RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM053E.rwl.conv LOG FILE PROCESSED: GERM053E.rwl.conv_log OPTION PLOT TREE-RING DATA TYPE 1 !TUCSON RING-WIDTH FORMAT MISSING DATA IN GAPS -9 0 !MISSING VALUES ESTIMATED (NO PLOTS) DATA TRANSFORMATION 0 0 !NO DATA TRANSFORMATION (NO PLOTS) FIRST DETRENDING 1 0 !1ST-NEG EXPONENTIAL CURVE, NO = OPT 3 SECOND DETRENDING -67 0 !2ND-SPLINE CURVE (PCT N 50% CUTOFF) ROBUST DETRENDING 1 !NON-ROBUST DETRENDING METHODS USED INTERACTIVE DETREND 0 !NO INTERACTIVE DETRENDING INDEX CALCULATION 1 !TREE-RING INDICES OR RATIOS (Rt/Gt) AR MODELING METHOD 1 0 !NON-ROBUST AUTOREGRESSIVE MODELING POOLED AR ORDER 0 0 !MINIMUM AIC POOLED AR MODEL ORDER FIT SERIES AR ORDER 0 !POOLED AR ORDER FIT TO ALL SERIES MEAN CHRONOLOGY 2 0 !ROBUST CHRONOLOGY (NO BIWEIGHT PLOTS) STABILIZE VARIANCE 1 !RBAR WEIGHTED STABILIZATION METHOD COMMON PERIOD YEARS 0 0 !NO COMMON PERIOD ANALYSIS PERFORMED SITE-TREE-CORE MASK SSSTTCC !SITE-TREE-CORE SEPARATION MASK RUNNING RBAR 20 10 0 !RUNNING RBAR WINDOW/OVERLAP (NO PLOTS) PRINTOUT OPTION 2 !SUMMARY & SERIES STATISTICS PRINTED CORE SERIES SAVE 1 !SERIES SAVED IN TUCSON RAW DATA FORMAT SUMMARY PLOT DISPLAYS 0 !NO SPAGHETTI AND MEAN CHRONOLOGY PLOTS STAND DYNAMICS ANALYSES 0 !NO STAND DYNAMICS ANALYSES DONE RUNNING MEAN WINDOW WIDTH 0 !RUNNING MEAN WINDOW WIDTH PERCENT GROWTH CHANGE 0 !PERCENT GROWTH CHANGE THRESHOLD STANDARD ERROR THRESHOLD 0 !STANDARD ERROR LIMIT THRESHOLD |======================== RAW DATA STATISTICAL ANALYSES =======================| |------------------- TREE-RING SERIES READ IN FOR PROCESSING ------------------| DATA HEADER LINES: 050 1 Mźnstertal (D), EU-Pr. WIDTH_EARLY PCAB - 050 2 Germany Norway spruce 490 4751-747 1881 1995 - 050 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 7 050075 MISSING VALUES FOUND: 5 IN 1 GAPS / 1890 1894 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 050061 1882 1995 114 1.755 0.755 0.645 2.814 0.295 0.656 2 050063 1883 1995 113 1.421 0.588 0.618 2.774 0.286 0.698 3 050065 1882 1995 114 1.285 0.544 1.145 4.212 0.295 0.667 4 050067 1883 1995 113 1.397 0.550 0.343 2.396 0.295 0.623 5 050071 1881 1995 115 1.553 0.820 0.868 2.915 0.325 0.685 6 050073 1881 1958 78 1.208 0.574 1.170 4.222 0.310 0.581 7 050075 1881 1926 46 1.223 0.584 2.202 7.323 0.311 0.525 8 050077 1881 1995 115 1.211 0.623 1.316 5.842 0.299 0.656 9 050081 1883 1995 113 1.171 0.475 0.761 3.448 0.250 0.701 10 050083 1881 1995 115 1.578 0.730 0.343 2.381 0.316 0.674 11 050085 1881 1995 115 1.247 0.650 1.227 4.743 0.296 0.722 12 050087 1893 1995 103 1.105 0.442 1.111 4.757 0.260 0.723 13 050091 1882 1995 114 1.795 1.418 3.072 13.849 0.302 0.790 14 050093 1885 1995 111 2.085 1.223 1.836 6.495 0.324 0.582 15 050095 1896 1995 100 2.033 0.992 2.108 11.244 0.319 0.633 16 050097 1881 1995 115 1.684 0.851 0.751 3.049 0.309 0.715 17 050101 1884 1995 112 1.167 0.427 0.644 3.266 0.304 0.561 18 050103 1884 1995 112 1.425 0.722 1.536 5.815 0.306 0.722 19 050105 1887 1995 109 1.143 0.659 1.066 3.817 0.310 0.783 