RUN: ITAL002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: ITAL008L.rwl.conv LOG FILE PROCESSED: ITAL008L.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 50 25 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: 614 1 Mt.Falterona WIDTH_LATE ABAL - 614 2 Italy silver fir, European fir 1450 4352-1140 1827 1980 - 614 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 1 614011 MISSING VALUES FOUND: 1 IN 1 GAPS / 1953 1953 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 614011 1862 1980 119 0.481 0.282 1.189 4.258 0.313 0.702 2 614012 1873 1980 108 0.483 0.300 1.119 3.281 0.336 0.662 3 614021 1875 1980 106 0.692 0.287 0.121 2.593 0.292 0.583 4 614022 1866 1980 115 0.693 0.466 2.100 9.376 0.261 0.813 5 614031 1888 1980 93 0.527 0.333 0.782 3.013 0.304 0.744 6 614033 1894 1980 87 0.667 0.373 1.205 4.083 0.322 0.725 7 614041 1885 1980 96 0.789 0.336 0.330 2.820 0.292 0.662 8 614042 1875 1980 106 0.506 0.362 2.611 11.603 0.331 0.687 9 614052 1868 1980 113 0.456 0.158 0.923 3.988 0.257 0.589 10 614061 1869 1980 112 0.318 0.162 0.716 3.440 0.320 0.638 11 614062 1869 1980 112 0.407 0.208 0.867 3.764 0.302 0.652 12 614071 1827 1980 154 0.636 0.337 0.880 3.123 0.270 0.809 13 614072 1888 1978 91 0.813 0.559 1.155 4.743 0.341 0.853 14 614081 1894 1980 87 0.660 0.336 0.355 2.925 0.298 0.778 15 614082 1886 1980 95 0.606 0.275 0.199 2.985 0.291 0.683 16 614091 1885 1980 96 0.552 0.241 0.471 2.787 0.269 0.688 17 614101 1877 1980 104 0.384 0.173 0.280 2.614 0.273 0.726 18 614102 1875 1980 106 0.518 0.239 0.014 2.168 0.265 0.790 19 614111 1892 1980 89 0.830 0.305 0.318 3.324 0.254 0.612 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 614112 1883 1980 98 0.593 0.227 0.486 2.419 0.293 0.565 21 614121 1902 1980 79 0.590 0.454 2.519 9.998 0.320 0.785 22 614122 1879 1980 102 0.458 0.205 0.491 2.707 0.297 0.631 NUMBER OF SERIES READ IN: 22 FROM 1827 TO 1980 154 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 0.575 0.301 0.870 4.182 0.296 0.699 STANDARD DEVIATION 15 0.138 0.102 0.726 2.602 0.026 0.081 MEDIAN (50TH QUANTILE) 103 0.571 0.293 0.749 3.202 0.295 0.687 INTERQUARTILE RANGE 19 0.186 0.110 0.825 1.296 0.051 0.140 MINIMUM VALUE 79 0.318 0.158 0.014 2.168 0.254 0.565 LOWER HINGE (25TH QUANTILE) 93 0.481 0.227 0.330 2.787 0.270 0.638 UPPER HINGE (75TH QUANTILE) 112 0.667 0.337 1.155 4.083 0.320 0.778 MAXIMUM VALUE 154 0.830 0.559 2.611 11.603 0.341 0.853 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.226 0.233 0.015 -0.097 2.175 -0.272 0.738 MINIMUM CORRELATION: -0.272 SERIES 614033 AND 614101 87 YEARS MAXIMUM CORRELATION: 0.738 SERIES 614072 AND 614121 77 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 61.63 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1905. 1930. 1955. CORR 66. 231. 210. RBAR 0.373 0.206 0.189 SDEV 0.253 0.277 0.296 SERR 0.031 0.018 0.020 EPS 0.923 0.851 0.836 NSS 20.1 22.0 22.0 |======================== 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 1827 1980 154 0.639 0.276 1.499 5.371 0.210 0.778 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.327 -0.166 0.311 44 110 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.35 1.05 1.00 1.06 2.11 8.30 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.87 0.92 0.00 0.00 0.92 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 103. 19. 79. 93. 112. 