RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM054W.rwl.conv LOG FILE PROCESSED: GERM054W.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_RING 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 2.230 1.445 0.841 3.514 0.284 0.843 2 051013 1873 1995 123 2.383 1.379 0.887 4.267 0.301 0.808 3 051015 1871 1995 125 2.046 1.132 1.024 4.800 0.273 0.810 4 051017 1871 1995 125 1.918 1.090 1.617 8.310 0.303 0.752 5 051021 1879 1995 117 2.589 1.419 1.763 7.773 0.322 0.433 6 051023 1879 1995 117 3.053 1.308 1.531 7.175 0.261 0.721 7 051025 1879 1995 117 2.500 1.133 1.699 8.869 0.256 0.704 8 051027 1879 1995 117 2.647 1.387 1.906 7.248 0.295 0.704 9 051031 1870 1995 126 2.612 0.976 -0.259 2.364 0.263 0.625 10 051033 1871 1995 125 2.615 1.458 0.379 2.357 0.291 0.831 11 051035 1871 1995 125 2.790 1.183 0.335 2.701 0.297 0.655 12 051037 1872 1995 124 2.204 1.085 0.475 2.869 0.270 0.745 13 051041 1904 1995 92 3.040 1.214 0.456 4.270 0.267 0.616 14 051043 1904 1995 92 3.609 1.498 0.636 4.013 0.294 0.639 15 051045 1904 1995 92 3.000 1.531 0.557 3.232 0.336 0.726 16 051047 1903 1995 93 2.805 1.421 0.333 2.485 0.347 0.627 17 051051 1864 1995 132 1.997 1.407 1.332 5.227 0.290 0.885 18 051053 1864 1995 132 2.529 1.602 1.231 5.167 0.314 0.810 19 051055 1865 1995 131 2.236 1.647 1.066 3.920 0.279 0.861 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 051057 1864 1995 132 1.981 1.385 1.062 3.844 0.294 0.859 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 2.539 1.335 0.943 4.720 0.292 0.733 STANDARD DEVIATION 13 0.435 0.186 0.583 2.076 0.025 0.112 MEDIAN (50TH QUANTILE) 123 2.559 1.386 0.955 4.140 0.292 0.735 INTERQUARTILE RANGE 10 0.581 0.294 0.965 3.151 0.030 0.174 MINIMUM VALUE 92 1.918 0.976 -0.259 2.357 0.256 0.433 LOWER HINGE (25TH QUANTILE) 115 2.217 1.158 0.466 3.050 0.272 0.647 UPPER HINGE (75TH QUANTILE) 125 2.798 1.451 1.431 6.201 0.302 0.821 MAXIMUM VALUE 132 3.609 1.647 1.906 8.869 0.347 0.885 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.336 0.283 0.021 0.048 2.090 -0.247 0.909 MINIMUM CORRELATION: -0.247 SERIES 051023 AND 051041 92 YEARS MAXIMUM CORRELATION: 0.909 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 0.871 0.377 0.601 0.540 0.598 0.487 0.591 0.575 0.365 0.242 SDEV 0.042 0.504 0.209 0.205 0.180 0.237 0.360 0.221 0.306 0.366 SERR 0.024 0.046 0.019 0.019 0.013 0.017 0.026 0.016 0.022 0.027 EPS 0.985 0.906 0.963 0.958 0.968 0.950 0.967 0.964 0.920 0.865 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 0.357 SERR 0.026 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 2.470 0.894 0.403 3.519 0.231 0.725 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.265 0.131 0.681 39 93 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.27 1.31 1.01 1.10 2.41 7.47 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.44 0.86 0.92 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 0.720 0.576 0.477 0.404 0.298 0.237 0.150 0.119 0.079 0.106 PACF 0.720 0.121 0.053 0.036 -0.080 0.012 -0.082 0.040 -0.015 0.112 95% C.L. 0.174 0.248 0.286 0.309 0.325 0.333 0.338 