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 050107 1884 1995 112 1.222 0.527 0.687 2.992 0.271 0.746 NUMBER OF SERIES READ IN: 20 FROM 1881 TO 1995 115 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 107 1.435 0.708 1.172 4.918 0.299 0.672 STANDARD DEVIATION 17 0.299 0.255 0.691 2.990 0.020 0.072 MEDIAN (50TH QUANTILE) 113 1.341 0.636 1.088 4.014 0.303 0.680 INTERQUARTILE RANGE 4 0.422 0.240 0.760 2.875 0.015 0.094 MINIMUM VALUE 41 1.105 0.427 0.343 2.381 0.250 0.525 LOWER HINGE (25TH QUANTILE) 110 1.209 0.547 0.666 2.953 0.295 0.628 UPPER HINGE (75TH QUANTILE) 114 1.631 0.788 1.426 5.829 0.311 0.722 MAXIMUM VALUE 115 2.085 1.418 3.072 13.849 0.325 0.790 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.547 0.170 0.012 -0.482 2.856 0.061 0.881 MINIMUM CORRELATION: 0.061 SERIES 050085 AND 050091 114 YEARS MAXIMUM CORRELATION: 0.881 SERIES 050105 AND 050107 109 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 86.91 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1891. 1910. 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 21. 190. 171. 171. 171. 153. 153. 153. 153. RBAR 0.434 0.489 0.662 0.715 0.780 0.765 0.576 0.227 0.562 SDEV 0.270 0.242 0.181 0.158 0.096 0.129 0.194 0.292 0.225 SERR 0.059 0.018 0.014 0.012 0.007 0.010 0.016 0.024 0.018 EPS 0.930 0.950 0.975 0.980 0.985 0.984 0.962 0.841 0.958 NSS 17.2 20.0 19.9 19.4 19.0 19.0 18.5 18.0 18.0 |======================== RAW DATA CHRONOLOGY STATISTICS ======================| |----------------- ROBUST MEAN RAW DATA CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1881 1995 115 1.384 0.509 0.355 2.364 0.252 0.699 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.801 0.366 -0.035 55 60 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.55 1.15 1.01 1.15 2.31 37.31 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 0.64 0.87 0.94 0.99 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 113. 4. 46. 110. 114. 115. |----------- RAW DATA CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.693 0.585 0.519 0.398 0.345 0.331 0.244 0.218 0.187 0.122 PACF 0.693 0.202 0.113 -0.074 0.030 0.087 -0.076 0.018 -0.007 -0.052 95% C.L. 0.187 0.261 0.303 0.333 0.349 0.361 0.371 0.377 0.381 0.384 |------------------ 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 3 0.519 0.520 0.133 0.140 |================== DETRENDED DATA CURVE FITS AND STATISTICS ==================| |------------------------ RESULTS OF FIRST DETRENDING -------------------------| |--------------- GROWTH CURVE USED FOR DETRENDING TREE-RING DATA --------------| CURVE OPTION -2: REGIONAL CURVE DETRENDING F(I) = ONE AGE-ALIGNED CURVE CURVE OPTION -1: FIRST-DIFFERENCES F(I) = Y(I) - Y(I-1) CURVE OPTION 1: NEG EXPON CURVE, NO = OPT 3 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 2: NEG EXPON CURVE, NO = OPT 4 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 3: LINEAR REGRESSION (ANY SLOPE) F(I) = +/-C*T(I) + D CURVE OPTION 4: LINEAR REGRESSION (NEG SLOPE) F(I) = -C*T(I) + D CURVE OPTION 5: HORIZONTAL LINE THROUGH MEAN F(I) = MEAN(Y(I)) = D CURVE