154. |----------- 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 0.773 0.712 0.602 0.525 0.423 0.396 0.383 0.355 0.364 0.373 PACF 0.773 0.285 -0.032 -0.009 -0.079 0.102 0.131 0.001 0.073 0.068 95% C.L. 0.161 0.239 0.289 0.320 0.341 0.355 0.366 0.376 0.385 0.394 |------------------ 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 0.645 0.546 0.301 |================== 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 614011 1 0.38869643 0.04911508 0.00000000 0.41379315 2 614012 1 0.61702222 0.04002677 0.00000000 0.34473684 3 614021 1 0.74310058 0.08830818 0.00000000 0.61586893 4 614022 1 0.36134133 0.08619235 0.00000000 0.65770441 5 614031 1 0.52888137 0.09304617 0.00000000 0.46900231 6 614033 3 0.00000000 0.00000000 0.00302635 0.53373694 7 614041 3 0.00000000 0.00000000 -0.00681816 1.11974347 8 614042 1 1.23075378 0.05906585 0.00000000 0.31567267 9 614052 3 0.00000000 0.00000000 0.00041254 0.43294564 10 614061 1 0.42719087 0.27200955 0.00000000 0.30601278 11 614062 3 0.00000000 0.00000000 -0.00121357 0.47588804 12 614071 1 0.46787739 0.02814160 0.00000000 0.53125405 13 614072 3 0.00000000 0.00000000 -0.01412406 1.46311355 14 614081 1 0.60244167 0.05171166 0.00000000 0.53051788 15 614082 1 0.66655415 0.00546706 0.00000000 0.08764011 16 614091 1 0.33166513 0.05863748 0.00000000 0.49508157 17 614101 1 0.48478305 0.06742117 0.00000000 0.31726602 18 614102 1 0.47128969 0.05013215 0.00000000 0.43158349 19 614111 3 0.00000000 0.00000000 -0.00502162 1.05586052 SERIES IDENT OPTION A B C D 20 614112 3 0.00000000 0.00000000 -0.00496280 0.83820957 21 614121 1 1.84119081 0.10671616 0.00000000 0.38347834 22 614122 3 0.00000000 0.00000000 -0.00342169 0.63396233 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 614011 1862 1980 119 0.999 0.587 1.622 6.319 0.319 0.756 2 614012 1873 1980 108 0.999 0.604 2.108 7.159 0.333 0.656 3 614021 1875 1980 106 1.000 0.389 0.323 3.320 0.290 0.474 4 614022 1866 1980 115 1.000 0.690 2.432 11.040 0.259 0.819 5 614031 1888 1980 93 0.999 0.660 1.393 4.631 0.302 0.719 6 614033 1894 1980 87 1.001 0.543 1.051 3.564 0.318 0.665 7 614041 1885 1980 96 0.999 0.380 0.718 3.951 0.288 0.541 8 614042 1875 1980 106 0.998 0.382 0.640 2.688 0.327 0.403 9 614052 1868 1980 113 1.000 0.342 0.801 3.695 0.255 0.577 10 614061 1869 1980 112 1.000 0.504 0.866 4.006 0.318 0.633 11 614062 1869 1980 112 0.999 0.522 1.106 4.436 0.299 0.655 12 614071 1827 1980 154 0.999 0.498 0.737 2.727 0.268 0.769 13 614072 1888 1978 91 0.971 0.558 1.575 6.061 0.334 0.686 14 614081 1894 1980 87 0.999 0.496 0.695 4.204 0.295 0.765 15 614082 1886 1980 95 1.000 0.444 0.185 2.977 0.288 0.657 16 614091 1885 1980 96 1.000 0.427 0.653 3.286 0.266 0.659 17 614101 1877 1980 104 0.999 0.387 0.098 3.076 0.269 0.606 18 614102 1875 1980 106 0.999 0.452 0.503 3.231 0.262 0.783 19 614111 1892 1980 89 0.998 0.353 0.927 5.041 0.250 0.586 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 614112 1883 1980 98 0.999 0.305 0.685 2.949 0.290 0.288 21 614121 1902 1980 79 0.997 0.440 0.806 3.694 0.312 0.571 22 614122 1879 1980 102 0.991 0.389 0.639 3.175 0.293 0.543 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 0.998 0.471 0.935 4.329 0.293 0.628 STANDARD DEVIATION 15 0.006 0.105 0.580 1.921 0.026 0.128 MEDIAN (50TH QUANTILE) 103 0.999 0.448 0.769 3.695 0.291 0.655 INTERQUARTILE RANGE 19 0.001 0.156 0.466 1.456 0.050 0.148 MINIMUM VALUE 79 0.971 0.305 0.098 2.688 0.250 0.288 LOWER HINGE (25TH QUANTILE) 93 0.999 0.387 0.640 3.175 0.268 0.571 UPPER HINGE (75TH QUANTILE) 112 1.000 0.543 1.106 4.631 0.318 0.719 MAXIMUM VALUE 154 1.001 0.690 2.432 11.040 0.334 0.819 |------------------------ 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 614011 