0.340 0.341 0.342 |------------------ 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 0.539 0.635 0.127 |================== 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 -0.02344707 3.68371844 2 051013 3 0.00000000 0.00000000 -0.01646283 3.40378523 3 051015 1 2.08862901 0.01120971 0.00000000 0.92866766 4 051017 3 0.00000000 0.00000000 -0.01576381 2.91088009 5 051021 1 2.82916617 0.32782283 0.00000000 2.52638698 6 051023 3 0.00000000 0.00000000 0.00960328 2.46732736 7 051025 1 2.49146962 0.18319082 0.00000000 2.39382386 8 051027 3 0.00000000 0.00000000 0.00398537 2.41187143 9 051031 3 0.00000000 0.00000000 -0.00566011 2.97132182 10 051033 3 0.00000000 0.00000000 -0.02187963 3.99345684 11 051035 3 0.00000000 0.00000000 -0.01507779 3.73958063 12 051037 3 0.00000000 0.00000000 -0.01322924 3.03045630 13 051041 3 0.00000000 0.00000000 -0.02094200 4.01402044 14 051043 3 0.00000000 0.00000000 -0.01232642 4.18176556 15 051045 3 0.00000000 0.00000000 -0.01559946 3.72537518 16 051047 3 0.00000000 0.00000000 -0.01393677 3.46051192 17 051051 1 3.67629194 0.01253862 0.00000000 0.21121074 18 051053 1 2.78219032 0.01572950 0.00000000 1.36670923 19 051055 3 0.00000000 0.00000000 -0.03192717 4.32260847 SERIES IDENT OPTION A B C D 20 051057 1 3.39987302 0.02146351 0.00000000 0.84264791 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 051011 1873 1995 123 0.979 0.528 0.885 3.376 0.281 0.733 2 051013 1873 1995 123 1.006 0.538 0.550 2.776 0.297 0.750 3 051015 1871 1995 125 1.001 0.535 0.984 3.721 0.270 0.784 4 051017 1871 1995 125 0.995 0.464 0.904 4.315 0.300 0.637 5 051021 1879 1995 117 1.000 0.551 1.966 8.677 0.320 0.415 6 051023 1879 1995 117 1.001 0.393 0.944 4.958 0.263 0.664 7 051025 1879 1995 117 1.000 0.449 2.094 11.279 0.253 0.683 8 051027 1879 1995 117 1.000 0.505 1.620 6.211 0.292 0.691 9 051031 1870 1995 126 1.000 0.372 -0.125 2.489 0.260 0.618 10 051033 1871 1995 125 0.984 0.461 0.411 2.551 0.288 0.755 11 051035 1871 1995 125 0.997 0.387 0.761 4.256 0.295 0.578 12 051037 1872 1995 124 0.997 0.465 0.780 3.602 0.269 0.706 13 051041 1904 1995 92 0.998 0.390 1.346 7.210 0.264 0.542 14 051043 1904 1995 92 1.000 0.426 0.983 4.480 0.291 0.620 15 051045 1904 1995 92 0.999 0.549 1.363 5.126 0.332 0.730 16 051047 1903 1995 93 1.000 0.526 0.781 3.320 0.343 0.577 17 051051 1864 1995 132 1.010 0.622 1.023 3.540 0.289 0.818 18 051053 1864 1995 132 1.001 0.622 1.606 6.502 0.312 0.733 19 051055 1865 1995 131 1.150 0.851 1.917 6.573 0.297 0.857 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 051057 1864 1995 132 1.006 0.655 1.429 4.942 0.303 0.751 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.006 0.514 1.111 4.995 0.291 0.682 STANDARD DEVIATION 14 0.035 0.114 0.557 2.222 0.024 0.104 MEDIAN (50TH QUANTILE) 123 1.000 0.515 0.983 4.398 0.292 0.698 INTERQUARTILE RANGE 8 0.004 0.113 0.736 2.898 0.032 0.131 MINIMUM VALUE 92 0.979 0.372 -0.125 2.489 0.253 0.415 LOWER HINGE (25TH QUANTILE) 117 0.997 0.438 0.781 3.458 0.270 0.619 UPPER HINGE (75TH QUANTILE) 125 1.001 0.550 1.517 6.356 0.301 0.750 