OPTION 6: HUGERSHOFF GROWTH FUNCTION F(I) = A*T(I)**B * EXP(C*T(I)) CURVE OPTION 7: GENERAL EXPONENTIAL CURVE F(I) = A*T(I) * EXP(-B*T(I)) CURVE OPTION >9: CUBIC SMOOTHING SPLINE FIXED 50 PCT VARIANCE CUTOFF CURVE OPTION <-9: CUBIC SMOOTHING SPLINE PCT N 50 PCT VARIANCE CUTOFF SERIES IDENT OPTION A B C D 1 050061 3 0.00000000 0.00000000 0.00491051 1.47229469 2 050063 1 1.52875257 0.10262153 0.00000000 1.29596972 3 050065 1 1.54718196 0.08474842 0.00000000 1.13155973 4 050067 1 1.52777052 0.07514505 0.00000000 1.22387302 5 050071 3 0.00000000 0.00000000 0.00981133 0.98398626 6 050073 1 1.86532176 0.21947749 0.00000000 1.11025238 7 050075 1 1.70633817 0.15972924 0.00000000 1.02512813 8 050077 1 1.54603136 0.07001638 0.00000000 1.02582431 9 050081 1 1.40247428 0.05993541 0.00000000 0.96991891 10 050083 1 1.62039769 0.05657823 0.00000000 1.33604062 11 050085 1 1.91746509 0.03492930 0.00000000 0.78687310 12 050087 3 0.00000000 0.00000000 0.00222818 0.98908621 13 050091 3 0.00000000 0.00000000 0.01701027 0.81734824 14 050093 3 0.00000000 0.00000000 0.01501869 1.24408841 15 050095 3 0.00000000 0.00000000 0.01218488 1.41756368 16 050097 3 0.00000000 0.00000000 0.00551558 1.36426997 17 050101 1 0.61539871 0.11342386 0.00000000 1.12094903 18 050103 3 0.00000000 0.00000000 0.00561887 1.10717666 19 050105 1 1.74964821 0.09867928 0.00000000 0.98871851 SERIES IDENT OPTION A B C D 20 050107 1 1.13943636 0.07608645 0.00000000 1.09294653 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 050061 1882 1995 114 1.000 0.411 0.427 2.457 0.293 0.625 2 050063 1883 1995 113 0.999 0.371 0.374 2.336 0.285 0.602 3 050065 1882 1995 114 0.999 0.344 0.611 4.047 0.293 0.481 4 050067 1883 1995 113 1.000 0.348 0.322 2.626 0.292 0.502 5 050071 1881 1995 115 1.011 0.509 0.875 3.209 0.322 0.664 6 050073 1881 1958 78 1.000 0.439 1.253 4.777 0.305 0.473 7 050075 1881 1926 46 1.000 0.354 1.376 5.384 0.320 0.131 8 050077 1881 1995 115 1.000 0.450 0.907 3.399 0.295 0.631 9 050081 1883 1995 113 1.000 0.328 0.563 3.552 0.246 0.496 10 050083 1881 1995 115 1.000 0.435 0.622 3.190 0.314 0.597 11 050085 1881 1995 115 1.000 0.360 0.406 3.289 0.294 0.491 12 050087 1893 1995 103 1.000 0.389 0.852 3.826 0.258 0.700 13 050091 1882 1995 114 1.025 0.682 2.068 7.863 0.300 0.738 14 050093 1885 1995 111 1.006 0.512 1.310 4.628 0.322 0.539 15 050095 1896 1995 100 0.998 0.435 1.941 10.843 0.316 0.536 16 050097 1881 1995 115 1.000 0.490 0.672 3.065 0.306 0.690 17 050101 1884 1995 112 1.000 0.349 0.333 2.444 0.302 0.505 18 050103 1884 1995 112 1.003 0.486 1.235 4.340 0.303 0.708 19 050105 1887 1995 109 0.999 0.530 1.170 4.392 0.308 0.749 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 050107 1884 1995 112 0.999 0.397 0.729 3.541 0.270 0.673 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 107 1.002 0.431 0.902 4.160 0.297 0.577 STANDARD DEVIATION 16 0.006 0.087 0.508 2.018 0.020 0.140 MEDIAN (50TH QUANTILE) 113 1.000 0.423 0.791 3.547 0.301 0.600 INTERQUARTILE RANGE 4 0.001 0.131 0.749 1.382 0.018 0.182 MINIMUM VALUE 46 0.998 0.328 0.322 