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 614012 -67 72 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 614021 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 614022 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 614031 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 614033 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 614041 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 614042 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 614052 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 614061 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 614062 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 614071 -67 103 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 614072 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 614081 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 614082 -67 63 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 614091 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 614101 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 614102 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 614111 -67 59 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 614112 -67 65 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 614121 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 614122 -67 68 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 614011 1862 1980 119 0.989 0.467 0.791 4.473 0.318 0.653 2 614012 1873 1980 108 0.987 0.461 1.180 4.177 0.333 0.514 3 614021 1875 1980 106 0.989 0.349 0.361 3.169 0.289 0.406 4 614022 1866 1980 115 0.954 0.458 1.643 7.764 0.259 0.736 5 614031 1888 1980 93 0.951 0.462 0.914 3.632 0.301 0.590 6 614033 1894 1980 87 0.976 0.458 1.102 4.092 0.316 0.602 7 614041 1885 1980 96 0.993 0.357 0.615 3.769 0.288 0.491 8 614042 1875 1980 106 0.995 0.358 0.474 2.523 0.327 0.337 9 614052 1868 1980 113 0.998 0.328 0.702 3.752 0.255 0.543 10 614061 1869 1980 112 0.987 0.451 0.477 2.806 0.317 0.574 11 614062 1869 1980 112 0.975 0.399 0.822 3.750 0.298 0.492 12 614071 1827 1980 154 0.978 0.408 0.720 3.249 0.269 0.688 13 614072 1888 1978 91 0.967 0.441 1.479 5.852 0.330 0.579 14 614081 1894 1980 87 0.986 0.482 1.320 6.445 0.294 0.756 15 614082 1886 1980 95 0.981 0.404 0.383 3.386 0.286 0.623 16 614091 1885 1980 96 0.984 0.362 0.369 2.952 0.265 0.567 17 614101 1877 1980 104 0.992 0.352 0.065 3.319 0.269 0.564 18 614102 1875 1980 106 0.988 0.358 -0.003 2.830 0.261 0.663 19 614111 1892 1980 89 0.988 0.285 0.669 3.932 0.250 0.426 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 614112 1883 1980 98 0.997 0.288 0.536 2.687 0.290 0.204 21 614121 1902 1980 79 0.994 0.317 0.690 3.177 0.314 0.262 22 614122 1879 1980 102 0.995 0.328 0.511 2.611 0.293 0.345 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 0.984 0.390 0.719 3.834 0.292 0.528 STANDARD DEVIATION 15 0.013 0.063 0.421 1.310 0.026 0.147 MEDIAN (50TH QUANTILE) 103 0.987 0.380 0.679 3.509 0.292 0.565 INTERQUARTILE RANGE 19 0.015 0.109 0.440 1.140 0.048 0.197 MINIMUM VALUE 79 0.951 0.285 -0.003 2.523 0.250 0.204 LOWER HINGE (25TH QUANTILE) 93 0.978 0.349 0.474 2.952 0.269 0.426 UPPER HINGE (75TH QUANTILE) 112 0.993 0.458 0.914 4.092 0.316 0.623 MAXIMUM VALUE 154 0.998 0.482 1.643 7.764 0.333 0.756 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.258 0.187 0.012 -0.399 2.961 -0.360 0.641 MINIMUM CORRELATION: -0.360 SERIES 614033 AND 614101 87 YEARS MAXIMUM CORRELATION: 0.641 SERIES 614091 AND 614111 89 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 61.63 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1905. 