RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM054L.rwl.conv LOG FILE PROCESSED: GERM054L.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_LATE 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 0.688 0.457 0.693 2.780 0.433 0.662 2 051013 1873 1995 123 0.861 0.596 0.790 2.834 0.469 0.571 3 051015 1871 1995 125 0.644 0.447 1.270 4.101 0.434 0.598 4 051017 1871 1995 125 0.592 0.365 0.790 3.029 0.473 0.460 5 051021 1879 1995 117 0.876 0.777 3.657 17.205 0.395 0.724 6 051023 1879 1995 117 1.096 0.667 1.732 6.720 0.389 0.588 7 051025 1879 1995 117 0.771 0.553 2.814 11.727 0.384 0.724 8 051027 1879 1995 117 0.851 0.719 3.108 13.284 0.419 0.679 9 051031 1870 1995 126 0.607 0.353 1.306 4.441 0.454 0.400 10 051033 1871 1995 125 0.651 0.465 2.522 11.505 0.487 0.454 11 051035 1871 1995 125 0.832 0.524 1.290 4.917 0.483 0.416 12 051037 1872 1995 124 0.542 0.335 1.657 6.489 0.463 0.470 13 051041 1904 1995 92 0.595 0.274 0.569 2.798 0.434 0.285 14 051043 1904 1995 92 0.830 0.531 2.240 8.276 0.466 0.538 15 051045 1904 1995 92 0.665 0.477 2.137 9.099 0.495 0.542 16 051047 1903 1995 93 0.518 0.285 0.907 3.688 0.444 0.417 17 051051 1864 1995 132 0.467 0.300 0.957 3.498 0.443 0.482 18 051053 1864 1995 132 0.614 0.497 2.592 11.130 0.475 0.592 19 051055 1865 1995 131 0.552 0.399 0.913 3.516 0.442 0.651 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 051057 1864 1995 132 0.505 0.403 1.492 5.262 0.446 0.586 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 0.688 0.471 1.672 6.815 0.446 0.542 STANDARD DEVIATION 13 0.161 0.142 0.897 4.201 0.032 0.118 MEDIAN (50TH QUANTILE) 123 0.648 0.461 1.399 5.090 0.445 0.556 INTERQUARTILE RANGE 10 0.259 0.183 1.471 6.607 0.037 0.167 MINIMUM VALUE 92 0.467 0.274 0.569 2.780 0.384 0.285 LOWER HINGE (25TH QUANTILE) 115 0.572 0.359 0.910 3.507 0.434 0.457 UPPER HINGE (75TH QUANTILE) 125 0.831 0.542 2.381 10.115 0.471 0.625 MAXIMUM VALUE 132 1.096 0.777 3.657 17.205 0.495 0.724 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.236 0.235 0.017 0.232 2.268 -0.276 0.746 MINIMUM CORRELATION: -0.276 SERIES 051023 AND 051055 117 YEARS MAXIMUM CORRELATION: 0.746 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 0.561 0.483 0.558 0.578 0.404 0.260 0.433 0.416 0.277 0.278 SDEV 0.164 0.278 0.192 0.190 0.289 0.283 0.302 0.244 0.280 0.290 SERR 0.094 0.025 0.018 0.017 0.021 0.021 0.022 0.018 0.020 0.021 EPS 0.927 0.937 0.956 0.963 0.931 0.876 0.939 0.935 0.884 0.885 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 0.230 SDEV 0.313 SERR 0.023 EPS 0.857 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 0.616 0.245 0.470 2.575 0.331 0.456 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.754 0.618 -0.070 66 66 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 2.04 1.88 1.00 1.52 3.40 23.14 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.08 0.69 0.87 0.95 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 0.452 0.334 0.368 0.333 0.080 0.125 0.095 0.044 -0.072 -0.047 PACF 0.452 0.163 0.217 