MAXIMUM VALUE 132 1.150 0.851 2.094 11.279 0.343 0.857 |------------------------ 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 0.499 1.415 4.983 0.281 0.670 2 051013 1873 1995 123 0.973 0.472 0.887 3.904 0.298 0.667 3 051015 1871 1995 125 0.983 0.467 0.781 3.248 0.270 0.718 4 051017 1871 1995 125 0.990 0.445 1.097 4.953 0.300 0.604 5 051021 1879 1995 117 0.983 0.474 1.501 7.692 0.318 0.376 6 051023 1879 1995 117 0.995 0.353 0.557 4.227 0.263 0.596 7 051025 1879 1995 117 0.985 0.374 1.590 9.808 0.252 0.594 8 051027 1879 1995 117 0.987 0.414 1.308 5.731 0.292 0.602 9 051031 1870 1995 126 0.993 0.357 0.018 2.645 0.260 0.568 10 051033 1871 1995 125 0.991 0.403 0.375 2.827 0.288 0.606 11 051035 1871 1995 125 0.993 0.364 0.820 4.442 0.294 0.518 12 051037 1872 1995 124 0.993 0.437 0.595 3.240 0.268 0.673 13 051041 1904 1995 92 0.995 0.339 0.718 5.239 0.264 0.456 14 051043 1904 1995 92 0.993 0.367 0.411 3.699 0.289 0.509 15 051045 1904 1995 92 0.982 0.467 1.249 5.386 0.330 0.686 16 051047 1903 1995 93 0.985 0.492 0.770 3.543 0.344 0.546 17 051051 1864 1995 132 0.962 0.474 0.575 2.778 0.287 0.741 18 051053 1864 1995 132 0.968 0.431 0.659 3.402 0.311 0.613 19 051055 1865 1995 131 0.965 0.420 0.659 3.356 0.296 0.679 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 051057 1864 1995 132 0.963 0.464 0.922 4.164 0.303 0.637 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 0.983 0.426 0.845 4.463 0.290 0.603 STANDARD DEVIATION 14 0.011 0.051 0.408 1.756 0.024 0.090 MEDIAN (50TH QUANTILE) 123 0.985 0.434 0.776 4.034 0.291 0.605 INTERQUARTILE RANGE 8 0.015 0.099 0.588 1.809 0.032 0.114 MINIMUM VALUE 92 0.962 0.339 0.018 2.645 0.252 0.376 LOWER HINGE (25TH QUANTILE) 117 0.978 0.371 0.585 3.302 0.269 0.557 UPPER HINGE (75TH QUANTILE) 125 0.993 0.469 1.173 5.111 0.301 0.671 MAXIMUM VALUE 132 0.995 0.499 1.590 9.808 0.344 0.741 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.333 0.230 0.017 0.137 2.267 -0.173 0.860 MINIMUM CORRELATION: -0.173 SERIES 051021 AND 051047 93 YEARS MAXIMUM CORRELATION: 0.860 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 0.807 0.409 0.635 0.610 0.541 0.500 0.605 0.591 0.384 0.261 SDEV 0.099 0.439 0.177 0.157 0.176 0.242 0.310 0.212 0.297 0.334 SERR 0.057 0.040 0.016 0.014 0.013 0.018 0.022 0.015 0.022 0.024 EPS 0.976 0.917 0.968 0.968 0.959 0.952 0.968 0.967 0.926 0.876 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 0.207 SDEV 0.339 SERR 0.025 EPS 0.840 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 0.960 0.273 0.139 2.697 0.226 0.541 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.425 0.266 0.037 36 96 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.26 0.70 1.00 1.06 1.76 3.25 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.05 0.44 0.87 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 0.537 0.371 0.277 0.175 0.032 -0.021 -0.152 -0.152 -0.160 -0.132 PACF 0.537 0.115 0.055 -0.025 -0.124 -0.031 -0.164 0.008 -0.023 0.021 95% C.L. 0.174 0.219 0.237 0.246 0.250 0.250 0.250 0.253 0.256 0.259 |------------------ 