1930. 1955. CORR 66. 231. 210. RBAR 0.352 0.253 0.263 SDEV 0.173 0.233 0.242 SERR 0.021 0.015 0.017 EPS 0.916 0.882 0.887 NSS 20.1 22.0 22.0 |======================== 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 1827 1980 154 0.981 0.287 0.033 2.296 0.232 0.518 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.155 0.088 0.150 34 120 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.33 0.72 1.00 1.07 1.79 17.29 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.87 0.92 0.00 0.00 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 0.515 0.434 0.306 0.180 0.071 0.012 -0.116 -0.153 -0.122 -0.093 PACF 0.515 0.231 0.022 -0.067 -0.084 -0.031 -0.139 -0.058 0.056 0.058 95% C.L. 0.161 0.199 0.223 0.233 0.237 0.237 0.237 0.239 0.241 0.243 |------------------ 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 0.317 0.393 0.247 |======================= 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 0.492 0.391 0.320 0.192 0.086 0.005 -0.242 -0.264 -0.191 -0.220 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 0.492 2 0.395 0.197 3 0.376 0.160 0.095 4 0.381 0.168 0.114 -0.052 5 0.377 0.178 0.128 -0.021 -0.083 6 0.371 0.176 0.138 -0.008 -0.054 -0.075 7 0.347 0.159 0.135 0.036 0.001 0.042 -0.316 8 0.317 0.163 0.136 0.039 0.014 0.057 -0.283 -0.096 9 0.326 0.192 0.130 0.038 0.010 0.044 -0.299 -0.128 0.101 10 0.324 0.194 0.135 0.037 0.010 0.043 -0.301 -0.131 0.095 0.017 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) 1177.33 1136.71 1132.60 1133.21 1134.79 1135.73 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1136.87 1122.67 1123.25 1123.67 1125.62 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 0.395 0.197 R-SQUARED DUE TO POOLED AUTOREGRESSION: 27.13 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 137.22 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.395 0.353 0.217 0.155 0.104 0.072 0.049 0.033 0.023 0.0156 0.011 0.007 0.005 0.003 0.002 0.002 0.001 0.001 0.001 0.0003 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 614011 2 0.474 0.492 0.255 2 614012 2 0.279 0.469 0.098 3 614021 2 0.191 0.371 0.097 4 614022 2 0.561 0.713 0.033 5 614031 2 0.439 0.427 0.285 6 614033 2 0.393 0.528 0.138 7 614041 2 0.267 0.410 0.170 8 614042 2 0.136 0.323 0.063 9 614052 2 0.307 0.568 -0.035 10 614061 2 0.412 0.384 0.338 11 614062 2 0.266 0.412 0.167 12 614071 2 0.506 0.611 0.124 13 614072 2 0.346 0.513 0.117 14 614081 2 0.604 0.892 -0.177 15 614082 2 0.403 0.556 0.109 16 614091 2 0.348 0.521 0.104 17 614101 2 0.341 0.480 0.149 18 614102 2 0.475 0.498 0.249 19 614111 2 0.198 0.378 0.122 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 614112 2 0.077 0.183 0.105 21 614121 2 0.091 0.285 -0.085 22 614122 2 0.141 0.319 0.109 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.330 0.470 0.115 STANDARD DEVIATION 0 0.150 0.151 0.116 MEDIAN 2 0.344 0.475 0.113 INTERQUARTILE RANGE 0 0.241 0.150 0.070 MINIMUM VALUE 2 0.077 0.183 -0.177 LOWER HINGE 2 0.198 0.378 0.097 UPPER HINGE 2 0.439 0.528 0.167 MAXIMUM VALUE 2 0.604 0.892 0.338 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 614011 1862 1980 119 1.000 0.339 1.338 5.809 0.359 -0.011 2 614012 1873 1980 108 1.002 0.387 0.520 4.076 0.426 0.019 3 614021 1875 1980 106 1.000 0.317 0.491 3.138 0.324 -0.008 4 614022 1866 1980 115 1.000 0.309 2.130 13.754 0.320 -0.005 5 614031 1888 1980 93 1.000 0.355 1.170 4.786 0.349 -0.057 6 614033 1894 1980 87 1.000 0.359 0.869 4.551 0.368 0.019 7 614041 1885 1980 96 1.000 0.306 0.894 