0.110 -0.223 0.042 -0.035 0.008 -0.098 -0.044 95% C.L. 0.174 0.207 0.222 0.240 0.254 0.255 0.256 0.257 0.258 0.258 |------------------ 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 5 0.316 0.339 0.111 0.201 0.195 -0.218 |================== 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 -0.00641027 1.08564842 2 051013 3 0.00000000 0.00000000 -0.00301241 1.04774487 3 051015 3 0.00000000 0.00000000 -0.00097518 0.70527613 4 051017 3 0.00000000 0.00000000 -0.00306144 0.78455096 5 051021 3 0.00000000 0.00000000 0.00784621 0.41262895 6 051023 3 0.00000000 0.00000000 0.01026783 0.47986132 7 051025 3 0.00000000 0.00000000 0.00612305 0.41010758 8 051027 3 0.00000000 0.00000000 0.00923856 0.30603597 9 051031 3 0.00000000 0.00000000 0.00327649 0.39924446 10 051033 3 0.00000000 0.00000000 -0.00154949 0.74889809 11 051035 3 0.00000000 0.00000000 -0.00378157 1.06983876 12 051037 3 0.00000000 0.00000000 -0.00160497 0.64208496 13 051041 3 0.00000000 0.00000000 -0.00043671 0.61563307 14 051043 3 0.00000000 0.00000000 0.00457701 0.61673439 15 051045 3 0.00000000 0.00000000 0.00002805 0.66347826 16 051047 3 0.00000000 0.00000000 0.00045731 0.49646330 17 051051 3 0.00000000 0.00000000 -0.00157433 0.57188988 18 051053 3 0.00000000 0.00000000 0.00149155 0.51444829 19 051055 3 0.00000000 0.00000000 -0.00600238 0.93885899 SERIES IDENT OPTION A B C D 20 051057 1 0.30311173 0.02428758 0.00000000 0.41019464 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 051011 1873 1995 123 0.986 0.608 1.149 4.963 0.430 0.554 2 051013 1873 1995 123 1.001 0.699 0.911 3.155 0.465 0.566 3 051015 1871 1995 125 1.000 0.711 1.478 4.951 0.430 0.601 4 051017 1871 1995 125 0.997 0.616 1.138 4.053 0.469 0.385 5 051021 1879 1995 117 1.003 0.642 2.615 12.369 0.392 0.607 6 051023 1879 1995 117 1.003 0.446 0.950 4.219 0.400 0.282 7 051025 1879 1995 117 1.002 0.540 1.825 8.059 0.381 0.584 8 051027 1879 1995 117 1.012 0.618 2.337 9.740 0.416 0.519 9 051031 1870 1995 126 0.996 0.505 0.836 3.096 0.450 0.286 10 051033 1871 1995 125 0.998 0.698 2.446 10.874 0.483 0.438 11 051035 1871 1995 125 0.996 0.578 1.067 4.121 0.479 0.355 12 051037 1872 1995 124 0.998 0.612 1.950 8.671 0.459 0.441 13 051041 1904 1995 92 1.000 0.463 0.633 2.888 0.429 0.288 14 051043 1904 1995 92 1.000 0.569 1.679 6.302 0.461 0.471 15 051045 1904 1995 92 1.000 0.717 2.132 9.074 0.490 0.536 16 051047 1903 1995 93 1.000 0.544 0.832 3.551 0.439 0.413 17 051051 1864 1995 132 1.000 0.663 1.245 4.272 0.440 0.464 18 051053 1864 1995 132 1.002 0.761 2.077 8.004 0.471 0.558 19 051055 1865 1995 131 1.008 0.689 1.193 4.426 0.486 0.582 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 051057 1864 1995 132 0.999 0.837 1.895 7.340 0.449 0.557 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.000 0.626 1.520 6.206 0.446 0.474 STANDARD DEVIATION 14 0.005 0.099 0.605 2.852 0.032 0.109 MEDIAN (50TH QUANTILE) 123 1.000 0.617 1.362 4.957 0.449 0.495 INTERQUARTILE RANGE 8 0.004 0.142 1.005 4.278 0.040 0.163 MINIMUM VALUE 92 0.986 