 0.862 1.949 9.988 0.328 0.740 4 051017 1871 1995 125 1.326 0.852 2.599 15.032 0.307 0.718 5 051021 1879 1995 117 1.884 1.220 2.219 10.594 0.353 0.567 6 051023 1879 1995 117 1.957 0.919 1.132 4.540 0.317 0.617 7 051025 1879 1995 117 1.728 0.822 1.276 5.657 0.285 0.648 8 051027 1879 1995 117 1.796 0.914 1.031 3.956 0.325 0.652 9 051031 1870 1995 126 2.005 0.843 -0.036 2.419 0.295 0.611 10 051033 1871 1995 125 1.964 1.194 0.360 2.344 0.334 0.796 11 051035 1871 1995 125 1.958 0.875 0.386 2.642 0.307 0.610 12 051037 1872 1995 124 1.662 0.880 0.515 2.953 0.296 0.691 13 051041 1904 1995 92 2.445 1.095 0.605 4.054 0.335 0.559 14 051043 1904 1995 92 2.779 1.279 0.676 3.967 0.351 0.622 15 051045 1904 1995 92 2.335 1.279 0.629 3.252 0.394 0.642 16 051047 1903 1995 93 2.288 1.242 0.385 2.318 0.392 0.595 17 051051 1864 1995 132 1.529 1.220 1.508 5.385 0.318 0.878 18 051053 1864 1995 132 1.916 1.327 1.475 6.084 0.351 0.801 19 051055 1865 1995 131 1.683 1.368 1.400 4.923 0.314 0.805 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 051057 1864 1995 132 1.476 1.108 1.241 4.060 0.303 0.876 NUMBER OF SERIES READ IN: 20 FROM 1864 TO 1995 132 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.860 1.065 1.107 5.326 0.326 0.702 STANDARD DEVIATION 13 0.378 0.188 0.687 3.305 0.030 0.104 MEDIAN (50TH QUANTILE) 123 1.840 1.078 1.082 4.057 0.321 0.671 INTERQUARTILE RANGE 10 0.449 0.353 0.932 2.768 0.039 0.188 MINIMUM VALUE 92 1.326 0.822 -0.036 2.318 0.285 0.559 LOWER HINGE (25TH QUANTILE) 115 1.536 0.877 0.560 3.102 0.305 0.614 UPPER HINGE (75TH QUANTILE) 125 1.984 1.231 1.491 5.870 0.343 0.803 MAXIMUM VALUE 132 2.779 1.368 2.599 15.032 0.394 0.878 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.387 0.258 0.019 0.161 2.207 -0.196 0.922 MINIMUM CORRELATION: -0.196 SERIES 051021 AND 051047 93 YEARS MAXIMUM CORRELATION: 0.922 SERIES 051051 AND 051057 132 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 83.80 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1874. 1890. 1900. 1910. 1920. 1930. 1940. 1950. 1960. 1970. CORR 3. 120. 120. 120. 190. 190. 190. 190. 190. 190. RBAR 0.914 0.363 0.560 0.463 0.534 0.537 0.616 0.530 0.344 0.209 SDEV 0.013 0.484 0.202 0.216 0.189 0.218 0.326 0.239 0.300 0.377 SERR 0.008 0.044 0.018 0.020 0.014 0.016 0.024 0.017 0.022 0.027 EPS 0.991 0.901 0.956 0.943 0.958 0.959 0.970 0.958 0.913 0.841 NSS 9.9 16.0 17.2 19.2 20.0 20.0 20.0 20.0 20.0 20.0 YEAR 1980. CORR 190. RBAR 0.194 SDEV 0.327 SERR 0.024 EPS 0.828 NSS 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 1864 1995 132 1.794 0.790 0.704 3.683 0.257 0.747 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.388 0.175 0.451 49 83 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.71 1.34 1.00 1.18 2.53 8.65 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.10 0.51 0.84 0.94 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 124. 8. 92. 117. 126. 132. |----------- 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 0.741 0.617 0.492 0.431 0.395 0.319 0.249 0.186 0.190 0.197 PACF 0.741 0.150 -0.019 0.077 0.076 -0.071 -0.047 -0.019 0.102 0.054 95% C.L. 0.174 0.252 0.294 0.318 0.336 0.349 0.358 0.363 0.366 0.369 |------------------ 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 0.570 0.631 0.156 |================== 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 051011 3 0.00000000 0.00000000 -0.01703680 2.59807014 2 051013 3 0.00000000 0.00000000 -0.01345043 2.35604024 3 051015 1 2.03755522 0.00951628 0.00000000 0.21616234 4 051017 3 0.00000000 0.00000000 -0.01270237 2.12632895 5 051021 1 2.95753264 0.27622265 0.00000000 1.80464745 6 051023 1 2.97372103 0.23203418 0.00000000 1.84241569 7 051025 1 2.54451227 0.10489066 0.00000000 1.53172338 8 051027 1 2.40088058 0.10711651 0.00000000 1.61440647 9 051031 3 0.00000000 0.00000000 -0.00893660 2.57207751 10 051033 3 0.00000000 0.00000000 -0.02033014 3.24455881 11 051035 3 0.00000000 0.00000000 -0.01129622 2.66974187 12 051037 3 0.00000000 0.00000000 -0.01162426 2.38837123 13 051041 3 0.00000000 0.00000000 -0.02050529 3.39838743 14 051043 3 0.00000000 0.00000000 -0.01690343 3.56503105 15 051045 1 2.30282474 0.09454630 0.00000000 2.08283496 16 051047 3 0.00000000 0.00000000 -0.01439408 2.96404862 17 051051 1 3.32238173 0.01375186 0.00000000 0.00782029 18 051053 1 3.09412861 0.01249685 0.00000000 0.41003042 19 051055 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 051057 1 3.10692024 0.02072532 0.00000000 0.40846860 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 051011 1873 1995 123 0.975 0.546 1.070 4.060 0.295 0.699 2 051013 1873 1995 123 1.011 0.523 0.804 3.795 0.323 0.704 3 051015 1871 1995 125 1.002 0.544 1.238 4.748 0.325 0.663 4 051017 1871 1995 125 0.995 0.479 1.520 7.908 0.304 0.603 5 051021 1879 1995 117 1.000 0.652 2.579 12.725 0.349 0.545 6 051023 1879 1995 117 1.000 0.456 1.477 6.239 0.315 0.556 7 051025 1879 1995 117 1.000 0.434 1.724 9.363 0.283 0.547 8 051027 1879 1995 117 1.000 0.499 1.744 6.931 0.322 0.594 9 051031 1870 1995 126 0.999 0.398 0.031 2.651 0.292 0.565 10 051033 1871 1995 125 0.979 0.482 0.326 2.410 0.331 0.667 11 051035 1871 1995 125 0.999 0.415 0.873 4.495 0.304 0.539 12 051037 1872 1995 124 0.999 0.505 0.966 4.443 0.294 0.648 13 051041 1904 1995 92 0.996 0.430 1.549 7.874 0.332 0.441 14 051043 1904 1995 92 0.999 0.462 1.142 5.127 0.347 0.566 15 051045 1904 1995 92 1.000 0.557 1.183 5.013 0.391 0.605 16 051047 1903 1995 93 1.000 0.563 0.902 3.452 0.387 0.528 17 051051 1864 1995 132 1.022 0.693 1.412 5.389 0.317 0.771 18 051053 1864 1995 132 1.007 0.630 1.433 5.547 0.348 0.669 19 051055 1865 1995 131 0.979 0.472 1.050 3.797 0.324 0.608 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 051057 1864 1995 132 1.015 0.642 1.513 5.251 0.311 0.765 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 0.999 0.519 1.227 5.561 0.325 0.614 STANDARD DEVIATION 14 0.011 0.084 0.540 2.449 0.029 0.084 MEDIAN (50TH QUANTILE) 123 1.000 0.502 1.210 5.070 0.322 0.604 INTERQUARTILE RANGE 8 0.004 0.102 0.583 2.657 0.035 0.116 MINIMUM VALUE 92 0.975 0.398 0.031 2.410 0.283 0.441 LOWER HINGE (25TH QUANTILE) 117 0.997 0.459 0.934 3.928 0.304 0.551 UPPER HINGE (75TH QUANTILE) 125 1.001 0.560 1.517 6.585 0.339 0.668 MAXIMUM VALUE 132 1.022 0.693 2.579 12.725 0.391 0.771 |------------------------ 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 051011 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 051013 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 051015 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 051017 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 051021 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 051023 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 051025 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 051027 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 