4.199 0.328 0.010 8 614042 1875 1980 106 1.000 0.334 0.334 2.962 0.370 -0.010 9 614052 1868 1980 113 1.000 0.274 0.754 3.949 0.300 0.006 10 614061 1869 1980 112 1.000 0.346 0.436 2.891 0.361 0.010 11 614062 1869 1980 112 1.000 0.341 0.817 4.262 0.362 -0.001 12 614071 1827 1980 154 1.000 0.289 0.137 3.093 0.344 0.020 13 614072 1888 1978 91 1.000 0.357 0.994 4.717 0.380 -0.003 14 614081 1894 1980 87 1.000 0.310 0.803 5.481 0.363 -0.033 15 614082 1886 1980 95 1.000 0.313 0.663 3.095 0.345 0.011 16 614091 1885 1980 96 1.000 0.291 0.551 3.774 0.321 0.005 17 614101 1877 1980 104 1.000 0.287 0.727 3.957 0.298 -0.016 18 614102 1875 1980 106 1.000 0.259 0.203 2.926 0.308 0.005 19 614111 1892 1980 89 1.000 0.255 0.300 3.056 0.291 0.002 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 614112 1883 1980 98 1.000 0.280 0.306 2.737 0.315 -0.017 21 614121 1902 1980 79 1.000 0.305 0.566 3.211 0.350 -0.011 22 614122 1879 1980 102 1.000 0.304 0.539 2.511 0.335 -0.010 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 1.000 0.314 0.706 4.224 0.342 -0.003 STANDARD DEVIATION 15 0.000 0.035 0.441 2.312 0.032 0.018 MEDIAN (50TH QUANTILE) 103 1.000 0.309 0.614 3.861 0.344 -0.002 INTERQUARTILE RANGE 19 0.000 0.052 0.434 1.495 0.042 0.020 MINIMUM VALUE 79 1.000 0.255 0.137 2.511 0.291 -0.057 LOWER HINGE (25TH QUANTILE) 93 1.000 0.289 0.436 3.056 0.320 -0.011 UPPER HINGE (75TH QUANTILE) 112 1.000 0.341 0.869 4.551 0.362 0.010 MAXIMUM VALUE 154 1.002 0.387 2.130 13.754 0.426 0.020 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.285 0.125 0.008 -0.111 3.468 -0.086 0.630 MINIMUM CORRELATION: -0.086 SERIES 614033 AND 614101 87 YEARS MAXIMUM CORRELATION: 0.630 SERIES 614112 AND 614122 98 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 61.63 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1905. 1930. 1955. CORR 66. 231. 210. RBAR 0.377 0.298 0.290 SDEV 0.150 0.172 0.145 SERR 0.018 0.011 0.010 EPS 0.924 0.903 0.900 NSS 20.1 22.0 22.0 |======================== 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 1827 1980 154 0.992 0.206 0.124 3.109 0.242 -0.088 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.151 0.093 0.092 49 105 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.31 0.53 1.01 1.09 1.62 21.90 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.87 0.91 0.00 0.00 0.91 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 -0.088 0.062 0.075 0.054 -0.018 0.058 -0.121 -0.119 -0.031 -0.029 PACF -0.088 0.055 0.086 0.066 -0.017 0.041 -0.123 -0.153 -0.052 -0.007 95% C.L. 0.161 0.162 0.163 0.164 0.164 0.164 0.165 0.167 0.169 0.170 |------------------ 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 -0.004 0.004 0.092 0.054 -0.006 0.052 -0.126 -0.135 -0.037 -0.024 PACF -0.004 0.004 0.092 0.055 -0.007 0.043 -0.137 -0.144 -0.050 -0.006 95% C.L. 0.161 0.161 0.161 0.163 0.163 0.163 0.163 0.166 0.169 0.169 |----------------- 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 0.009 -0.004 0.004 |========================= 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 1827 1980 154 0.996 0.244 0.029 2.626 0.196 0.505 |------------ 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 0.502 0.405 0.301 0.194 0.069 0.016 -0.132 -0.179 -0.149 -0.131 PACF 0.502 0.205 0.050 -0.032 -0.103 -0.036 -0.169 -0.079 0.042 0.038 95% C.L. 0.161 0.198 0.218 0.229 0.233 0.233 0.234 0.235 0.239 0.241 |------------------- 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 0.297 0.396 0.220 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.19 MINUTES