0.446 0.633 2.888 0.381 0.282 LOWER HINGE (25TH QUANTILE) 117 0.998 0.556 1.009 4.087 0.430 0.399 UPPER HINGE (75TH QUANTILE) 125 1.002 0.698 2.013 8.365 0.470 0.562 MAXIMUM VALUE 132 1.012 0.837 2.615 12.369 0.490 0.607 |------------------------ 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 0.983 0.593 1.711 7.977 0.430 0.511 2 051013 1873 1995 123 0.959 0.623 1.263 5.046 0.463 0.481 3 051015 1871 1995 125 0.968 0.584 1.238 4.323 0.429 0.479 4 051017 1871 1995 125 0.983 0.578 1.200 4.259 0.468 0.347 5 051021 1879 1995 117 0.982 0.573 2.200 9.905 0.391 0.558 6 051023 1879 1995 117 0.997 0.434 0.874 3.892 0.400 0.250 7 051025 1879 1995 117 0.981 0.468 1.451 6.804 0.379 0.497 8 051027 1879 1995 117 0.986 0.532 2.021 8.328 0.416 0.458 9 051031 1870 1995 126 0.994 0.478 0.896 3.510 0.449 0.217 10 051033 1871 1995 125 0.989 0.535 1.607 6.630 0.481 0.279 11 051035 1871 1995 125 0.983 0.534 1.480 6.228 0.480 0.271 12 051037 1872 1995 124 0.991 0.543 1.815 8.174 0.459 0.350 13 051041 1904 1995 92 0.995 0.431 0.531 3.016 0.429 0.211 14 051043 1904 1995 92 0.994 0.532 1.457 5.768 0.462 0.435 15 051045 1904 1995 92 0.981 0.655 2.351 10.618 0.489 0.495 16 051047 1903 1995 93 0.989 0.522 0.874 3.901 0.438 0.365 17 051051 1864 1995 132 0.970 0.577 1.082 4.050 0.439 0.401 18 051053 1864 1995 132 0.966 0.536 1.166 4.117 0.472 0.397 19 051055 1865 1995 131 0.964 0.566 0.882 3.863 0.485 0.455 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 051057 1864 1995 132 0.944 0.623 1.509 6.109 0.450 0.431 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 0.980 0.546 1.380 5.826 0.445 0.394 STANDARD DEVIATION 14 0.014 0.060 0.477 2.222 0.032 0.104 MEDIAN (50TH QUANTILE) 123 0.983 0.539 1.357 5.407 0.450 0.416 INTERQUARTILE RANGE 8 0.021 0.054 0.670 3.415 0.041 0.167 MINIMUM VALUE 92 0.944 0.431 0.531 3.016 0.379 0.211 LOWER HINGE (25TH QUANTILE) 117 0.969 0.527 0.989 3.975 0.429 0.313 UPPER HINGE (75TH QUANTILE) 125 0.990 0.581 1.659 7.391 0.470 0.480 MAXIMUM VALUE 132 0.997 0.655 2.351 10.618 0.489 0.558 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.311 0.185 0.013 0.040 2.438 -0.122 0.749 MINIMUM CORRELATION: -0.122 SERIES 051021 AND 051047 93 YEARS MAXIMUM CORRELATION: 0.749 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 0.469 0.475 0.600 0.591 0.420 0.277 0.452 0.413 0.281 0.280 SDEV 0.269 0.292 0.160 0.186 0.260 0.280 0.268 0.238 0.277 0.267 SERR 0.156 0.027 0.015 0.017 0.019 0.020 0.019 0.017 0.020 0.019 EPS 0.898 0.935 0.963 0.965 0.935 0.884 0.943 0.934 0.887 0.886 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 0.240 SDEV 0.291 SERR 0.021 EPS 0.863 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 0.937 0.322 0.390 2.579 0.317 0.359 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.625 0.398 -0.008 47 85 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.34 0.71 1.01 1.18 1.89 9.22 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.73 0.87 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 0.357 0.223 0.287 