051031 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 051033 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 051035 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 051037 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 051041 -67 61 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 051043 -67 61 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 051045 -67 61 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 051047 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 051051 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 051053 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 051055 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 051057 -67 88 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 051011 1873 1995 123 0.984 0.506 1.399 4.786 0.295 0.643 2 051013 1873 1995 123 0.979 0.456 1.126 5.122 0.324 0.628 3 051015 1871 1995 125 0.988 0.500 1.190 4.581 0.325 0.601 4 051017 1871 1995 125 0.992 0.465 1.719 8.807 0.305 0.572 5 051021 1879 1995 117 0.978 0.544 1.893 10.232 0.348 0.503 6 051023 1879 1995 117 0.996 0.410 0.823 4.037 0.315 0.470 7 051025 1879 1995 117 0.987 0.393 1.718 9.528 0.282 0.484 8 051027 1879 1995 117 0.990 0.430 1.112 5.024 0.322 0.523 9 051031 1870 1995 126 0.992 0.384 0.131 2.761 0.292 0.522 10 051033 1871 1995 125 0.991 0.456 0.652 3.428 0.330 0.538 11 051035 1871 1995 125 0.994 0.392 0.731 4.055 0.305 0.492 12 051037 1872 1995 124 0.992 0.473 0.724 3.859 0.294 0.624 13 051041 1904 1995 92 0.994 0.378 0.892 5.420 0.332 0.341 14 051043 1904 1995 92 0.991 0.391 0.462 3.539 0.347 0.382 15 051045 1904 1995 92 0.983 0.491 1.273 5.859 0.390 0.559 16 051047 1903 1995 93 0.984 0.527 0.928 3.899 0.388 0.496 17 051051 1864 1995 132 0.956 0.497 0.795 3.192 0.317 0.663 18 051053 1864 1995 132 0.969 0.454 0.642 3.262 0.348 0.544 19 051055 1865 1995 131 0.993 0.444 0.856 3.613 0.324 0.540 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 051057 1864 1995 132 0.968 0.447 0.902 3.870 0.310 0.629 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 0.985 0.452 0.998 4.944 0.325 0.538 STANDARD DEVIATION 14 0.010 0.050 0.441 2.139 0.029 0.084 MEDIAN (50TH QUANTILE) 123 0.989 0.455 0.897 4.046 0.323 0.539 INTERQUARTILE RANGE 8 0.011 0.092 0.504 1.694 0.035 0.118 MINIMUM VALUE 92 0.956 0.378 0.131 2.761 0.282 0.341 LOWER HINGE (25TH QUANTILE) 117 0.981 0.402 0.727 3.576 0.305 0.494 UPPER HINGE (75TH QUANTILE) 125 0.992 0.494 1.232 5.271 0.339 0.613 MAXIMUM VALUE 132 0.996 0.544 1.893 10.232 0.390 0.663 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.330 0.229 0.017 0.249 2.301 -0.196 0.840 MINIMUM CORRELATION: -0.196 SERIES 051021 AND 051047 93 YEARS MAXIMUM CORRELATION: 0.840 SERIES 051011 AND 051015 123 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 83.80 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1874. 1890. 1900. 1910. 1920. 1930. 1940. 1950. 1960. 1970. CORR 3. 120. 120. 120. 190. 190. 190. 190. 190. 