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 0.303 0.541 |======================= 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 0.516 0.373 0.290 0.181 0.040 -0.001 -0.162 -0.133 -0.152 -0.139 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 0.516 2 0.440 0.146 3 0.430 0.115 0.070 4 0.432 0.119 0.084 -0.032 5 0.429 0.129 0.098 0.021 -0.122 6 0.426 0.129 0.100 0.023 -0.113 -0.021 7 0.422 0.107 0.105 0.043 -0.088 0.063 -0.198 8 0.430 0.105 0.108 0.041 -0.092 0.059 -0.215 0.041 9 0.431 0.098 0.110 0.039 -0.091 0.062 -0.212 0.054 -0.030 10 0.431 0.097 0.112 0.038 -0.090 0.062 -0.213 0.053 -0.035 0.010 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) 1065.29 1026.48 1025.64 1027.00 1028.86 1028.88 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1030.82 1027.56 1029.34 1031.22 1033.21 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 0.440 0.146 R-SQUARED DUE TO POOLED AUTOREGRESSION: 28.15 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 139.19 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.440 0.340 0.214 0.144 0.095 0.063 0.041 0.027 0.018 0.0120 0.008 0.005 0.003 0.002 0.002 0.001 0.001 0.000 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 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 051011 2 0.477 0.524 0.219 2 051013 2 0.449 0.710 -0.063 3 051015 2 0.527 0.686 0.053 4 051017 2 0.386 0.504 0.170 5 051021 2 0.255 0.312 0.180 6 051023 2 0.374 0.623 -0.032 7 051025 2 0.370 0.637 -0.051 8 051027 2 0.375 0.635 -0.043 9 051031 2 0.348 0.606 -0.031 10 051033 2 0.369 0.620 -0.022 11 051035 2 0.272 0.509 0.019 12 051037 2 0.471 0.569 0.159 13 051041 2 0.214 0.442 0.041 14 051043 2 0.266 0.492 0.037 15 051045 2 0.481 0.675 0.017 16 051047 2 0.328 0.470 0.145 17 051051 2 0.564 0.637 0.144 18 051053 2 0.383 0.648 -0.052 19 051055 2 0.471 0.692 -0.018 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 051057 2 0.459 0.474 0.261 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.392 0.573 0.057 STANDARD DEVIATION 0 0.095 0.103 0.103 MEDIAN 2 0.379 0.613 0.028 INTERQUARTILE RANGE 0 0.133 0.145 0.183 MINIMUM VALUE 2 0.214 0.312 -0.063 LOWER HINGE 2 0.338 0.498 -0.032 UPPER HINGE 2 0.471 0.643 0.152 MAXIMUM VALUE 2 0.564 0.710 0.261 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 051011 1873 1995 123 1.000 0.361 0.812 6.163 0.368 0.005 2 051013 1873 1995 123 1.000 0.350 1.415 6.660 0.336 -0.001 3 051015 1871 1995 125 1.000 0.321 0.913 4.617 0.330 0.006 4 051017 1871 1995 125 1.000 0.349 0.859 4.778 0.362 0.003 5 051021 1879 1995 117 1.004 0.419 1.838 9.895 0.363 0.001 6 051023 1879 1995 117 1.000 0.281 0.780 4.538 0.312 0.002 7 051025 1879 1995 117 1.000 0.297 1.140 5.858 0.319 0.012 8 051027 1879 1995 117 1.000 0.328 0.988 5.309 0.376 0.002 9 051031 1870 1995 126 1.000 0.287 -0.046 3.084 0.331 0.000 10 051033 1871 1995 125 1.000 0.320 0.372 4.294 0.360 0.002 11 051035 1871 1995 125 1.000 0.311 0.439 4.098 0.365 0.000 12 051037 1872 1995 124 1.000 0.317 0.340 4.712 0.344 0.000 13 051041 1904 1995 92 1.000 0.301 0.943 5.056 0.309 0.003 14 051043 1904 1995 92 1.000 