2.336 0.246 0.131 LOWER HINGE (25TH QUANTILE) 110 0.999 0.357 0.495 3.128 0.293 0.499 UPPER HINGE (75TH QUANTILE) 114 1.000 0.488 1.244 4.510 0.311 0.681 MAXIMUM VALUE 115 1.025 0.682 2.068 10.843 0.322 0.749 |------------------------ RESULTS OF SECOND DETRENDING ------------------------| |--------------- GROWTH CURVE USED FOR DETRENDING TREE-RING DATA --------------| CURVE OPTION -2: REGIONAL CURVE DETRENDING F(I) = ONE AGE-ALIGNED CURVE CURVE OPTION -1: FIRST-DIFFERENCES F(I) = Y(I) - Y(I-1) CURVE OPTION 1: NEG EXPON CURVE, NO = OPT 3 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 2: NEG EXPON CURVE, NO = OPT 4 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 3: LINEAR REGRESSION (ANY SLOPE) F(I) = +/-C*T(I) + D CURVE OPTION 4: LINEAR REGRESSION (NEG SLOPE) F(I) = -C*T(I) + D CURVE OPTION 5: HORIZONTAL LINE THROUGH MEAN F(I) = MEAN(Y(I)) = D CURVE OPTION 6: HUGERSHOFF GROWTH FUNCTION F(I) = A*T(I)**B * EXP(C*T(I)) CURVE OPTION 7: GENERAL EXPONENTIAL CURVE F(I) = A*T(I) * EXP(-B*T(I)) CURVE OPTION >9: CUBIC SMOOTHING SPLINE FIXED 50 PCT VARIANCE CUTOFF CURVE OPTION <-9: CUBIC SMOOTHING SPLINE PCT N 50 PCT VARIANCE CUTOFF SERIES IDENT OPTION A B C D 1 050061 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 050063 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 050065 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 050067 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 050071 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 050073 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 050075 -67 30 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 050077 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 050081 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 050083 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 050085 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 050087 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 050091 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 050093 -67 74 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 050095 -67 67 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 050097 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 050101 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 050103 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 050105 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 050107 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 050061 1882 1995 114 0.984 0.329 0.263 2.614 0.293 0.434 2 050063 1883 1995 113 0.993 0.326 0.271 2.440 0.285 0.466 3 050065 1882 1995 114 0.995 0.316 0.514 3.880 0.293 0.390 4 050067 1883 1995 113 0.992 0.316 0.314 2.817 0.292 0.407 5 050071 1881 1995 115 0.993 0.410 0.916 3.991 0.323 0.429 6 050073 1881 1958 78 0.994 0.407 0.958 3.946 0.305 0.454 7 050075 1881 1926 46 0.998 0.346 1.387 5.523 0.319 0.096 8 050077 1881 1995 115 0.988 0.404 0.845 3.479 0.295 0.532 9 050081 1883 1995 113 0.994 0.304 0.555 3.487 0.246 0.424 10 050083 1881 1995 115 0.983 0.376 0.425 2.808 0.313 0.469 11 050085 1881 1995 115 0.991 