190. RBAR 0.882 0.407 0.569 0.538 0.462 0.529 0.608 0.562 0.369 0.234 SDEV 0.040 0.405 0.189 0.183 0.209 0.235 0.295 0.216 0.287 0.345 SERR 0.023 0.037 0.017 0.017 0.015 0.017 0.021 0.016 0.021 0.025 EPS 0.987 0.917 0.958 0.957 0.945 0.957 0.969 0.963 0.921 0.859 NSS 9.9 16.0 17.2 19.2 20.0 20.0 20.0 20.0 20.0 20.0 YEAR 1980. CORR 190. RBAR 0.216 SDEV 0.318 SERR 0.023 EPS 0.846 NSS 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 1864 1995 132 0.959 0.293 0.254 2.818 0.253 0.484 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.497 0.311 0.012 39 93 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.25 1.08 1.00 1.06 2.14 7.13 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.09 0.30 0.85 0.94 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 0.480 0.334 0.181 0.119 0.056 -0.049 -0.173 -0.201 -0.138 -0.161 PACF 0.480 0.134 -0.029 0.011 -0.019 -0.108 -0.161 -0.062 0.054 -0.068 95% C.L. 0.174 0.210 0.226 0.230 0.232 0.233 0.233 0.237 0.242 0.244 |------------------ 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 0.249 0.419 0.136 |======================= 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 0.453 0.331 0.209 0.137 0.057 -0.041 -0.167 -0.163 -0.111 -0.156 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 0.453 2 0.382 0.158 3 0.379 0.153 0.014 4 0.379 0.153 0.014 0.001 5 0.379 0.153 0.020 0.017 -0.041 6 0.375 0.155 0.022 0.032 -0.005 -0.096 7 0.360 0.154 0.027 0.035 0.021 -0.035 -0.164 8 0.355 0.153 0.028 0.036 0.021 -0.030 -0.153 -0.029 9 0.356 0.161 0.029 0.035 0.020 -0.032 -0.161 -0.048 0.052 10 0.360 0.157 0.017 0.033 0.021 -0.029 -0.159 -0.036 0.079 -0.074 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) 1077.67 1049.33 1047.99 1049.96 1051.96 1053.74 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1054.50 1052.93 1054.81 1056.45 1057.73 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 0.382 0.158 R-SQUARED DUE TO POOLED AUTOREGRESSION: 22.53 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 129.07 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.382 0.304 0.176 0.115 0.072 0.046 0.029 0.018 0.011 0.0073 0.005 0.003 0.002 0.001 0.001 0.000 0.000 0.000 0.000 0.0001 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 051011 2 0.437 0.524 0.187 2 051013 2 0.409 0.626 0.003 3 051015 2 0.373 0.557 0.080 4 051017 2 0.338 0.538 0.064 5 051021 2 0.283 0.424 0.167 6 051023 2 0.244 0.442 0.066 7 051025 2 0.243 0.490 0.003 8 051027 2 0.288 0.498 0.060 9 051031 2 0.292 0.528 0.020 10 051033 2 0.293 0.561 -0.041 11 051035 2 0.248 0.462 0.064 12 051037 2 0.433 0.472 0.249 13 051041 2 0.129 0.314 0.095 14 051043 2 0.159 0.338 0.118 15 051045 2 0.323 0.514 0.082 16 051047 2 0.296 0.407 0.183 17 051051 2 0.470 0.529 0.206 18 051053 2 0.304 0.527 0.042 19 051055 2 0.299 0.527 0.032 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 051057 2 0.428 0.504 0.206 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.314 0.489 0.094 STANDARD DEVIATION 0 0.091 0.075 0.080 MEDIAN 2 0.297 0.509 0.073 INTERQUARTILE RANGE 0 0.126 0.076 0.138 MINIMUM VALUE 2 0.129 0.314 -0.041 LOWER HINGE 2 0.265 0.452 0.037 UPPER HINGE 2 0.391 0.528 0.175 MAXIMUM VALUE 2 0.470 0.626 0.249 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 051011 1873 1995 123 1.002 0.376 0.798 5.662 0.385 0.019 2 051013 1873 1995 123 1.000 0.355 0.720 4.113 0.380 0.002 3 051015 1871 1995 125 1.000 0.397 0.873 4.795 0.416 0.010 4 051017 1871 1995 125 1.001 0.376 1.331 7.833 0.367 0.015 5 051021 1879 1995 117 1.000 0.462 2.673 16.307 0.409 -0.005 6 051023 1879 1995 117 1.000 0.361 0.893 4.788 0.381 0.013 7 051025 1879 1995 117 1.000 0.342 1.664 8.554 0.341 0.008 8 051027 1879 1995 117 1.000 0.364 0.750 3.926 0.386 0.012 9 051031 1870 1995 126 1.000 0.322 0.083 2.948 0.371 -0.002 10 051033 1871 1995 125 1.000 0.384 0.778 5.115 0.411 0.003 11 051035 1871 1995 125 1.000 0.340 0.255 