0.270 -0.027 0.042 0.025 -0.017 -0.150 -0.086 PACF 0.357 0.110 0.206 0.123 -0.236 0.026 -0.052 0.005 -0.112 -0.037 95% C.L. 0.174 0.195 0.203 0.215 0.225 0.225 0.225 0.225 0.225 0.228 |------------------ 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 0.139 0.358 |======================= 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 0.359 0.220 0.297 0.245 -0.049 0.012 -0.032 -0.073 -0.148 -0.100 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 0.359 2 0.322 0.105 3 0.299 0.034 0.219 4 0.280 0.031 0.194 0.086 5 0.301 0.079 0.201 0.155 -0.247 6 0.302 0.078 0.201 0.155 -0.248 0.003 7 0.302 0.055 0.216 0.174 -0.240 0.032 -0.097 8 0.303 0.054 0.216 0.173 -0.241 0.032 -0.098 0.004 9 0.303 0.048 0.219 0.158 -0.230 0.046 -0.094 0.023 -0.064 10 0.301 0.049 0.216 0.159 -0.237 0.051 -0.087 0.025 -0.055 -0.031 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) 1123.60 1107.35 1107.89 1103.39 1104.42 1098.12 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1100.12 1100.89 1102.88 1104.33 1106.21 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 0.359 R-SQUARED DUE TO POOLED AUTOREGRESSION: 12.91 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 114.83 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.359 0.129 0.046 0.017 0.006 0.002 0.001 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 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 1 0.284 0.514 2 051013 1 0.233 0.483 3 051015 1 0.272 0.483 4 051017 1 0.182 0.349 5 051021 1 0.319 0.564 6 051023 1 0.106 0.252 7 051025 1 0.258 0.505 8 051027 1 0.212 0.460 9 051031 1 0.065 0.219 10 051033 1 0.089 0.281 11 051035 1 0.085 0.272 12 051037 1 0.141 0.352 13 051041 1 0.047 0.211 14 051043 1 0.199 0.435 15 051045 1 0.250 0.497 16 051047 1 0.141 0.373 17 051051 1 0.220 0.401 18 051053 1 0.163 0.397 19 051055 1 0.246 0.457 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 051057 1 0.243 0.432 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.188 0.397 STANDARD DEVIATION 0 0.079 0.105 MEDIAN 1 0.206 0.417 INTERQUARTILE RANGE 0 0.125 0.168 MINIMUM VALUE 1 0.047 0.211 LOWER HINGE 1 0.123 0.315 UPPER HINGE 1 0.248 0.483 MAXIMUM VALUE 1 0.319 0.564 |------------------- 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 0.504 1.587 8.870 0.540 -0.080 2 051013 1873 1995 123 1.000 0.545 1.643 7.027 0.548 0.000 3 051015 1871 1995 125 1.002 0.506 1.285 5.127 0.502 -0.076 4 051017 1871 1995 125 1.000 0.542 1.141 4.316 0.548 -0.090 5 051021 1879 1995 117 1.001 0.472 1.818 8.149 0.497 -0.019 6 051023 1879 1995 117 1.000 0.420 1.028 3.891 0.438 -0.051 7 051025 1879 1995 117 1.000 0.403 1.020 4.455 0.432 0.038 8 051027 1879 1995 117 1.000 0.473 1.604 7.217 0.492 0.018 9 051031 1870 1995 126 1.000 0.466 0.947 3.619 0.488 -0.027 10 051033 1871 1995 125 1.000 0.513 1.426 5.913 0.534 -0.025 11 051035 1871 1995 125 1.000 0.514 1.162 4.988 0.563 -0.030 12 051037 1872 1995 124 1.000 0.508 1.761 8.331 0.521 -0.048 13 051041 1904 1995 92 1.000 0.421 0.576 3.275 0.464 0.011 14 