0.328 0.457 3.533 0.295 0.403 12 050087 1893 1995 103 0.988 0.305 0.559 3.389 0.256 0.505 13 050091 1882 1995 114 0.970 0.494 2.551 11.351 0.299 0.621 14 050093 1885 1995 111 0.981 0.396 1.501 6.802 0.321 0.305 15 050095 1896 1995 100 0.982 0.317 1.545 8.900 0.316 0.262 16 050097 1881 1995 115 0.973 0.374 0.491 3.126 0.305 0.504 17 050101 1884 1995 112 0.997 0.326 0.314 2.657 0.302 0.415 18 050103 1884 1995 112 0.984 0.342 0.961 4.519 0.303 0.429 19 050105 1887 1995 109 0.975 0.420 1.652 7.487 0.309 0.616 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 050107 1884 1995 112 0.989 0.320 0.253 2.997 0.270 0.488 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 107 0.987 0.358 0.836 4.487 0.297 0.432 STANDARD DEVIATION 16 0.008 0.050 0.612 2.382 0.020 0.116 MEDIAN (50TH QUANTILE) 113 0.989 0.335 0.557 3.510 0.301 0.432 INTERQUARTILE RANGE 4 0.011 0.082 0.805 2.114 0.018 0.091 MINIMUM VALUE 46 0.970 0.304 0.253 2.440 0.246 0.096 LOWER HINGE (25TH QUANTILE) 110 0.982 0.319 0.369 2.907 0.293 0.405 UPPER HINGE (75TH QUANTILE) 114 0.993 0.400 1.174 5.021 0.311 0.496 MAXIMUM VALUE 115 0.998 0.494 2.551 11.351 0.323 0.621 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.562 0.129 0.009 -0.484 3.403 0.127 0.870 MINIMUM CORRELATION: 0.127 SERIES 050091 AND 050101 112 YEARS MAXIMUM CORRELATION: 0.870 SERIES 050071 AND 050073 78 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 86.91 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1891. 1910. 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 21. 190. 171. 171. 171. 153. 153. 153. 153. RBAR 0.436 0.492 0.649 0.771 0.813 0.754 0.535 0.219 0.537 SDEV 0.169 0.250 0.173 0.106 0.076 0.133 0.200 0.277 0.207 SERR 0.037 0.018 0.013 0.008 0.006 0.011 0.016 0.022 0.017 EPS 0.930 0.951 0.974 0.985 0.988 0.983 0.955 0.834 0.954 NSS 17.2 20.0 19.9 19.4 19.0 19.0 18.5 18.0 18.0 |======================== STANDARD CHRONOLOGY STATISTICS ======================| *** VARIANCE STABILIZED WITH BRIFFA RBAR-WEIGHTED METHOD *** |----------------- ROBUST MEAN STANDARD CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1881 1995 115 0.972 0.270 0.276 3.246 0.245 0.452 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.604 0.171 0.046 41 74 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.24 0.60 1.00 1.11 1.70 4.69 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 0.76 0.86 0.92 0.99 |----------- 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 0.448 0.288 0.208 0.052 0.000 -0.013 -0.132 -0.144 -0.134 -0.202 PACF 0.448 0.109 0.056 -0.101 -0.030 0.001 -0.136 -0.049 -0.026 -0.108 95% C.L. 0.187 0.221 0.233 0.240 0.240 0.240 0.240 0.243 0.246 0.248 |------------------ 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 0.216 0.454 |======================= 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 0.443 0.295 0.212 0.051 -0.001 -0.024 -0.136 -0.136 -0.109 -0.167 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 0.443 2 0.389 0.122 3 0.383 0.101 0.055 4 0.388 0.112 0.095 -0.107 5 0.385 0.115 0.099 -0.094 -0.033 6 0.385 0.114 