0.315 0.316 3.764 0.360 0.004 15 051045 1904 1995 92 1.000 0.339 1.206 7.963 0.392 0.003 16 051047 1903 1995 93 1.000 0.406 0.821 4.159 0.419 0.016 17 051051 1864 1995 132 1.000 0.313 0.321 3.702 0.343 -0.006 18 051053 1864 1995 132 1.000 0.339 0.702 4.302 0.373 -0.003 19 051055 1865 1995 131 1.000 0.308 0.020 3.140 0.361 0.001 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 051057 1864 1995 132 1.000 0.343 0.593 5.613 0.359 -0.032 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.000 0.330 0.739 5.085 0.354 0.001 STANDARD DEVIATION 14 0.001 0.035 0.465 1.642 0.027 0.009 MEDIAN (50TH QUANTILE) 123 1.000 0.321 0.796 4.664 0.360 0.002 INTERQUARTILE RANGE 8 0.000 0.037 0.609 1.607 0.033 0.004 MINIMUM VALUE 92 1.000 0.281 -0.046 3.084 0.309 -0.032 LOWER HINGE (25TH QUANTILE) 117 1.000 0.309 0.356 4.128 0.334 0.000 UPPER HINGE (75TH QUANTILE) 125 1.000 0.346 0.965 5.735 0.367 0.004 MAXIMUM VALUE 132 1.004 0.419 1.838 9.895 0.419 0.016 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.438 0.154 0.011 0.025 2.841 0.045 0.804 MINIMUM CORRELATION: 0.045 SERIES 051021 AND 051047 93 YEARS MAXIMUM CORRELATION: 0.804 SERIES 051015 AND 051017 125 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 0.823 0.481 0.716 0.690 0.615 0.595 0.606 0.652 0.497 0.380 SDEV 0.039 0.283 0.114 0.120 0.136 0.144 0.171 0.140 0.186 0.246 SERR 0.022 0.026 0.010 0.011 0.010 0.010 0.012 0.010 0.013 0.018 EPS 0.979 0.937 0.978 0.977 0.970 0.967 0.968 0.974 0.952 0.924 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 0.375 SDEV 0.265 SERR 0.019 EPS 0.923 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 0.989 0.224 0.024 2.894 0.276 -0.101 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.389 0.183 0.024 48 84 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.31 0.58 1.01 1.11 1.69 5.43 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.07 0.69 0.86 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 -0.100 -0.028 0.053 0.044 -0.066 0.053 -0.142 -0.029 -0.096 -0.072 PACF -0.100 -0.039 0.047 0.054 -0.054 0.041 -0.144 -0.052 -0.116 -0.094 95% C.L. 0.174 0.176 0.176 0.176 0.177 0.178 0.178 0.181 0.182 0.183 |------------------ 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 0.007 0.049 0.044 -0.061 0.031 -0.150 -0.056 -0.113 -0.079 PACF 0.002 0.007 0.049 0.044 -0.062 0.029 -0.155 -0.053 -0.113 -0.074 95% C.L. 0.174 0.174 0.174 0.175 0.175 0.175 0.176 0.179 0.180 0.182 |----------------- 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 0.003 0.002 0.007 |========================= 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 0.992 0.263 0.071 2.831 0.218 0.521 |------------ 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 0.517 0.376 0.245 0.139 -0.002 -0.046 -0.186 -0.174 -0.192 -0.145 PACF 0.517 0.149 0.003 -0.036 -0.124 -0.026 -0.171 0.000 -0.038 0.024 95% C.L. 0.174 0.216 0.235 0.242 0.245 0.245 0.245 0.249 0.253 0.257 |------------------- 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 0.288 0.443 0.149 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.22 MINUTES