3.943 0.386 0.003 12 051037 1872 1995 124 1.000 0.355 0.436 4.963 0.391 0.005 13 051041 1904 1995 92 1.000 0.352 1.077 5.342 0.365 0.004 14 051043 1904 1995 92 1.000 0.358 0.266 3.243 0.415 0.005 15 051045 1904 1995 92 1.000 0.406 1.787 9.712 0.455 0.007 16 051047 1903 1995 93 1.000 0.449 1.065 4.170 0.431 0.026 17 051051 1864 1995 132 1.000 0.362 0.659 4.301 0.389 -0.015 18 051053 1864 1995 132 1.000 0.378 0.798 4.028 0.404 0.003 19 051055 1865 1995 131 1.000 0.372 0.547 3.641 0.409 0.002 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 051057 1864 1995 132 1.000 0.337 0.158 3.962 0.377 -0.006 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.000 0.372 0.881 5.567 0.393 0.005 STANDARD DEVIATION 14 0.000 0.035 0.619 3.081 0.026 0.009 MEDIAN (50TH QUANTILE) 123 1.000 0.363 0.788 4.544 0.388 0.005 INTERQUARTILE RANGE 8 0.000 0.027 0.580 1.550 0.031 0.009 MINIMUM VALUE 92 1.000 0.322 0.083 2.948 0.341 -0.015 LOWER HINGE (25TH QUANTILE) 117 1.000 0.354 0.491 3.952 0.379 0.002 UPPER HINGE (75TH QUANTILE) 125 1.000 0.381 1.071 5.502 0.410 0.011 MAXIMUM VALUE 132 1.002 0.462 2.673 16.307 0.455 0.026 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.398 0.153 0.011 0.542 3.021 0.062 0.797 MINIMUM CORRELATION: 0.062 SERIES 051021 AND 051047 93 YEARS MAXIMUM CORRELATION: 0.797 SERIES 051011 AND 051017 123 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 83.80 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1874. 1890. 1900. 1910. 1920. 1930. 1940. 1950. 1960. 1970. CORR 3. 120. 120. 120. 190. 190. 190. 190. 190. 190. RBAR 0.875 0.453 0.625 0.581 0.511 0.588 0.589 0.571 0.442 0.296 SDEV 0.021 0.291 0.154 0.165 0.204 0.182 0.215 0.206 0.195 0.244 SERR 0.012 0.027 0.014 0.015 0.015 0.013 0.016 0.015 0.014 0.018 EPS 0.986 0.930 0.966 0.964 0.954 0.966 0.966 0.964 0.941 0.894 NSS 9.9 16.0 17.2 19.2 20.0 20.0 20.0 20.0 20.0 20.0 YEAR 1980. CORR 190. RBAR 0.298 SDEV 0.248 SERR 0.018 EPS 0.895 NSS 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 1864 1995 132 0.985 0.249 0.200 3.268 0.301 -0.064 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.370 0.187 0.060 41 91 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.42 0.85 1.02 1.15 2.00 3.95 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.55 0.86 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 -0.064 0.022 -0.029 0.027 0.043 0.010 -0.121 -0.111 -0.030 -0.082 PACF -0.064 0.018 -0.026 0.024 0.047 0.014 -0.121 -0.128 -0.045 -0.094 95% C.L. 0.174 0.175 0.175 0.175 0.175 0.175 0.175 0.178 0.180 0.180 |------------------ 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 -0.002 -0.026 0.028 0.048 0.006 -0.129 -0.120 -0.040 -0.086 PACF 0.001 -0.002 -0.026 0.028 0.048 0.006 -0.128 -0.121 -0.045 -0.099 95% C.L. 0.174 0.174 0.174 0.174 0.174 0.175 0.175 0.178 0.180 0.180 |----------------- 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 0.001 -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 1864 1995 132 0.987 0.281 0.274 2.811 0.242 0.443 |------------ 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 0.439 0.311 0.157 0.107 0.045 -0.046 -0.176 -0.200 -0.159 -0.156 PACF 0.439 0.146 -0.030 0.016 -0.020 -0.092 -0.168 -0.072 0.014 -0.041 95% C.L. 0.174 0.205 0.219 0.222 0.224 0.224 0.224 0.228 0.234 0.237 |------------------- 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 0.214 0.378 0.147 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 1.78 MINUTES