0.100 -0.093 -0.028 -0.011 7 0.383 0.110 0.088 -0.080 -0.014 0.038 -0.127 8 0.378 0.111 0.088 -0.083 -0.011 0.042 -0.112 -0.038 9 0.379 0.112 0.088 -0.083 -0.010 0.042 -0.112 -0.039 0.002 10 0.379 0.108 0.078 -0.079 -0.011 0.034 -0.104 -0.029 0.036 -0.090 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) 920.40 897.22 897.50 899.16 899.85 901.72 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 903.71 903.85 905.69 907.68 908.76 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 0.443 R-SQUARED DUE TO POOLED AUTOREGRESSION: 19.66 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 124.48 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.443 0.197 0.087 0.039 0.017 0.008 0.003 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 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 050061 1 0.213 0.445 2 050063 1 0.225 0.469 3 050065 1 0.170 0.401 4 050067 1 0.195 0.408 5 050071 1 0.186 0.431 6 050073 1 0.220 0.468 7 050075 1 0.031 0.097 8 050077 1 0.285 0.533 9 050081 1 0.223 0.433 10 050083 1 0.247 0.478 11 050085 1 0.174 0.410 12 050087 1 0.276 0.514 13 050091 1 0.397 0.626 14 050093 1 0.119 0.306 15 050095 1 0.071 0.263 16 050097 1 0.267 0.514 17 050101 1 0.176 0.419 18 050103 1 0.190 0.431 19 050105 1 0.387 0.621 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 050107 1 0.256 0.499 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.215 0.438 STANDARD DEVIATION 0 0.088 0.118 MEDIAN 1 0.217 0.439 INTERQUARTILE RANGE 0 0.087 0.097 MINIMUM VALUE 1 0.031 0.097 LOWER HINGE 1 0.175 0.409 UPPER HINGE 1 0.262 0.506 MAXIMUM VALUE 1 0.397 0.626 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 050061 1882 1995 114 1.000 0.293 0.637 4.025 0.345 -0.066 2 050063 1883 1995 113 1.000 0.287 0.107 2.646 0.352 -0.041 3 050065 1882 1995 114 1.000 0.288 0.429 3.725 0.352 -0.050 4 050067 1883 1995 113 1.000 0.288 0.449 2.668 0.344 -0.074 5 050071 1881 1995 115 1.000 0.370 1.194 6.036 0.382 -0.001 6 050073 1881 1958 78 1.000 0.359 1.266 4.573 0.358 0.028 7 050075 1881 1926 46 1.000 0.344 1.312 5.515 0.331 0.013 8 050077 1881 1995 115 1.000 0.342 0.852 4.279 0.353 0.011 9 050081 1883 1995 113 1.000 0.274 0.672 4.009 0.300 -0.079 10 050083 1881 1995 115 1.000 0.329 0.553 2.923 0.370 -0.074 11 050085 1881 1995 115 1.000 0.298 0.579 3.715 0.348 -0.038 12 050087 1893 1995 103 1.000 0.261 0.450 2.968 0.316 -0.058 13 050091 1882 1995 114 1.000 0.385 2.646 15.682 0.377 0.060 14 050093 1885 1995 111 1.000 0.377 1.890 8.932 0.351 -0.051 15 050095 1896 1995 100 1.000 0.306 1.560 9.536 0.341 -0.009 16 050097 1881 1995 115 1.000 0.319 0.604 3.297 0.367 -0.044 17 050101 1884 1995 112 1.000 0.295 0.274 2.824 0.352 -0.012 18 050103 1884 1995 112 1.000 0.308 0.891 4.379 0.356 -0.031 19 050105 1887 1995 109 1.000 0.329 1.190 5.366 0.368 -0.028 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 050107 1884 1995 112 1.000 0.276 0.455 3.637 0.327 -0.056 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 107 1.000 0.317 0.901 5.037 0.350 -0.030 STANDARD DEVIATION 16 0.000 0.036 0.616 3.135 