051043 1904 1995 92 1.000 0.479 1.026 4.169 0.507 0.046 15 051045 1904 1995 92 1.002 0.565 1.574 6.488 0.564 0.036 16 051047 1903 1995 93 1.004 0.473 1.009 4.604 0.486 0.012 17 051051 1864 1995 132 1.001 0.526 1.276 4.793 0.505 -0.102 18 051053 1864 1995 132 1.000 0.492 1.167 4.335 0.488 0.030 19 051055 1865 1995 131 1.004 0.494 0.907 4.251 0.554 -0.080 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 051057 1864 1995 132 1.004 0.553 1.781 8.488 0.524 -0.068 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.001 0.493 1.287 5.615 0.510 -0.025 STANDARD DEVIATION 14 0.001 0.044 0.346 1.798 0.038 0.047 MEDIAN (50TH QUANTILE) 123 1.000 0.499 1.221 4.890 0.506 -0.026 INTERQUARTILE RANGE 8 0.002 0.048 0.572 2.839 0.056 0.087 MINIMUM VALUE 92 1.000 0.403 0.576 3.275 0.432 -0.102 LOWER HINGE (25TH QUANTILE) 117 1.000 0.472 1.023 4.283 0.488 -0.072 UPPER HINGE (75TH QUANTILE) 125 1.002 0.520 1.596 7.122 0.544 0.015 MAXIMUM VALUE 132 1.004 0.565 1.818 8.870 0.564 0.046 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.329 0.153 0.011 0.054 2.642 -0.020 0.694 MINIMUM CORRELATION: -0.020 SERIES 051015 AND 051045 92 YEARS MAXIMUM CORRELATION: 0.694 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 0.605 0.465 0.622 0.619 0.435 0.315 0.424 0.391 0.277 0.320 SDEV 0.115 0.242 0.148 0.186 0.286 0.295 0.216 0.234 0.246 0.237 SERR 0.066 0.022 0.014 0.017 0.021 0.021 0.016 0.017 0.018 0.017 EPS 0.938 0.933 0.966 0.969 0.939 0.902 0.936 0.928 0.885 0.904 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 0.295 SDEV 0.230 SERR 0.017 EPS 0.893 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 0.966 0.294 0.348 2.635 0.350 -0.070 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.612 0.354 -0.009 51 81 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.28 0.95 1.00 1.09 2.04 4.42 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.74 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 -0.070 -0.021 0.139 0.207 -0.166 0.043 0.024 0.013 -0.153 -0.027 PACF -0.070 -0.026 0.137 0.232 -0.135 0.004 -0.040 0.012 -0.104 -0.083 95% C.L. 0.174 0.175 0.175 0.178 0.185 0.190 0.190 0.190 0.190 0.194 |------------------ 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 -0.016 0.153 0.207 -0.150 0.033 0.027 0.004 -0.156 -0.037 PACF -0.002 -0.016 0.153 0.212 -0.149 0.011 -0.040 0.007 -0.110 -0.074 95% C.L. 0.174 0.174 0.174 0.178 0.185 0.189 0.189 0.189 0.189 0.193 |----------------- 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 0.000 -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 0.967 0.316 0.362 2.549 0.297 0.377 |------------ 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 0.374 0.184 0.244 0.220 -0.042 0.013 0.007 -0.045 -0.161 -0.087 PACF 0.374 0.052 0.185 0.083 -0.208 0.046 -0.053 -0.018 -0.117 -0.011 95% C.L. 0.174 0.197 0.202 0.211 0.218 0.218 0.218 0.218 0.218 0.222 |------------------- 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 0.143 0.375 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.13 MINUTES