0.020 0.038 MEDIAN (50TH QUANTILE) 113 1.000 0.307 0.655 4.017 0.352 -0.040 INTERQUARTILE RANGE 4 0.000 0.055 0.778 2.308 0.019 0.052 MINIMUM VALUE 46 1.000 0.261 0.107 2.646 0.300 -0.079 LOWER HINGE (25TH QUANTILE) 110 1.000 0.288 0.453 3.133 0.343 -0.057 UPPER HINGE (75TH QUANTILE) 114 1.000 0.343 1.230 5.441 0.362 -0.005 MAXIMUM VALUE 115 1.000 0.385 2.646 15.682 0.382 0.060 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.563 0.109 0.008 -0.226 3.463 0.207 0.864 MINIMUM CORRELATION: 0.207 SERIES 050075 AND 050083 46 YEARS MAXIMUM CORRELATION: 0.864 SERIES 050071 AND 050073 78 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 86.91 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1891. 1910. 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 21. 190. 171. 171. 171. 153. 153. 153. 153. RBAR 0.476 0.499 0.642 0.794 0.804 0.710 0.502 0.314 0.564 SDEV 0.155 0.223 0.153 0.078 0.077 0.131 0.200 0.232 0.173 SERR 0.034 0.016 0.012 0.006 0.006 0.011 0.016 0.019 0.014 EPS 0.940 0.952 0.973 0.987 0.987 0.979 0.949 0.892 0.959 NSS 17.2 20.0 19.9 19.4 19.0 19.0 18.5 18.0 18.0 |======================== RESIDUAL CHRONOLOGY STATISTICS ======================| *** VARIANCE STABILIZED WITH BRIFFA RBAR-WEIGHTED METHOD *** |----------------- ROBUST MEAN RESIDUAL CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1881 1995 115 0.988 0.236 0.363 3.651 0.287 -0.043 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.601 0.179 0.009 49 66 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.18 0.61 1.00 1.07 1.68 3.15 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 0.63 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 -0.042 0.056 0.126 -0.032 -0.018 0.056 -0.083 -0.070 -0.006 -0.151 PACF -0.042 0.054 0.131 -0.025 -0.036 0.042 -0.070 -0.079 -0.017 -0.126 95% C.L. 0.187 0.187 0.187 0.190 0.191 0.191 0.191 0.192 0.193 0.193 |------------------ RESIDUAL CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 0 0.000 |---------- REWHITENED CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS -----------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.003 0.060 0.127 -0.028 -0.017 0.052 -0.084 -0.074 -0.016 -0.155 PACF 0.003 0.060 0.127 -0.032 -0.033 0.040 -0.075 -0.076 -0.019 -0.128 95% C.L. 0.187 0.187 0.187 0.190 0.190 0.190 0.191 0.192 0.193 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 0.004 0.003 |========================= ARSTAN CHRONOLOGY STATISTICS =======================| |----------------- ROBUST MEAN ARSTAN CHRONOLOGY STATISTICS -------------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1881 1995 115 0.989 0.269 0.298 3.239 0.231 0.481 |------------ 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 0.477 0.289 0.205 0.057 0.003 -0.012 -0.115 -0.141 -0.142 -0.213 PACF 0.477 0.080 0.053 -0.096 -0.022 -0.002 -0.119 -0.055 -0.039 -0.120 95% C.L. 0.187 0.225 0.237 0.244 0.244 0.244 0.244 0.246 0.249 0.252 |------------------- 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 0.239 0.483 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.25 MINUTES